Numbers –Tricky Tricky Numbers: Part 3.5

Guest Opinion by Kip Hansen –  27 July 2022

A great deal of controversy arose in response to the first three parts of this series, which came as no surprise.  One well-respected reader implied that the Global Warming hypothesis and all the fuss for 30 years wasn’t about the Earth Climate gaining heat energy (despite all the emphasis on the Global Energy Budget) but only about temperature rise (as measured by thermometers).  Some seemed to be appalled at the suggestion that temperatures from disparate places and times could not be averaged to produce meaningful numeric results.

This brief addendum is to give an example, which if extended to the broader question, will help to explain the chief problem inherent in averaging 2-meter air temperatures (in degrees by any method) from around the world and claiming the result as evidence of Global Warming.

Take a perfectly insulated box 2 meters by 1 meter by 1 meter.  This box will have a volume of two cubic meters and, since it is perfectly insulated, will not allow any heat/energy to flow into or out of the box.

At the first instant, the box contains one cubic meter of water at 20 °C and one cubic meter of air with a temperature of 30 °C.

Allow enough time for the temperatures to become equalized – for the energy in the water and air in the box to reach equilibrium (we will ignore any phase changes such as evaporation).

What will be the resultant equilibrium temperature of the whole system (air and water)?

And why will it NOT be the mathematical average (the mean)calculated as 20+30/2 = 25 °C?

Bonus Question: (My high school science teacher always included Bonus Questions – allowing some of us to score over 100% on tests.)

If we raised the initial air temperature by 2°C, to 32°C, how much would it change the final answer of the system temperature at equilibrium?

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Author’s Comment:

I’ll ask readers to provide the correct answer, at least to good back-of-envelope estimates.  Most important is the second question, why won’t result be the “average” (the mean) between 20 and 30 °C?

Those familiar with the Earth climate as a system can then explain to others why this also answers the question as to why, if the global warming hypothesis is based on the imbalance of the Global Energy Budget, at least in part due to the increase in the Greenhouse Effect due to rising atmospheric CO2  concentrations (and other anthropogenic GHG emissions), then this example also explains one of the reasons why any Global Average Surface Air Temperature metric (in degrees, or as anomalies, or as land and sea skin surface temperature combinations) is not a proper metric to use as evidence for Global Warming by CO2 .

# # # # #

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Crowcatcher
August 27, 2022 10:15 am

I’m getting old and can’t remember (or be bothered to look up) the specific heats of water and air but, I would guess, about 21C as that of water is much higher than air.

Zig Zag Wanderer
August 27, 2022 11:09 am

And the heat capacity of the oceans is roughly 1000 times the heat capacity of the atmosphere

Richard Page
August 27, 2022 12:16 pm

Increased pressure at depth should change the properties of the water, shouldn’t it?

Tim Gorman
August 27, 2022 1:23 pm

Water isn’t very compressible. You’ll probably not see much more than 1% compression at depth.

Richard Page
August 27, 2022 4:31 pm

Not necessarily compression but increased pressure does shift the freezing point (as does salinity) as well as maximum density. And that’s about the limit of my limited knowledge on the subject!

Felix
August 27, 2022 6:09 pm

Let me ask a really naive ignorant question about water compressibility: How can submarines move underwater? They have to push water aside. A surface ship makes waves by pushing water into the air, more or less. A submarine 500 feet deep can’t do that.

I am willing to give fish a pass as they have somewhat compressible bodies, at least more so than submarines. Yes, I know submarines do compress some, but they don’t compress when moving and expand when still. Or do they?

Well, I am serious about not understanding how submarines can move through uncompressible water. The rest, not so much.

Tommyboy
August 27, 2022 8:41 pm

Probably in the same manner a water current would flow around a submerged obstacle. A flow of water from the front to the back along the surface of the sub.

Tim Gorman
August 28, 2022 4:16 am

Correct. An airplane wing doesn’t move by compressing the air in front of it (at least not primarily). The air flows around it.

I suspect that is why post-50’s submarines changed design to become more aerodynamic.

Jack
August 28, 2022 6:56 am

“Hydrodynamic” would be better for a submarine…

DipChip
August 28, 2022 9:39 am

The water Displacement volume of the sub never changes.

Loren C. Wilson
August 27, 2022 8:35 pm

Interestingly, the heat capacity of water at 5°C decreases from 4.1768 J/g-K at 1000 psi (a depth of about 2000 feet) to 3.9204 J/g-K at 15,000 psi (a depth of approximately 30,000 feet). NIST Webbook used for these data.

August 28, 2022 1:59 am

Specific heat capacity is in joules per Kelvin per kg.

Volumetric heat capacity is in joules per Kelvin per metres cubed.

Heat capacity is an extensive property measured in joules per Kelvin, so you need to take into consideration that specific heat capacity of air is about a quarter of water but the density is almost 1/1000 or use volumetric since each is a metre cubed.

Angryscotonfragglerock
August 28, 2022 2:01 am

I have just seen an article claiming all the oceans would fit into a sphere, radius 700km

Charles Garner
August 29, 2022 11:37 am

Yes but it seems relatively small. Fresh water and ice volumes were not considered, right? Can we have a link to the source of that estimate?

Kevin kilty
August 27, 2022 12:40 pm

Specific means per unit mass. Specific heat of air is 1.005 kJ/kg and that of water about 4.186 kJ/kg; so about a ratio of 4 not 6. But ignoring that the air will eventually reach a saturation at the final temperature of the container, and is the container rigid, and did the air start out dry, and what was the original pressure, and ….

I can recognize that many of these detail are unimportant if a temperature to +/- one degree C is what is needed, but what is needed?

Kevin kilty
August 27, 2022 1:23 pm

There are two specific heats for air. Constant Volume, Constant pressure. You see path taken during a quasi-static process is important. Trick details, tricky tricky details.

It’s why I asked is the container rigid.

ferdberple
August 27, 2022 5:13 pm

==> I use the figures from this Penn State course outline. 4184 for water, 700 for air.
=======
What are your units? These are not dimentionless numbers.

The problem was stated in terms of volume but specific heat is goven in terms of mass.

Svend Ferdinandsen
August 27, 2022 1:30 pm

There is ~1kg air and 1000kg water. The air changes 1kj/degr and the water changes 4000kj/degr.
There will not be any measurable change from 20 degr. of the final temperature.

Kevin kilty
August 27, 2022 1:47 pm

Indeed, not measureable with a typical thermometer, but then why the question in the first place? Are we still trying to say that averaging temperature does not produce a meaningful result? There is a lot of calibration that is meaningless then, not to mention the operation of many a sensor.

Tim Gorman
August 28, 2022 4:36 am

The calibration *is* meaningful, but only on a station-by-station basis.

See the attached graphic of afternoon temps in NE Kansas. What would an average of these tell you? Even if the thermometers were calibrated to .001C would it help the averages to tell you anything? This range of temperatures is *not* unusual for the area. Different terrain and geography (think flat prairie to the rolling hills of the Flint Hills to north/south of the Kansas River).

The biggest gem I’ve taken from all this was Kip’s reference to the Essex paper where it pointed out that temperature doesn’t act at a distance. The temperature at each point in space is based solely on the microclimate at that location and not on the microclimate at other locations. That’s even more profound than the assertion that you can’t add intensive qualities.

How would you infill or homogenize the temps in the graphic for a missing station? Topeka to Osage City/Lawrence/Holton is only about 20 miles and to Emporia is only 50 miles. Yet you see temps separated by 1F +/- 1F (0.5C ≈ 1F)

You could, of course, average the daytime temps for each individual station but, again, I’m not sure what that *average* station temp would actually tell you about climate change, even with .001C calibration.

OweninGA
August 28, 2022 7:09 am

Of course averaging temperature is a meaningless result, the number NEVER takes into account the water content of the air being measured, or more specifically the change in specific heat due to the composition of the air mass being measured at the different locations.

80 degrees Fahrenheit in the Mojave desert (dew point ~ 40 degrees F) is far cooler than 80 degrees Fahrenheit in the swamps of Florida (dew point ~79.8 degrees F). The air in the moist location carries more heat.

10 degrees F in Missouri with a 8 degree F dew point has more heat than a balmy 10 degree F day in the Arctic circle with a less than -30 degree F dew point. (Though both are too cold for my preference!)

The composition of the air definitely makes a difference.

Kevin kilty
August 28, 2022 9:14 am

Please note what I said at 2:03 pm yesterday just below and you will see it is the point you made in a more general form.

OweninGA
August 28, 2022 3:18 pm

I was more expanding on what you wrote rather than disagreeing.

Your point about two points 50 miles apart having entirely different microclimates was exactly correct. I have seen temperature variation over short distances like that many times. It especially is prevalent around the west plains dry line, where two stations 50 miles apart on either side of the line will have wildly different conditions.

Kevin kilty
August 27, 2022 2:03 pm

You know, and perhaps Kip will read this too, if the point to be made is that there are details that make averaging the temperature of air that has traveled on many different process paths not meaningful, then we might have something to talk about. Perhaps Pat Frank could be persuaded to think about it and weigh in…

ferdberple
August 27, 2022 5:03 pm

Yes, that is the correct approach. You muat convert to units of mass.

michel
August 28, 2022 1:30 am

This makes sense. I forgot to allow for the difference in weight! Oh dear!

Rico Suave
August 27, 2022 5:44 pm

True, however 1 cubic meter of water has significantly more mass that 1 cubic meter of air. (kJ/kg). Assuming google is correct (i know, big assumption), 1m^3 of air weighs 1.225 kg. 1 m^3 of water weighs 1000 kilograms, so the specific heat difference by weight is 4x, but a little less than 4000 by volume.

Ken Irwin
August 28, 2022 3:10 am

Kip did say back of a [napkin] and ignore vapour
Specific heat air ±0.2 and water 1

Then(20×1)+(30×0.2) =1.2x x=21.6°C

Apparently, old timey slang for “cigarette” triggers the system… -mod

ferdberple
August 27, 2022 5:01 pm

specific heat of water is about six times that of air.
≠==========
Specific heat is calculated from mass. They air in the cube is by volume. Based on volume the specific heat water/air is over 1000 from memory.

August 28, 2022 1:50 am

Specific but the air is also less dense.

Michael S. Kelly
August 28, 2022 9:55 pm

Kip ===> You puzzled me with your statement that the specific heat of water is about six times that of air. Then I remembered the context of the closed box example, and you’re right about that. The constant volume specific heat of air is 0.714 times its constant pressure specific heat, so that water has 5.8333… higher specific heat than air (actually, specific heat capacity, but I usually omit the “capacity” part, myself). For the atmosphere, we’re talking about enthalpy rather than internal energy – the latter referring to a closed volume. So the specific heat value to use for the atmosphere is the constant pressure specific heat. In that case, water has only 4.167 times the heat capacity of air.

However, there are 321 million cubic miles of ocean, with a mass of 3E21 pounds. Its specific heat capacity is 0.932 B/lb-F, for a total of 2.8E21 B/F. The mass of the atmosphere can be easily approximated by multiplying the Earth’s surface area by the pressure at sea level, for a value of 1.16 E19 pounds. Air’s specific heat is 0.24 B/lb-F, so the atmosphere (neglecting humidity) has a heat capacity of 2.8 E18 B/F.

The ratio of ocean to air heat capacity thus is indeed 1,000.

Sorry about the English Engineering units. I got my BSME and MSME from Purdue 40 something years ago, and thus still think in those units (as an added bonus, my absolute temperature scale is Rankine).

Dena
August 27, 2022 10:20 am

The change in the water temperature will be small however not mention is the water content of the air because some cooling may take place through evaporation so an exact number isn’t possible without additional information!

Dena
August 27, 2022 11:54 am

Something I didn’t think of when I made the post but the moisture in the air changes the density and specific heat of the air. Part of the reason why older jets (water wagons) used water injection on takeoff to produce more thrust. This problem keeps getting more complicate the more I think about it and I haven’t worked with that stuff in over 50 years.

Clyde Spencer
August 27, 2022 3:02 pm

What this all boils down to is that a simple average will not give the correct average for air parcels. What is needed is a weighted average, where the weighting factor is the absolute humidity of the air, absent any phase changes. This information isn’t usually available, particularly for historical measurements. So, any claims for infilling (homogenization) being done correctly, needs information on the absolute humidity, and pressure, as well as the temperature at the stations being used to interpolate. Absent that detailed information, any claims for long-term changes need to establish that evapotranspiration rates have been constant since before the industrial revolution, and/or that the average global absolute humidity has had a negligible change over the last 150 years.

The best that can be claimed legitimately is that, as a first-order approximation, ignoring all the interacting variables, there appears to be a long-term increase in the averaged raw, global temperatures. Without doing the detailed work, it is not obvious that there is an increase in the enthalpy of the atmosphere.

August 27, 2022 9:01 pm

Kip, OT but I’ve previously expressed concern that the powers that be mix atmospheric temperatures with SSTs in calculating average global temperatures.

D Boss
August 28, 2022 5:16 am

While I whole heartedly agree with the premise of these “Tricky Numbers” posts; actual unadulterated surface temperatures are NOT going up:

http://temperature.global/?fbclid=IwAR1mhZfsFG7WnZYOjTznx_Yvy-_MguXETmvV-cioDlJGGsEqNoWppwAMrUo

Most of the data at the above site is from METAR reports. These cannot be fudged or aircraft will crash! (or overrun runways on takeoffs and landings) (METARS also include dewpoint, pressure, etc and aircraft operations calculate the density of the air for several critical performance determinations)

Yes, surface temperature readings alone do not indicate energy of the atmosphere. But even when you “average” global surface temps, there is no “climate emergency”! (unless you fudge the numbers as most agencies have done as per the attached chart of temperature adjustments vs CO2 from Tony Heller’s site) (for the logically challenged, if the amount of temperature adjustment for all US stations for 120 years plotted against CO2 concentration is a straight line, then you are altering the data to fit a theory – period, no debate, no argument) (that is the more ominous “tricky numbers” problem in my view)

D Boss
August 29, 2022 3:29 am

Kip: no email received, directly or in spam folder. If you are inquiring the source of the chart see here:

And I double checked, my email is correct in the entry below this post.

Old Cocky
August 27, 2022 3:57 pm

I think the humidity values and air pressure are available for a large proportion of the observations.

Calculating enthalpies and the trends would be a big, but enlightening, project.

Tim Gorman
August 28, 2022 5:40 am

Don’t hold your breath. Too much money at stake!

Old Cocky
August 28, 2022 2:23 pm

Think of it as the Surface Stations exercise writ large.

Old Cocky
August 28, 2022 3:08 pm

P.S. The Australian BoM weather observations include temperature, relative humidity and air pressure, which is sufficient to derive absolute humidity and hence enthalpy.

However, if only the max and min for each of these are recorded for any given day, that probably doesn’t help. Even if we assume an inverse relationship between RH and T, P will be independent. That gives far too large an envelope to be very useful.

One could possibly use the midpoints (note, carefully avoiding the “a” word) to come up with a rough approximation, and calculate the lower and upper bounds using the 3 minima and 3 maxima.

Still, it might be a useful proof of concept exercise to use recent data to see how far such an approach diverges from calculations based on hourly observations.

Tim Gorman
August 28, 2022 3:24 pm

It’s still going to have an uncertainty interval larger than the differential you are trying to find. You still won’t know exactly what is happening.

Old Cocky
August 28, 2022 4:24 pm

Unfortunately, that is almost certainly the case.
A little PoC might help to quantify it.

Old Cocky
August 28, 2022 5:42 pm

If it does nothing else, it should give some indication of the goodness of fit of temperature change as an approximation for enthalpy change.

Tim Gorman
August 29, 2022 6:05 am

Perhaps. Measurement uncertainty, especially of mid-range values, smears the ability to render accurate residuals so even the goodness of fit becomes vague and unreliable.

Old Cocky
August 29, 2022 2:20 pm

That is rather a limitation of insufficient data, unfortunately.

It would still be an interesting exercise, and there don’t appear to have been any such analyses published.

August 27, 2022 3:25 pm

Add a very thin layer of oil – evaporation is then essentially insignificant.

AndyHce
August 27, 2022 3:31 pm

You would also need to know the air pressure (or mass of the air). The problem as stated probably intends that one assume standard pressure (1 Earth atmosphere), but another question that could be formulated is: at what air pressure would the specific heat per volume be the same for both the air and the water? Of course under that condition considerably more air would be dissolved in the water, complicating the calculations, but the question is about temperature at equilibrium.

commieBob
August 27, 2022 10:25 am

You didn’t tell us the relative humidity of the air. 🙂

A given volume of water has a far greater specific heat than the same volume of air. So, the equilibrium temperature of the whole system will closely approximate that of the water. It won’t change much if you raise the temperature of the air a couple of degrees.

The specific heat of air and water are about the same on a weight/weight basis. However:

There is about 1000 kg of water per cubic meter.
There is about 1.3 kg of air per cubic meter.

So, on a volume basis, the water will hold about 800 times the heat as the water. ie. The air temperature doesn’t matter a lot.

commieBob
August 27, 2022 10:55 am

Oops. Rud (below) is right of course. I was mentally mixing joules and calories when I was comparing the specific heat of water and air.

August 27, 2022 10:35 am

Climate scientist Roger Pielke Sr. has long said that ocean heat content (OHC) is the most appropriate metric by which to measure global warming. See these two of his many writings about this:

His 2003 paper in BAMS: HEAT STORAGE WITHIN THE EARTH SYSTEM
https://pielkeclimatesci.files.wordpress.com/2009/10/r-247.pdf

in 2008 this was deemed heresy by climate activists, receiving a barrage of critical (largely bogus) attacks. Like so many of their attacks on Pielke Sr, they don’t read so well now.

Once data was found showing that the oceans were warming fast, OHC became allowable for study again. As in this:

https://www.carbonbrief.org/guest-post-observations-and-models-agree-that-the-oceans-are-warming-faster/

Michael in Dublin
August 27, 2022 10:52 am

Larry, does this mean that the alarmism over the hottest day ever in this or that city or district is in the bigger picture actually meaningless?

August 27, 2022 1:54 pm

Speaking as an amateur (others here can give better answers), those hottest day events express a different dimension of global warming. As many climate scientists have said, more warming means more extreme heat events. It’s a probabilistic thing.

As such, they are imo meaningless for different reasons than changes in the Earth’s heat content (ocean + atmosphere).

First, the reliable records for most of the Earth are too short to reliably calculate odds of a record hot or cold day. If looking at cities or airports, the record must be adjusted for heat island effects (seldom done). Another problem with short records – they’re affected by the various decadal cycles (e.g., AMO, PDO).

Second, those few areas with multi-century records have another problem – in the early 19th century we emerged from the Little Ice Age. The warming from that is natural. So the frequent use of a 1860 baseline is nuts – despite claims otherwise, industrialization was a microscopic factor on global temperatures until circa WW1. And small until WW2 (these are very rough dates).

Third, looking at events in a specific geographical area tell us little. With no warming, how many areas (eg, 1000 sq miles) of the Earth for which we have a 100 year record should we expect to have a record hot day every year? Not zero.

Shorter answer: None if this matters. The Left has “information dominance” (borrowing the military term) in the US press. They can lie about the climate with impunity. No matter how outrageous the claim, few climate scientists will issue rebuttals. And few will hear the rebuttals (“if a tree falls in the forest but nobody …’). Leftists would have to be fools or saints not to use this advantage. They are neither.

I wrote about this in 2019, my 400th and last post about the climate wars: “Why climate skeptics will lose. How they can win.“ I was too optimistic, as usual.

https://fabiusmaximus.com/2019/11/07/who-wins-the-climate-debate/

Clyde Spencer
August 27, 2022 3:08 pm

As many climate scientists have said, more warming means more extreme heat events.

However, there is not supporting evidence for the claim, at least in the US:
https://wattsupwiththat.com/2019/09/06/the-gestalt-of-heat-waves/

August 27, 2022 3:42 pm

The data about heat waves in the US is an interesting subject. The Heat Wave Index 1895 – 2022 shows no trend:

https://www.epa.gov/climate-indicators/climate-change-indicators-heat-waves

Not to worry! At that page the EPA has new indexes that show scary trends!

NOAA also has pitched to this great project, producing indexes showing that we are living in the end times. See their Extremes in Maximum Temperatures Index:

https://www.ncei.noaa.gov/access/monitoring/cei/graph/us/01-12/2c

Tim Gorman
August 28, 2022 4:58 am

As many climate scientists have said, more warming means more extreme heat events. It’s a probabilistic thing.”

More warming of what? Minimum temps? Maximum temps? A combination of the two?

Max temps don’t show increased warming. Min temps do. How would minimum temps going up mean more extreme heat events?

Most climate scientists look only at the mid-range temp and ASSume that if it is going up it must mean that maximum temps are going up. The mid-range temp can’t tell you that – that is why so many CAGW predictions, which assume Tmax is going up and is going to turn the Earth into a cinder, never turn out to be true!

August 28, 2022 5:41 am

Tim,

More warming of what? Minimum temps? Maximum temps? A combination of the two?”

What do they mean by extreme heat events? You will find the answers in my comment to which you replied. Click on the two links provided in it!

https://wattsupwiththat.com/2022/08/27/numbers-tricky-tricky-numbers-part-3-5/#comment-3587587

Jack
August 28, 2022 7:18 am

I would be very interested to know on which scientific basis they’re reIying in cIaiming that the extreme heat events wiII be hotter and more frequent. The actuaI warming is modest, 1°-1,5° C. How can this produce 5 to 10°C hotter temperatures every year or so?
We know for certain now that the peak of the MedievaI Optimum was aImost 2°C warmer than today. What does the actuaI historic documents tell us ?

Geoff Sherrington
August 29, 2022 10:04 pm

Kip,
I have extensive Australian data on the question of whether a baseline warming of 1degree C adds 1degC to heatwave maxima. It seems that mostly it does not, though some stations it does, numerically.
Mechanistically, much more complex. Melbourne has hotter heatwave maxima than Sydney or Brisbane. Reason seems to be that heatwaves form elsewhere like central desert and weather systems move them over our bigger coastal cities. So the past climate record at a station need not have much to do with heatwave statistics. Yours for the asking. Geoff S

Old Man Winter
August 27, 2022 1:43 pm

IIRC, wasn’t there some controversy about using sea surface temps
vs the temps ~ 2 meters above the H2O as land temps are
recorded @ ~2 meters? I haven’t seen anyone interject that point
lately.

August 27, 2022 8:28 pm

Kip,

That’s a vital point! As Roger Pielke Sr. wrote in 2004:

“It is imperative that the Earth’s climate system research community embraces this nonlinear paradigm if we are to move forward in the assessment of the human influence on climate.”

— “Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system”, Climatic Change, 2004.

http://pielkeclimatesci.wordpress.com/files/2009/10/r-260.pdf

To what degree has this happened?

FWIW, I searched Google scholar for papers in 2021 and 2022 about nonlinear AND “climate science.” Excluding those about peripheral aspects — such as AI, machine learning, and the climate science implications of old work by Manabe, Hasselmann, and Parisi (2021 Nobel Prize in Physics) – I found surprisingly few peer-reviewed papers about this. And they were, from a quick skim, not heavily cited or in major climate science journals.

Why should climate scientists change course? As I said years ago, the current paradigm is working fine – in terms of the metrics of success institutional leaders care about. Thomas Kuhn Rules!

StephenP
August 28, 2022 7:48 am

Sofar in relation to the heat content of oceans, no-one has mentioned the amount of heating occurring through thermal vents in the ocean floor.
I can only assume that it is insignificant in the grand scheme of things, but is the earth’s core cooling and will eventually become a solid mass, or is it IIRC reading somewhere once that there is a nuclear reaction in the core providing fresh heat?

Old Man Winter
August 27, 2022 11:01 am

Great comment, Larry, as you’re raising the least mentioned but probably
most important question concerning global temperature- ocean heat
content versus the relatively tiny amount of heat in the
atmosphere. Another thing- isn’t it a bit backwards to worry
about rising air T when much of that is due to the ocean’s releasing
heat? I’d think La Ninas cooling the air & taking in heat would
be of more concern long-term. It’s unfortunate that he quit
blogging because it seemed he used half his time just dodging/ignoring insults so he could keep his conversations on track &
meaningful. That gets very tiring after a while.

Yooper
August 27, 2022 11:15 am

Were the models that agreed the oceans are warming faster blondes or redheads, and did they do the sampling in bikinis?

Old Man Winter
August 27, 2022 2:23 pm

The Team™ may be desperate as this is the latest I’ve seen of
“positive proof of global warming”. They may have been distracted
too much to even notice the hair color! 😮

August 27, 2022 7:53 pm

Extrapolating to the current day… Hmm, I haven’t been to a beach in years, maybe should think about a day trip.

August 27, 2022 9:27 pm

Its already happened; I’ve personally investigated.

RickWill
August 27, 2022 3:44 pm

Climate scientist Roger Pielke Sr. has long said that ocean heat content (OHC) is the most appropriate metric by which to measure global warming.

Increasing OHC over a matter of decades indicates a change in net evaporation as the land surface temperature gets closer to the water surface temperature and latent heat transfer reduces. Deep oceans take centuries to get surface heat from the surface to depths below 1000m. Deep ocean warming is an indication of reduced net evaporation, which is occurring. That is due to northern hemisphere land masses warming up as solar intensity increases in response to changing orbit.

No climate model has predicted that land precipitation (run-off) would reduce as evidenced by the run-off data over the last 100 years or so.

Increasing OHC is a sign of global warming but it is not due to an energy imbalance in the atmosphere. It simply reflects the gradual shift in solar intensity following orbital precession. The change in phase occurred about 500 years ago; the last time perihelion occurred before the austral summer solstice. Perihelion now occurs around 4th of January. It will reach 7th January in the early 2100. Perihelion will occur at the boreal summer solstice in about 9,500 years time. By then the cause of glaciation will be experienced by whatever still exists on the planet.

mal
August 27, 2022 8:52 pm

If anyone think the oceans are warming “fast” I would like to ask do you want to buy a bridge?

August 28, 2022 5:52 am

Mal,

If anyone think the oceans are warming “fast” I would like to ask do you want to buy a bridge?”

I said “Once data was found showing that the oceans were warming fast, OHC became allowable for study again.” But ”fast” is subjective. I should have said “faster.” Still, I believe most readers understood my point.

Oceans warming isn’t my field, and I no longer follow climate science. But there are quite a few papers describing acceleration in ocean warming. This is one of the early ones, illustrating what I said:

“How fast are the oceans warming?”
“Observational records of ocean heat content show that ocean warming is accelerating.”
LIJING CHENG, JOHN ABRAHAM, ZEKE HAUSFATHER, AND KEVIN TRENBERTH.
SCIENCE, 11 Jan 2019

https://www.science.org/doi/10.1126/science.aav7619

August 28, 2022 6:33 pm

Kip,

I disagree with most statements that “the proper question is ….”

Few public policy questions can be reduced to a “proper question.” More importantly, I believe the process is far more important than any specific question. I worry that climate science as an institution is broken, which diminishes our ability to resolve questions about the climate.

That was the point of my comments, lost amidst the confident replies by so many commenters here who believe they have certain knowledge about so much on the fringes of science (yours are an appreciated exception). As I said…

“In 2008 this was deemed heresy by climate activists, receiving a barrage of critical (largely bogus) attacks. … Once data was found showing that the oceans were warming fast, OHC became allowable for study again.…”

Why should climate scientists change course? As I said years ago, the current paradigm is working fine – in terms of the metrics of success institutional leaders care about. Thomas Kuhn Rules!”

The Left has ‘information dominance’ (borrowing the military term) in the US press. They can lie about the climate with impunity. No matter how outrageous the claim, few climate scientists will issue rebuttals. And few will hear the rebuttals (“if a tree falls in the forest but nobody …’). Leftists would have to be fools or saints not to use this advantage. They are neither.”

Climate science is itself an example of a larger problem in America, the broad and accelerating collapse of our institutions. Like syphilis, the wide range of symptoms hinders diagnosis of the cause.

Perhaps how to fix America is the ‘proper question.’ See:

A new, dark picture of America’s future.
https://fabiusmaximus.com/2019/03/13/death-of-america/

August 27, 2022 9:20 pm

Larry, that chart purporting to show a relationship between atmospheric CO2 concentrations and OHC is a joke. Graphed OHC showed no change between the late 1950s and the early 1980s, a period where CO2 was rising significantly. Anyhow, since they adjusted ARGO temperatures upwards by about a degree and a quarter, the OHC after about 2005 is significantly exaggerated. The problem gets worse as the ARGO readings become a larger proportion of the data over time.

Rud Istvan
August 27, 2022 10:38 am

Specific heat of water is 4182J/kg. Specific heat of air is 718J/kg, less than a fifth. BUT 1 cubic meter of water weighs 1000kg. A cubic meter of dry air at sea level weighs 1.2kg. Almost a thousand times less mass. Now take 30C air with less than 1/5 the heat per kg and about a thousand time less kg in the box and the impact on the 20C water is essentially nil. Or to be more precise (but not exact) about 0.0002C

mkelly
August 27, 2022 3:17 pm

One minor quibble. The Cv of dry air is 718J/kg. The Cp of dry air is 1005J/kg. Both at 300 K.

Rud Istvan
August 27, 2022 5:05 pm

Quibble away. I was doing multiple orders of magnitude results. And Kip’s problem was expressed in volume. So my quicky look up was for the specified problem.

A lesson related here before, never forgotten, from college. I was taking a semester class taught by famous JKG (look him up). He was the Roosevelt OPA administrator during WW2. So, the question arose, how could he make so many numerical decisions in the era before calculators?

His answer was profound. He learned to sum long columns of numbers to within 10%. (Answer, trick is in remembering rounding of first decimals and summing plus/minus). Then said, if you need an answer more precise than 10%,then you have the wrong question. Works to this day.

Michael in Dublin
August 27, 2022 10:44 am

Second bonus question:
How does the answer apply to land and sea breezes and their effect on climate?

Michael in Dublin
August 27, 2022 11:12 am

Thanks Kip.

Complicated” is a word that does not seem to be part of the vocabulary of alarmist.

Speed
August 28, 2022 6:28 am

“In a more general sense, moving air tend to have a cooling effect on objects (and people)”.

Air moving past a sensor (or skin) remove heat energy from the sensor (or skin) or add heat energy to the sensor (or skin). The speed of the air as well as the area of the sensor will determine how fast heat energy is removed or added.

Frank from NoVA
August 27, 2022 10:52 am

Obviously a trick question! Since there is upwards of 400 ppm CO2 in the air, I’m going to guess 327.5 C, aka the melting point of lead.

Frank from NoVA
August 27, 2022 11:26 am

Aw shoot! I thought I was over at ‘Real Climate’…

Chaswarnertoo
August 27, 2022 9:13 pm

🤣 🤣

August 27, 2022 8:18 pm

Given the accuracy of typical temperature measuring devices in the field, still 20℃.

Chaswarnertoo
August 27, 2022 9:12 pm

See that missed point whizz pat. 😎

Old Man Winter
August 27, 2022 11:29 am

Others have noted you didn’t state the RH of the air. Regardless of what
it is, it could matter but probably won’t be enough to matter.

Since Ts were in whole digits, I’m assuming the range of accuracy
is the standard -0.5 to +0.49999… range for two significant digits. IIRC,
the ratio of the specific heats of air vs H2O is on the order of ~1:1000,
that means it’s either 20C or 21C, rounded to two significant digits,
depending on the actual total amount of heat contained in the two volumes
(Just quibbling to see if this is right, not to prove a point). The same is
true for 32C air.

It isn’t the average of the two- 25- because their heat contents are vastly
different.

Old Man Winter
August 27, 2022 12:00 pm

Since the H2O T could be 20.4999999C, rounded to 20C (2 significant digits), couldn’t the actual total heat push the overall
T of two volumes to at least 20.5C, thus rounded up to 21C?

BTW, a chem prof docked me a point for giving the
answer in 3 vs the correct 2 sig. digits. This was when
one had to sometimes squint using a slide rule to get a
third sig. digit. I was not a happy camper!

Old Man Winter
August 27, 2022 12:29 pm

Before I came up with the “significant digit” consideration, I would’ve gone with 20.0C for that
same reason. But since 20.49999…C(or the
24.999999C) needs << 0.1C to get to 20.5C,
I opted for either 20 or 21 as being the only
possible correct answers when rounding to 2 sig. digits. If I’ve broken a sig digit rule,
then I’m obviously completely wrong.

Old Man Winter
August 27, 2022 4:13 pm

What’s really funny is that I was looking for a tricky answer only cuz I know you’re a magician & the title leans towards that. It wasn’t until after I came up with 20.0 that I realized that was to 3 sig digits & thought that part 3.5 was written as a segue to part 3.6, dealing with sig digits.

Lesson learned: don’t let people know you’re a magician or use “tricky” titles otherwise people will be reading more into things than you really want them to- some quibbler may do so. Since you wrote this to get people to think & have fun doing it, give yourself a pat on the back, as I did both. Thanks again!

Old Man Winter
August 27, 2022 4:59 pm

Normally, I would have read it as such, but today
I had that nerdy, geeky quibbler hat on where being pedantic & obsessive is rewarded! 😮

When I was 5, I gave away the hand in which the marble was as my jaw would track which hand the marble was in. So when I brought them to the front, they always guessed correctly. Luckily, they eventually shared their secret. Obviously, I’m too uncoordinated & wasn’t magician material & have envied those who are. You would have been good enough to use that as misdirection!

August 27, 2022 9:41 pm

Kip, back when I was pursuing an electrical engineering degree I would have prepared two answers, one for each fundamental type of professor: 1) “About 20 ℃” for the aware professor; and 2) “Rud’s 20.0002 ℃” for the pedantic asshole professor. One can easily and accurately tell the difference between the two types.

Tim Gorman
August 28, 2022 6:11 am

One knew the rules for significant digits and the other didn’t!

August 28, 2022 1:59 pm

The best professor I had was my Statics professor who would say “This is the book process, now here is the quick and dirty way it is done in real-life engineering.”

Phil R
August 28, 2022 6:23 pm

That was our geophysics professor. He gave us a problem one time where the answer was to something ridiculous, like 7 or 8 decimal places. I got marked down on the problem because i rounded to the appropriate significant figures. Apparently, it wasn’t significant enough.

Richard Brimage
August 27, 2022 11:32 am

Essentially almost no change in water temperature to lower the air temperature 20 C.

Crispin Pemberton-Pigott
August 28, 2022 7:22 am

My calculation is:

1.150 kg dry air x 0.718 = 825.7 Joules/K
30.000 – 20.002 = 9.998 K
9.998 degrees x 825.7 Joules/K = 8255
Joules change in enthalpy

8255 Joules transferred to 1,000,000 g water = 0.008255 Joules per g.
0.008255 / 4.186 = 0.00197 C temperature rise.

20.000 + 0.00197 = 20.00197

Given that some inputs have 4 digits of precision the acceptable answer is 20.002.

As the answer is obtained by calculation, not measurement, providing a theoretical answer is acceptable. However if asked to prove by experiment what the result is, very few people have access to the equipment necessary to differentiate the air temperatures of 20.000 and 20.002 C. To be accepted, the instrument would have to be accurate to ±0.0007 degrees (one third of the difference indicated). A platinum RTD pair such as is used in the ARGO floats is reputed to be readable to ±0.001 C (rather special hardware) but details are lacking. With any lesser instrument an accusation of “false precision” would stand.

It is fair to conclude that the temperature of the cubic metre of water would not detectably change at all.

bdgwx
August 28, 2022 12:22 pm

I believe most of the ARGO floats use the Sea Bird SBE-41 instruments. The stated accuracy is ±0.002 C. The newer floats use the updated the SBE-61 instrument with a stated accuracy of ±0.001 C.

Carlo, Monte
August 28, 2022 12:38 pm

More green milli-Kelvin bullshite.

You haven’t the slightest clues about temperature measurements, yet you yap about them non-stop.

Clyde Spencer
August 28, 2022 1:13 pm

You said “accuracy.” Did you mean “precision?”

bdgwx
August 28, 2022 1:57 pm

Maybe. The datasheet used the word “accuracy”.

Tim Gorman
August 28, 2022 2:27 pm

.0002C the precision of the SENSOR, not of the float itself. A study of the floats came up with +/- 0.5C if I remember correctly. If I can find the study on my computer I’ll post it.

Tim Gorman
August 28, 2022 2:05 pm

Significant digits in an answer are based on the smallest number of significant digits in the values used. That would be 20C.

August 27, 2022 11:57 am

” all the emphasis on the Global Energy Budget”
Of course the energy budget is vitally important. A lot of GCM calculations are about the flow of heat (local budgets). Energy is conserved, and so you can do accountancy with it.

Money is conserved (kind of) and we spend a lot of time doing accountancy with that. But, famously, you can’t eat it. The fruits of money are something else.

There is a thermodynamic lesson in your mixing. Air at a higher temperature has more free energy. You could do work with the temperature difference before mixing – not afterwards, the mixing is an irreversible process. Our bodies need that free energy to keep our processes running. That is why body temperature is vitally important to us. It is different to the heat content of objects.

August 27, 2022 12:27 pm

The fact that heat does flow from the air to water tells what temperature is about. It is the potential variable for heat flow.

AndyHce
August 27, 2022 4:09 pm

While much of the energy the sun delivers to the oceans during the day is released from the oceans in the daily overturning of surface layers (I think that has a specific name I can’t recall at the moment), some of that energy will remain in the oceans much longer because more energetic solar frequencies penetrates quite a ways down. Also, as NASA states, “Ocean water tends to sink at high latitudes, drawing warm water and heat poleward from low latitudes” some of which feeds the Meridional Overturning. The cycle time for that overturning process has been estimated at up to at least 1000 years – a short time for the earth but a long time for humans.

Since that ocean heat will eventually resurface and at least some be released to the atmosphere, ‘global warming’ from the human perspective might well be an awareness of the release part of that cycle, without any additional “energy in the global climate system”.

AndyHce
August 27, 2022 9:45 pm

Yes. I was pointing out that even if there is current warming that is “unusual” relative to human record keeping per se, the greenhouse effect is not the only possible reason.

Peta of Newark
August 28, 2022 1:05 am

Yes and no..
The most significant error in there is that water reaches its maximum density at around 4°C = while still liquid

Thus, water that is colder than 4°C will become buoyant and so will warmer water.
It is that which puts a limit on how deep heat energy from the surface can penetrate into the ocean.

Check out the ARGO bouys, they don’t venture below A Certain Depth (wild guess = about 1,000metres) exactly because of that.
There is perfectly nothing changing and nothing to see down there

You can re-phrase what I said there = that there is a near infinite heatsink ## in the ocean, just below where all the existing mixing takes place.
So what Kip is trying to get across here is that Global Warming (the actual, imagined, modelled increases in global air temperatures) is precisely, to 3 decimal places, Diddly Squat

## I always understood that The Ocean has an average depth of 4,000 metres

To first approximation, in Kip’s thought experiment taken out into the real world, there is 3,000 metres depth of water at 4°C and about 10,000 metres depth of Tropospheric air at minus 15°C average temp.

So there’s a nice can-of-worms – why hasn’t the deep ocean warmed the Troposphere.
Maybe green house gases don’t do what they’re cracked up to do?
Even worse, isn’t that “minus 15 average” of the Troposphere exactly what the initial assumption of of the GHGE says it should be – about 30°C colder than we see (at the surface)
Maybe ‘something else’ is making the warm air we see near the surface and there’s only one thing anywhere that can do that.

El Sol

Tim Gorman
August 27, 2022 1:34 pm

Temperature only defines the beginning gradient end points. The actual heat transfer is dependent on the heat capacities and masses.

It’s why a 15watt soldering iron at 800F won’t transfer enough heat to solder a car radio but a 300 watt soldering iron at 800F will. One has a much higher mass and more joules available to transfer into the radiator. The radiator/soldering iron reach equilibrium at a much different temperature in each case.

Derg
August 28, 2022 5:58 am

Obfuscation is his objective.

Clyde Spencer
August 28, 2022 1:15 pm

Sophistry is his tool.

Richard Page
August 27, 2022 12:26 pm

Ah Nick Stokes at his best. Doesn’t answer the question but poses then answers an irrelevant question that has nothing to do with what’s being discussed. Presumably, if asked what 2 plus 2 equals, we’ll get a discussion on the habitat and diversity of ants – I look forward to that one.

August 27, 2022 12:42 pm

No, the question posed here is irrelevant. No-one wants to know what would happen if somehow our environment was sealed off and came to the same temperature. That isn’t going to happen. What we want to know is what will happen to the temperature we will continue to experience in our environment with it’s various heat flows and phase differences, And average temperature is a much better measure of that than a calculation of the heat content of something.

There is a question for the heat content/enthalpy fans. What exactly do you want to calculate the heat content of?

Carlo, Monte
August 27, 2022 12:44 pm

And average temperature is a much better measure of that than a calculation of the heat content of something.

Nonsense, on so many levels.

Tim Gorman
August 27, 2022 1:42 pm

If you are using the atmosphere as a gauge of climate change then you should find the heat content of the atmosphere.

For me, ocean temps and/or sub-soil temps (somewhere around 3′ to 6′ deep) would be far better metrics.

The biggest problem is that nothing in the atmosphere or ocean is ever stable. They are always changing with vastly different cyclical rates as time moves.. A snapshot in time is not a very good metric.

It’s like saying the earth is getting hotter because we are seeing more drought in CA and AZ. So what? Both are made up of semi-arid and arid deserts – which means they have had droughts regularly over the milllenia. It’s why the native plants there evolved as they have. It’s why the Great Plains are semi-arid deserts and the prairie grasses have root systems that go down 8′ or more to find water.

There’s not much new under the sun on this planet.

Old Cocky
August 27, 2022 4:32 pm

Actually, the Great Plains appear to have pretty good average annual rainfall, but it may be quite variable.

Tim Gorman
August 28, 2022 5:54 am

That’s why it’s called a “semi”-arid desert. For an example of a drought look at the 20’s and 30’s. The droughts don’t last as long as they do in the SW US but they do happen regularly. It’s still why the native grasses all have deep roots (otherwise the bison would have starved away).

Old Cocky
August 28, 2022 2:03 pm

I think they would just be defined as rangeland here. From memory, our semi-arid is under 18″, and arid is under 12″.

It’s always interesting to see how things are handled in different parts of the world.

Tim Gorman
August 29, 2022 12:49 pm

Not sure “rangeland” is a typical term to describe biomes. Grasslands would be.

Old Cocky
August 29, 2022 2:35 pm

Rangeland is a broader term than grassland, but, yes, the Great Plains are grasslands. Rangelands are essentially grazing and marginal cropping country, so include scrub.

I was mostly commenting on the “semi-arid” aspect, and trying to keep things broad.

We have a lot of arid and semi-arid areas in Aus.

Dave Gee
August 27, 2022 2:40 pm

Please stop saying “heat content”. Materials / things do not contain heat. The temperature of something is a manifestation of the thermal energy content. If you frame your thoughts by differentiating between thermal energy and heat it will enable you to make more appropriate responses which will perhaps give you greater credibility.

Dave Gee
August 28, 2022 11:08 am

Kip

Thank you for your response and my apologies for not being more clear in my comment. I wanted to make the point very emphatically that temperature is a manifestation of thermal energy content. In so doing, I wanted to point out that if we look at things in terms of energy as a baseline rather than in terms of evanescent and badly defined quantities like temperature, it is much more difficult to obfuscate issues by deliberate misunderstanding. And, for example, you wouldn’t have to spend much time in writing about average temperatures.

I also apologise for my editing failure – after “ Materials / things do not contain heat” I unfortunately deleted the words “they contain heat energy”. If we all agreed that heat was thermal energy then, as you say, there would be less confusion but, more importantly, those of your correspondents who delight in their inability to reason, would be less able to make statements without inherently showing their errors of thought.

As an aside, I very clearly remember the textbook we used for thermodynamics (far too many years ago) defined enthalpy as the total internal (thermal) energy of a system plus P*V. Indeed, and not to be pedantic, of the first 10 results of a DDG search for “what is enthalpy”, 7 returned a definition in terms of system energy and 5 of these did not mention (quantities of ) heat at all.

best regards

Tim Gorman
August 28, 2022 5:37 am

It is heat content that allows you to solder a radiator with a large 300watt soldering iron while you can’t do it with a smaller 15 watt soldering iron even if it is at the same temp (i.e. molecules have the same kinetic energy) as the 300 watt one.

More mass, more heat content (joules) available to transfer to another object.

It’s why a matchstick at 100F and a steel needle at 100F will melt a vinyl countertop very differently. One has more “heat content” to transfer to the countertop.

Heat content is a *real* thing.

Dave Gee
August 28, 2022 11:10 am

Tim

I enjoy immensely your often pithy comments in response to visitors to this site. I am therefore sorry to have to disagree with you completely regarding your comment about “heat content”. It is absolutely not heat content that “ …. allows you to solder a radiator with a large 300watt soldering iron while you can’t do it with a smaller 15 watt soldering iron”.

The reason is inherent in your comment. A 300 W iron is called a 300W iron because the power supply that drives its capable of supplying 300W – 300 Joules per second – to the iron.

If an iron is used to solder a large thermal energy sink – like a car radiator – then energy is transferred from the iron ( the energy source) to the radiator ( the energy sink) and, as you say, the kinetic energy of the molecules in the iron is reduced and the temperature drops.

There is a temperature measurement device inside the body of the iron which regulates the supply of energy dissipated by the soldering portion of the tool. If the temperature starts to drop then the thermostat allows more energy to be supplied to the iron which enables the temperature to be maintained and hence the rate of energy transfer to remain effectively constant. This then enables the heat sink to increase in thermal energy content despite its losses and increase its temperature so that solder will melt.

The 15W iron cannot be supplied with sufficient energy sufficiently fast to keep pace with the thermal losses in the radiator (because the radiator is doing its job of radiating) and so it can’t melt the solder.

When you say “more mass, more heat content” you, I think, are imagining those old soldering irons with a substantial lump of copper on the end which were energised by sticking them on the gas stove. They had quite bad temperature regulation as I recall and were very good at melting radiator hoses. My current heavy duty iron is rated at 350W and is the thickness of a pencil – it just has a very slick controllable switching power supply driving it.

You are, of course, correct about the thermal energy content of a matchstick and a needle although I’m not sure whether you are implying that the matchstick is alight of not.

Best regards

Tim Gorman
August 28, 2022 1:53 pm

David,

The reason is inherent in your comment. A 300 W iron is called a 300W iron because the power supply that drives its capable of supplying 300W – 300 Joules per second – to the iron. “

“When you say “more mass, more heat content” you, I think, are imagining those old soldering irons with a substantial lump of copper on the end which were energised by sticking them on the gas stove.”

Yep. The actual soldering iron I use for soldering radiators is not powered from the AC socket. It is warmed with an acetylene torch and then applied to the radiator. It’s actually an old blacksmith’s soldering iron made to be used in a forge inherited from my father. You usually have the radiator out of the car so you can remove the top, rod out the tubes, and then put the top back on. No hoses in the way.

You can buy various sizes of such torches. They only differ in the mass at the end of the soldering iron. You can heat them till they glow a nice, dark red – about 700F to 800F. The larger ones work much better for things like radiators and such. You don’t have to reheat them as often either.

Jim Gorman
August 28, 2022 6:16 am

What we want to know is what will happen to the temperature we will continue to experience in our environment with it’s various heat flows and phase differences, And average temperature is a much better measure of that than a calculation of the heat content of something”

You are dancing around the truth. You can’t talk about “heat flows” out of one side of your mouth and then “temperature is a much better measure” out of the other side.

Have you ever heard of dry heat in Phoenix vs wet heat in the swamps of Louisiana? There is a difference! Temperature just won’t work to measure both sensible AND latent heat. It is the combination that deals with the sun’s radiation.

You simply won’t accept that temperature alone provides little in the way of attributing the sun’s energy between two different measures. Do you think steam boilers turning turbines for electricity aren’t designed using enthalpy? Keep on dancing, you just entertain those who know what is really occurring!

Clyde Spencer
August 28, 2022 1:27 pm

And, the physiological effects of temperature are inadequately predicted by temperature alone. That is why the Heat Index was created. Humid air carries more heat energy and suppresses evaporation.

Clyde Spencer
August 28, 2022 1:19 pm

What exactly do you want to calculate the heat content of?

The parcel of air that wasn’t measured at a missing station, in order to interpolate temperatures between operating stations.

Leslie MacMillan
August 27, 2022 1:08 pm

Not true. Life is not a heat engine, thermodynamically. It matters nothing that body temperature is usually greater than ambient temperature. We don’t do metabolic work with the temperature difference. All our energy transformations are isothermic. They do give off waste heat, however, which is why we are warmer than our surroundings. You’ve confused cause and effect here.

b.nice
August 27, 2022 1:52 pm

A lot of trite words pertaining to nothing relevant.

A standard Stokes post.

Peta of Newark
August 28, 2022 12:46 am

Quote:”Air at a higher temperature has more free energy

‘free energy’
‘global warming’

If this stuff is ‘free’ and there is now sooooo much of it, why are energy/electric/petrol/gas prices rising so much and so fast?

Bob
August 27, 2022 1:00 pm

Very good.

MarkW
August 27, 2022 1:39 pm

Are we assuming that the air originally was completely dry? If so we have to calculate the loss in temperature from the water as enough water evaporates to saturate the air.

Tim Gorman
August 27, 2022 1:44 pm

Kip,

Simple yet thought provoking example! Makes people question their assumptions. Which is what learning *should* be about!

Good job!

August 27, 2022 9:48 pm

Kip, its hard to get a man to understand something when his paycheck depends on his not understanding it.

Anders Rasmusson
August 27, 2022 1:56 pm

Assume there is a normal atmospheric pressure (10 130 Pascal) in the box. Then there is 1,2 kg air at 30 °C with specific heat at 1,0 kJ/kg/°C.

There is 1 000 kg water at 20 °C, specific heat at 4,2 kJ/kg/°C.

Enthalpy for the inlet components :

Air : 1,2*1,0*30 = 36 kJ
Water : 1 000*4,2*20 = 84 000 kJ

Total inlet enthalpy : 84 036 kJ

With that enthalpy conserved then the steady state temperature (T) for both the components will come out at :

1,2*1,0*T + 1 000*4,2*T = 84 036 kJ
==>
T = 84 036 / (1,2 + 4 200) = 20 °C

If instead the inlet air temperature is 32 °C then the steady state temperature (T) will come out at :

T = (1,2*1,0*32 + 84 000) / (1,2 + 4 200) = 84 038 / 4 201 = 20 °C

In the global system the air temperature will follow the ocean and land temperatures.

The air is though also a heat transfer media beeing warmed up at the surfaces and cooled down at higher altitude by thermal radiation to space.

I don’t know how to accurately measure the global system enthalpy (temperature).

Kind regards
Anders Rasmusson

ferdberple
August 27, 2022 5:30 pm

T = (1,2*1,0*32 + 84 000) / (1,2 + 4 200) = 84 038 / 4 201 = 20 °C
======
A very nice demonstration of how to calculate average temperature.

Andy Plank
August 28, 2022 4:24 am

Just a quick comment. I don’t know if anyone has already mentioned this. The Specific Heat Capacity (or enthalpy) of a fluid is NOT a constant. It is a variable, which varies with temperature (amongst other things). This is one reason why there are NO analytical solutions to thermodynamic problems, only empirically-based approximations.

To try and put it more simply: The very properties (thermal coefficients) you need to calculate temperature changes are themselves changing with the temperature.

Typically, Specific Heat Capacities are given in huge tables, which are essentially tables of actual real-world measurements. For practical use the values are interpolated between the values given in the tables.

In addition, in the above problem if the water warms, it will expend – meaning that there will be more than a cubic metre of water.

True, in most cases these differences are small. But in computer models doing millions of calculations per second, these differences can significantly affect the model output.

Anders Rasmusson
August 28, 2022 10:44 am

Andy Plank : “…..The very properties (thermal coefficients) you need to calculate temperature changes are themselves changing with the temperature. ….”.

Yes, that’s true. For this back of an envelope calculation, the air specific heat at 1,0 kJ/kg/°C is used instead of 1,006 and 1,005 kJ/kg/°C at 10 and 20 °C respectively.

Kind regards
Anders Rasmusson

Tim Gorman
August 28, 2022 2:29 pm

Typically, Specific Heat Capacities are given in huge tables”

for moist air they are called Steam Tables.

August 27, 2022 2:03 pm

After criticizing the author for three full articles to explain that temperature is not heat, which should take one paragraph, just what we need is another article.

The average temperature statistic has accuracy problems, but it is used everywhere. It is not a “fantasy”. It will continue to be used. Better to spend your time explaining the many ways the data being averaged are not accurate. So the average can’t be accurate. And no one lives in an average temperature. And no one knows what a normal or optimal average temperature is. Minor problems like that ! But average temperature is not going away and no one cares if it measures heat.

The bottom line is “climate change” is nothing more than predictions of a coming climate crisis (CAGW) barely related to any past climate. Not even related to the warming from 1975 to 2022, which I suppose you don’t recognize because that warming trend is based on the global average temperature statistic?

CAGW is predictions of doom unrelated to PAST CLIMATES.
WRONG FOR 50+ YEARS SO FAR.

We Climate Realists are losing the CAGW propaganda war.
Attacking the global average temperature statistic won’t help defeat climate alarmism. The Geoff Sherrington article here on temperature data uncertainty is a step in the right direction:

Uncertainty Estimates for Routine Temperature Data Sets. – Watts Up With That?

miha
August 28, 2022 12:10 am

Skeptics will undoubtedly lose the war in terms of the views of ordinary people. Not because of any particular belief about hot summers, drought, wild fires, species extinction or any other phenonenon. It is simply because of elephant in the room. Namely – that the carbon dioxide level in the atmosphere relentlessly rises year by year and shows no sign of stopping. Not a smidgeon of argument against that hard fact. You can argue about the effects (positive or negative) but the public understand that in the very long run that spells trouble. If you disagree then you should make sure your argument is fully appreciated by everyone. Skeptics don’t appear to very much want to address this reality.

August 27, 2022 2:17 pm

Here is what ordinary people should care about:
The local weather where they live and work
And the trend over time, if they even notice one.
No one lives in the average temperature.

Here’s what ordinary people should not care about:
Predictions of climate doom that have been wrong for 50+ years so far.
The difference between heat and temperature

If people live in a warm climate, warmer could be thought of as bad news
If they live in a cold climate, warmer could be thought of as good news.

I live in SE Michigan, where winters arer not as cold as in the 1970s when I moved here from New York. That’s good news. Meaning the way that global warming that has affected my local climate is good news. Please give us more of that warming.

August 27, 2022 6:00 pm

You are dreamer.
Not a green dreamer, but a dreamer.
Heat versus temperature will not be asked on any high school test.
So no one will learn the difference, or care.
And it will not matter.
Because if they graduate high school believing the world is doomed from climate change, then they never learned how to think independently. They blindly trust the government. They blindly trust predictions of climate doom, And you want them to learn real science?

Heat is a measure of change, never a property possessed by an object or system. Therefore, it is classified as a process variable. Temperature describes the average kinetic energy of molecules within a material or system and is measured in Celsius (°C), Kelvin(K), Fahrenheit (°F), or Rankine (R).

Tim Gorman
August 28, 2022 5:32 am

Heat is a measure of change, never a property possessed by an object or system. Therefore, it is classified as a process variable.”

What do you mean heat is a “process” variable? Does the energy in a thunderstorm come from temperature or heat content? Does the energy in a hurricane come from temperature or heat content?

I would agree that heat content can’t be directly measured but that doesn’t mean it is a “process” variable. It is a *physical* quantity.

It’s heat content that allows you to solder a radiator with a 300 watt iron while you can’t do it with a 15 watt one even if both are at the same temperature.

﻿

Bellman
August 27, 2022 2:56 pm

Allow enough time for the temperatures to become equalized – for the energy in the water and air in the box to reach equilibrium (we will ignore any phase changes such as evaporation).

Not going to bother to work out an exact value as you don’t specify the humidity of the air, but obviously it’s going to be very close to 20°C because of the grater specific heat content of water, and the greater mass.

And why will it NOT be the mathematical average (the mean)calculated as 20+30/2 = 25 °C?

Gary Pearse
August 27, 2022 3:01 pm

Kip: The volumetric heat capacity of water of the water is about 3000 x that of air, so at equilibrium the the T of both are very near 20C.

I guess, if you could take a cubic foot of air from each 1° gridcell 2feet above the surface of the earth, and mixed them and take its temperature instantaneously, you would get an average. But having various water contents, the cold air from polar areas and temperate areas having winter and containing sub zero water vapor would end up releasing the heat of the phase change and warm the mix up a bit.

Robber
August 27, 2022 3:13 pm

In Singapore, the mean monthly maximum temperature ranges from 30-32C throughout the year, while the mean monthly minimum temperature varies from 24-26C.
The average water temperature varies from 27-29C. Equilibrium?
From 1980 to 2020, the annual mean temperature has increased from 26.9°C to 28.0°C.
https://weather-and-climate.com/average-monthly-Rainfall-Temperature-Sunshine,Singapore,Singapore

August 27, 2022 8:42 pm

Robber, I didn’t see the data on the changes in annual mean temperatures. I would be interested in the changes over about 100 years, rather than 42 years, if you have it.

Robber
August 27, 2022 8:52 pm
August 27, 2022 9:58 pm

Thanks for the information, Robber. Mk1 eyeballs say it looks like mid-20th Century cooling, late-20th Century warming and meh for the 21st Century to-date. It does not look anything like the evolution of atmospheric CO2 concentrations.

Along with a bunch of AGW nonsense, they do admit that urbanization could have resulted in an upward temperature trend. In talking about increasing temperatures since mid-1970s, they ignore the 21st Century pause.

Bellman
August 27, 2022 3:25 pm

OK maths is fun. Lets try it. Haven’t looked at any other comments.

Mass of water is 1000kg, specific heat capacity is 4182 J/kg°C.

Assume air is completely dry.

Mass of air is ~1.2kg, specific heat capacity is ~ 1000 J/kg°C.

Let T be equilibrium temperature.

Heat transfer needed to warm water is

1000*4182*(T – 20) = T*4182000 – 83640000

Heat transfer needed to cool air is

1.2*1000*(30 – T) = 36000 – T*1200

Both need to be equal so solving for T

T = 83676000/4183200 ~= 20.003°C

Bellman
August 27, 2022 3:35 pm

If we raised the initial air temperature by 2°C, to 32°C, how much would it change the final answer of the system temperature at equilibrium?

1.2*1000*(32 – T) = 38400 – T*1200

T = 83678400/4183200 ~= 20.003°C

Jim Gorman
August 28, 2022 6:27 am

So, the enthalpy of the atmosphere is important! Temperature won’t reliably tell you the total energy in a mass of air will it?

Bellman
August 28, 2022 12:13 pm

As I said in previous discussions it doesn’t seem to me that enthalpy is that important when there is a big difference between two bodies. The limiting factor is one or other of the temperatures.

In this case the water has far more enthalpy, yet it determines how much the air will cool by. The amount of water could be a million times greater, it would have a million times as much enthalpy, yet the effect of the temperature change would be beyond insignificant. The water cannot cool beyond 20°C and the air will cool to 20°C.

It’s the same in reverse if the water was small and the air massive. If the outside air temperature is 40°C and you put it in contact with a 1 liter bottle of water, the water will heat up, or cool, to 40°C, regardless of the humidity and enthalpy in the atmosphere.

Bellman
August 28, 2022 5:02 am

Another way of looking at this is the equilibrium temperature is simply average of the two temperatures, weighted by heat capacity.

Bellman
August 27, 2022 3:43 pm

Those familiar with the Earth climate as a system can then explain to others why this also answers the question as to why, if the global warming hypothesis is based on the imbalance of the Global Energy Budget, at least in part due to the increase in the Greenhouse Effect due to rising atmospheric COconcentrations (and other anthropogenic GHG emissions), then this example also explains one of the reasons why any Global Average Surface Air Temperature metric (in degrees, or as anomalies, or as land and sea skin surface temperature combinations) is not a proper metric to use as evidence for Global Warming by CO2

It’s an illustration of the objection made about the last so called pause. Even if air temperature is not increasing or is even decreasing for a period of time, it can still mean that total enthalpy is increasing, it’s just all going into warming the oceans. As Monckton kept saying, “the oceans ate the warming.”

Old Cocky
August 27, 2022 4:07 pm

What has the enthalpy increase of the oceans been (presumably since deployment of the Argo buoys)?
What has the temperature increase been?
What has the depth profile of the temperature and enthalpy increases been?

Richard Page
August 27, 2022 4:44 pm

Apart from the obvious, where ‘scientists’ have adjusted the Argo temperatures upwards to be more in line with random sampling from boats, it’s all pretty much nothing. You could put massive amounts of energy into the oceans and it won’t make any measurable difference whatsoever.

Derg
August 28, 2022 6:05 am

No pause…hahahaah.

CO2 as a control knob…even funnier.

MatrixTransform
August 27, 2022 4:27 pm

I need to know the pressure

Jim Gorman
August 28, 2022 6:31 am

Kip,

Very nice. A good tutorial. Hopefully, people who continue to promote temperature rise as the be all and end all of climate change will read your essay and comments.

Averaging temperatures to determine energy density is a not only wrong, but is unscientific. Any idea why so many climate scientists continue to promote it as something meaningful other than money? Someday they will come out on the short end of the stick.

ferdberple
August 27, 2022 5:09 pm

Earths atmosphere has a mimiscule effect on the correctly averaged temperature of the earths surface due to the mass difference and specific heat, assuming you take a very thin slice at the surface.

Tom.1
August 27, 2022 5:23 pm

I think the more informative thought experiment would be to start with half the box full of air at 20 deg and the other half full of air at 30 deg. Now what’s the answer?

Bellman
August 27, 2022 7:15 pm

therefore averaged temperature tells us almost nothing about whether the Global Climate System is gaining or losing heat energy — a prime requirement in the Global Warming by CO2 Hypothesis.

The Global Warming by CO2 Hypothesis predicts that increased CO2 will cause global warming, i.e. the average temperature surface of the globe will increase. It says it will do this by increasing the global total enthalpy.

Seeing the global average temperatures increase is in line with this prediction. Arguing that we don’t know if enthalpy has increased, ignores the primary evidence for global warming.

If global temperatures have increased but enthalpy has gone down, that just raises more questions.

Tim Gorman
August 28, 2022 6:09 am

Enthalpy can change without the temperature changing.

h = u + pv

Bellman
August 28, 2022 1:52 pm

Indeed, that’s what I was saying. But what we are really interested in is how likely it is that temperatures rise and enthalpy stays the same or decreases. Could happen if the mass of the air decreases or tspecific heat capacity changes, becasue the air becomes drier. Or I suppose if for some reason the air pressure or volume dropped. But none of these seem plausible, and it requires quite a coincidence for all that to happen just as temperatures are rising.

Tim Gorman
August 28, 2022 1:57 pm

Or I suppose if for some reason the air pressure or volume dropped.”

Weather fronts. Watch the pressure gradient maps around you for a while. The central states have been under a high pressure for almost two weeks now. And what happens as pressures change?

Bellman
August 28, 2022 3:09 pm

High pressure is associated with higher temperatures.

Doesn’t the ideal gas law mean that PV is directly related to temperature?

But, the main issue is we are not interested in specific weather fronts. We are talking about the global average temperature and the global atmospheric enthalpy. What would cause overall atmospheric pressure to drop whilst temperatures rise?

Tim Gorman
August 28, 2022 3:31 pm

High pressure is associated with higher temperatures.”

Because it blows away all the clouds? High pressure is also many times associated with lower humidity. Think deserts. What’s the enthalpy of the atmosphere above a desert? How many tornadoes happen in the Arizona desert?

“Doesn’t the ideal gas law mean that PV is directly related to temperature?”

If you had the atmosphere trapped in a box, yes. It isn’t. Lot’s of other factors abound.

“But, the main issue is we are not interested in specific weather fronts”

If you are interested in in what is happening then you are! Climate is weather over time.

“We are talking about the global average temperature and the global atmospheric enthalpy. What would cause overall atmospheric pressure to drop whilst temperatures rise?”

The GAT is supposedly made up of lots of little localities. So you *need* to know about all those localities.

Ever hear of the Polar Vortex? Is that a global thing? Or ENSO/AMO. Are those global? Do they affect the entire globe equally all at the same time? How about La Nina/El Nino? Do those affect the entire globe all at the same time?

Bellman
August 28, 2022 3:50 pm

If you had the atmosphere trapped in a box, yes. It isn’t. Lot’s of other factors abound.

What’s being in a box got to do with it? If the gas is in a box, the volume remains constant so increasing temperature will only increase pressure. If it’s not in a box but at a constant pressure then increasing temperature will increase volume. But whatever the conditions PV is proportional to temperature, and PV is part of enthalpy.

Tim Gorman
August 28, 2022 4:15 pm

The question is how do you increase pressure which is what increases temperature? You are trying to turn it around. When you heat the box you are adding energy to the system.

The atmosphere is *not* under constant pressure. As you add energy to the parcel of air what happens to it? What happens to the heated air in a hot air balloon as it rises?

Bellman
August 29, 2022 4:11 pm

I don’t know enough about meteorology to give any definitive answer, and this is quickly becoming another of your argumentative distractions.

In general, as I understand it, high pressure results from air in the upper atmosphere cooling, and so becoming denser, falling downwards, and letting more air in. Hence increasing the mass of air in the column and so increasing pressure.

As I’ve said before, this is irrelevant to the question I’m asking. If you think that rising temperatures have been happening despite enthalpy staying level or decreasing, what changes to the global atmosphere could account for that. Air pressure is related to the mass of air and gravity. The only way pressure could be decreasing is if the air was losing mass, which I can only see happening if humidity is decreasing. But that doesn’t make sense if temperatures are increasing.

Tim Gorman
August 30, 2022 4:41 am

In general, as I understand it, high pressure results from air in the upper atmosphere cooling, and so becoming denser, falling downwards, and letting more air in. Hence increasing the mass of air in the column and so increasing pressure.”
“Once again, be careful about what you read on the internet. I’ve attached another picture from my weather station. Look at the barometer and rain. Rain cools the atmosphere which should, based on your “generality”, cause pressure to go up. Yet it went down significantly. Rain is, most times, associated with a falling barometer (a good time to go fishing as well).
Now, the “generality” is correct insofar as it goes. During winter barometric pressure is generally higher than in the summer. But temperature also has a higher variance in the winter. Smaller amounts of sun insolation can cause lower temps but small changes  in temp are also working against a smaller base.
As I’ve said before, this is irrelevant to the question I’m asking. If you think that rising temperatures have been happening despite enthalpy staying level or decreasing, what changes to the global atmosphere could account for that.”
Who says enthalpy is changing? Who says temperatures are rising? Because of the uncertainty associated with the global average temperature who can tell for sure?
The only way pressure could be decreasing is if the air was losing mass, which I can only see happening if humidity is decreasing. But that doesn’t make sense if temperatures are increasing.”
The CAGW crowd is all over the map on this. Some say WV in the atmosphere is going down, some say it’s going up. You would think warmer atmosphere would hold more WV. If WV is going down then you would think the atmosphere would be cooler.
It’s all contradictory. I *know* that this is the first year for at least five years that we’ve had +100F summer temps, and even then we only had two days. I just graphed the CDD’s for the past 100 months and the trend is downward. 2016 was the warmest out of the past 100 months. Not even this year is as high. Summer humidities are on a par with last year, averaging about 80% (visual estimate).
I know it is easy to dismiss data from one location as being “anecdotal”, but the overall picture is made up of lots of “anecdotal” information put together. I can only judge from things I see, like while traveling to CO for vacation, that the corn and soybeans are doing fine, even if we are supposed to be in a drought. There was sufficient rain apparently, at least when it was needed, and temperatures haven’t cooked either one. The USDA is forecasting a very good bushel/acre yield for corn. I haven’t looked up the forecast for soybeans for a while.

Jim Gorman
August 28, 2022 6:39 am

Look at the example of what you posted last. Why do you think a temperature increase of the air temperature will result in massive amount of enthalpy incease?

Work it out. What would a 4 degree increase in air temperature mean in terms of overall enthalpy while keeping water the same? What if water increased by 5%?

Bellman
August 28, 2022 12:30 pm

Why do you think a temperature increase of the air temperature will result in massive amount of enthalpy incease?

Another question where you don’t seem to have read what I was saying. It’s always possible that an increase in global air pressure could occur without an increase in enthalpy, but the purpose of scientific inquiry is to see if it agrees with the prediction or not.

It’s predicted that rising CO2 levels will increase the enthalpy and so increase temperature. If you can’t measure total enthalpy but do see temperatures increase that is a confirmation of your prediction, or at least is not a falsification of it.

If you can show that enthalpy hasn’t increased despite the temperature increase, then that’s a possible counter argument. But you can’t just assume that it might have happened.

And, it seems to me there’s very little sense in assuming that a rise in temperature could have happened without an increase in enthalpy. If you are just talking about the atmospheric surface temperature, how does that happen? The only ways I could see is if the heat capacity of the atmosphere were to decrease, or the volume or pressure of the atmosphere has to change. The only logical way I could see that happening is if the air became drier, but why would that happen if the atmosphere is warming up?

And if that were the case, it just raises more questions. Why did the climate change to cause the air to become drier, and isn’t it a big coincidence that the effect of this change was to make the temperature to increase in line with the CO2 increase?

Tim Gorman
August 28, 2022 2:01 pm

The only ways I could see is if the heat capacity of the atmosphere were to decrease, or the volume or pressure of the atmosphere has to change.”

What happens when it rains?

Why do the CAGW advocates predict increased desertification with rising temperatures?

Bellman
August 28, 2022 3:23 pm

What happens when it rains?

I’m not entirely sure. I think it will depend on a lot of things, how hot it is, the time of day, etc. But in general I think the air becomes more humid, owing to the evaporation of the rain from the surface.

But again, these are short term local effects, not a change in the global average humidity. How much humidity there is in the air is going to depend to a large extent on the temperature.

Why do the CAGW advocates predict increased desertification with rising temperatures?

You’d have to ask the CAGW, whoever they are.

As far as global warming, there are multiple possible effects. Higher humidity can mean heavier rain in places, which might mean there is no rain elsewhere. But higher temperatures can also mean that more water is retained in the air and there is less rain.

Tim Gorman
August 28, 2022 3:37 pm

I’m not entirely sure. I think it will depend on a lot of things, how hot it is, the time of day, etc. But in general I think the air becomes more humid, owing to the evaporation of the rain from the surface.”

The air becomes more humid when it loses water?

“But again, these are short term local effects”

Short term effects add up to long term effects. It’s why Arizona has arid deserts and Kansas doesn’t. What’s the humidity difference short term and long term between them?

Higher humidity can mean heavier rain in places, which might mean there is no rain elsewhere. But higher temperatures can also mean that more water is retained in the air and there is less rain.”

If all that atmosphere were trapped in vertical silo’s you might be correct. I’d have to think about it. But the atmosphere isn’t fixed in that manner. Higher humidity also means more energy to fuel storms – meaning more rain. And that humidity moves with the wind, all the way up to the jet stream if not higher.

Bellman
August 28, 2022 4:17 pm

The air becomes more humid when it loses water?

Don’t make me tap the sign -> ” owing to the evaporation of the rain from the surface.”

As I said, I’m not sure and it depends on circumstances.

Random internet wisdom:

Outside environments have direct exposure to rain, meaning the humidity mainly changes depending on the temperature. Rain evaporates and increases moisture when it’s warm, making it more humid. But it cools the air when the temperature is already cold, which reduces humidity instead.

https://hvacseer.com/does-rain-cause-humidity/

Tim Gorman
August 29, 2022 6:01 am

Don’t make me tap the sign -> ” owing to the evaporation of the rain from the surface.”

Evaporation = rain in quantity? Over what time period?

“As I said, I’m not sure and it depends on circumstances.”

Of course it depends on circumstances. Consider that over land precipitation doesn’t just result in surface water that evaporates. Much of it goes into subsoil moisture where it can’t evaporate. Some of it does get put back into the atmosphere due to evapotranspiration of vegetation but that is over a long period of time.

“Random internet wisdom:”

From your link: “Yes, humidity levels increase during and after it rains primarily because of evaporation. When rain evaporates, the moisture it carries transfers to the air. And so, the more it rains, the higher humidity will become. The same goes for when the surrounding temperature gets warmer as it rains and when it stops.”

Attached is a graph of recent humidity and rain at my location. Outside humidity dropped substantially following the rain on the 28th. As of this morning it still hasn’t returned to the prior level the week before.

Question everything you read on the internet.

Bellman
August 28, 2022 12:33 pm

Work it out. What would a 4 degree increase in air temperature mean in terms of overall enthalpy while keeping water the same? What if water increased by 5%?

Not sure what you are saying here. If air increased by 4°C, it would be in spite of much of the increased energy going into the water. Remember in this example air temperature drops by 10°C just to warm the water by an imperceptible amount.

ferdberple
August 27, 2022 5:48 pm

Even using outging radiation in place of average temperature is a problem because radiation is the 4th power of temperature.

Solving for the 4th root you end up with multiple different average temperatures that yield the same outgoing radiation. Which answer is the correct one?

a^4+b^4 = c^4+d^4
(a+b)/2 != (c+d)/2
a != b != c != d

There are an infinite number of values for a,b,c,d that satisfy. As such you cannot calculate average temperature from outgoing radiation.

Tim Gorman
August 28, 2022 6:02 am

(a+b)/2 != (c+d)/2
a != b != c != d”

It’s *exactly* the same problem with trying to use mid-range temperatures to determine the GAT. Multiple combinations of Tmax and Tmin give the same mid-range value, meaning the same contribution from different climates. So how do you derive the original values?

bdgwx
August 27, 2022 6:16 pm

Density of water 997 kg/m3
Density of air 1.16 kg/m3
Specific heat capacity of water 4180 j/kg.C
Specific heat capacity of air 1000 j/kg.C (isobaric).
Tw = 20 C
Ta = 30 C
Mw = 997 kg/m3 * 1 m3 = 997 kg
Ma = 1.16 kg/m3 * 1 m3 = 1.16 kg
Qa = 1.16 kg * 1000 j/kg.C * (30 C -20 C) = 11600 j
ΔTw = 11600 j / (997 kg * 4180 j/kg.C) = 0.003 C

The equilibrium temperature will be approximately 20.003 C.

michel
August 28, 2022 1:37 am

Yes. Its the amount of heat the different bodies contain that matters. Obvious as soon as it occurs to you. Back to another cup of coffee!

Tim Gorman
August 28, 2022 6:05 am

You forgot the significant digits rules.

Jim Gorman
August 28, 2022 6:43 am

Do you see now why averaging temperatures (even if it was allowed under proper scientific practice) provides little knowledge towards the allocation of energy distribution in the atmosphere? Do you think the standard radiation diagrams that are in use take this into account properly?

mal
August 27, 2022 8:47 pm

I don’t know the answer but one big elephant in the room is what is the relative humidity of the air? Granted air between water the water is the 600lb gorilla regardless of humidity of the air!

Loren C. Wilson
August 27, 2022 9:34 pm

You have to make a few assumptions here because the problem is underdefined but they are reasonable ones: the pressure is one atmosphere, heat capacities are constant (very close to the truth), and as stated above, ignore heat involved in phase changes. The mass of water is 998.21 kg (NIST) and the mass of air is 1.165 kg. The heat capacity of water is 4184.1 J/kg-K and the heat capacity of dry air is 1006 J/kg-K. The approach is to determine what temperature between 20°C and 30°C balances the amount of heat transferred from the air to the water.
deltaH(water) = mass(water)*Cp(water)*(20+x)
deltaH(air) = mass(air)*Cp(air)*(30-x)
Set these two equations equal to each other and solve for x.

I calculate that the final temperature of the system at equilibrium is 20.0028°C. If we include the heat required to humidify the dry air, the water evaporating from the liquid will actually cool the system so the final temperature will be 19.993°C.

kzb
August 29, 2022 1:45 pm

But should we use the heat capacity of air at constant volume, because the experimental setup is a closed box ?

Here you have used the heat capacity at constant pressure (Cp).

The heat capacity at constant volume is approx. 717 J/K/kg and not 1006 J/K/kg as used in your calculation.

Loren C. Wilson
August 29, 2022 6:19 pm

Probably so.

Izaak Walton
August 27, 2022 9:44 pm

Kip,
one further question that is more relevant. Suppose you take measure the air temperature regularly and over the course of a year you notice that it has risen by a degree can you say that the box has gotten warmer or not?

Derg
August 28, 2022 6:07 am

If over the year it has gotten colder can you say that the box has gotten cooler or not 😉

Jim Gorman
August 28, 2022 6:51 am

That is not exactly the point of the articles. Even attempting to average temps at a single location doesn’t include the varying water vapor in the air at each measurement. At the same temp, you may have more or less energy in a volume air. A rising average just doesn’t let you determine scientifically what is going on.

Now to your question. What does “warmer” mean to you? Higher temps, higher enthalpy, higher water vapor? You must answer these in your own mind before making a decision. “Warmer” has a different meaning colloquially than scientifically.

kzb
August 29, 2022 1:50 pm

Yes of course you can. “Warmer” is a description of temperature. It is the same as stating that the temperature of the box has increased.

However you did say the box is “perfectly insulated” so the temperature would not change.

Ben Vorlich
August 27, 2022 11:54 pm

Because water at 50’C holds a lot more energy than air at the same temperature this winter Britons will be using hot water bottles to keep warm.

michel
August 28, 2022 1:40 am

Yes indeed. There are actually people in the UK who will be hesitating to turn on the kettle for a hot water bottle this winter because of the cost of electricity. Many will be miserable, and some will die. All of whom could have been saved by a sensible use of the money wasted on renewable subsidies.

Peta of Newark
August 28, 2022 12:36 am

Good job there was no CO2 in that box.

According the well established and settled science of the green house gas effect – you’d have a supernova on your hands
:-O

michel
August 28, 2022 1:27 am

Well, always ready to have a rough guess at these things! I don’t understand the math and theory of specific heat, so I tried a shortcut.

Air I think (from Wikipedia, which I may have misunderstood) will contain about one quarter of the heat of water, and if this is right it will take four times as much heat to warm the water through one degree as it does the air.

Suppose we cool the air by one degree and transfer the heat lost to the water. This will raise the water temp by 0.25. Lets cool it by 8 degrees, and transfer the heat. This will raise the water temp by 2 degrees and lower the water temp by 8.

The water will now be 22 degrees, as will the water, which should be equilibrium.

I’m a bit surprised by this, if its right – I would have expected water to contain much more heat than air, by much more than a ratio of 4:1. Maybe I didn’t understand Wikipedia on specific heat?

[checking what others have said before posting, I see Kip reports the difference is 6:1. So lower air by 9 degrees and get enough heat to raise water by 1.5. The answer must be a bit over 21 degrees in this case.]

michel
August 28, 2022 1:33 am

And this was completely wrong, because it doesn’t take account of mass. Oh dear, not enough coffee this morning! There’s too little heat in that mass of air to make any but the tiniest of differences. Obvious as soon as it occurs to you.

August 28, 2022 1:39 am

Is bugger all good enough?

The heat capacity (not specific which is heat capacity per unit of mass) of the air will be something like 4000 less than of the water, so the 2°C extra heat of the air is enough energy to raise the temperature of the system by a couple of 10 000th of a degree, so bugger all – unless you measure the temperature a million times.

Bellman
August 28, 2022 12:40 pm

Time change. The village in Under Milk Wood was called Llareggub, but in the 50s the BBC objected and it had to be changed to Llaregyb.

August 28, 2022 10:04 pm

I was a bit slow to spot that.

August 28, 2022 1:59 pm

It’s like “fanny” raises a few eyebrows in England.

Speed
August 28, 2022 4:02 am

It’s not about temperature, it’s about energy — something we all should have learned in high school.

I learned early on that some people seem to have a natural affinity and interest in science and engineering while others prefer humanities. Is it nature or nurture?

Next question — why do humans sweat?

Clyde Spencer
August 28, 2022 1:43 pm

… why do humans sweat?

Because they can. 🙂

DipChip
August 28, 2022 9:23 am

It requires 3.4 watt hrs of energy to change temp of 1 cu M dry air at 20 C and 1 bar 10 deg C

It requires 11,400 watt hrs of energy to change the temp of 1 cu M of 20 C water 10 deg C

There would be quite a few zeros after 20 and the decimal to state the actual temp rise of water, maybe 20.000298 Deg C

Now consider the heat sink capacity of the ocean compared to the temp rise of the atmosphere do to green house gasses.