Ideal Gases

Guest Post by Willis Eschenbach

Over at the Notrickszone, there’s much buzz over a new paper entitled Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity, by Robert Holmes. The Notrickszone article is headlined with the following quotation from the paper:

“In particular, formula 5 (and 6) as presented here, totally rules out any possibility that a 33°C greenhouse effect of the type proposed by the IPCC in their reports can exist in the real atmosphere.”

– Holmes, 2017

And here’s the abstract:

Abstract: It has always been complicated mathematically, to calculate the average near surface atmospheric temperature on planetary bodies with a thick atmosphere. Usually, the Stefan Boltzmann (S-B) black body law is used to provide the effective temperature, then debate arises about the size or relevance of additional factors, including the ‘greenhouse effect’. Presented here is a simple and reliable method of accurately calculating the average near surface atmospheric temperature on planetary bodies which possess a surface atmospheric pressure of over 10kPa.

This method requires a gas constant and the knowledge of only three gas parameters; the average near-surface atmospheric pressure, the average near surface atmospheric density and the average mean molar mass of the near-surface atmosphere. The formula used is the molar version of the ideal gas law. It is here demonstrated that the information contained in just these three gas parameters alone is an extremely accurate predictor of atmospheric temperatures on planets with atmospheres >10kPa. This indicates that all information on the effective plus the residual near-surface atmospheric temperature on planetary bodies with thick atmospheres, is automatically ‘baked-in’ to the three mentioned gas parameters.

Given this, it is shown that no one gas has an anomalous effect on atmospheric temperatures that is significantly more than any other gas. In short; there can be no 33°C ‘greenhouse effect’ on Earth, or any significant ‘greenhouse effect’ on any other planetary body with an atmosphere of >10kPa.

Instead, it is a postulate of this hypothesis that the residual temperature difference of 33°C between the S-B effective temperature and the measured near-surface temperature is actually caused by adiabatic auto-compression.

Dang … “adiabatic auto-compression” as a permanent energy source. Is it patented yet?

Please forgive my sarcasm, I just get tired of endless claims of endless energy … onwards. Here is a look at the various planetary atmospheres:

And finally, here is his math that leads to his mystery formula. From the paper:

Molar Mass Version of Ideal Gas Law Calculates

Planetary Surface Temperatures

The ideal gas law may be used to more accurately determine surface temperatures of planets with thick atmospheres than the S-B black body law [4], if a density term is added; and if kg/m³ is used for density instead of gms/m³, the volume term V may be dropped. This formula then may be known as the molar mass version of the ideal gas law. The ideal gas law is;

P V = n R T (1)

Convert to molar mass;

P V = m/M R T (2)

Convert to density;

PM / RT = m / V = ρ (3)

Drop the volume, find for density;

ρ = P / (R T / M) (4)

Find for temperature;

T = P / (R ρ/M) (5)

[VARIABLES]

V = volume

m = mass

n = number of moles

T = near-surface atmospheric temperature in Kelvin

P = near-surface atmospheric pressure in kPa

R = gas constant (m³, kPa, kelvin⁻¹, mol⁻¹) = 8.314

ρ = near-surface atmospheric density in kg/m³

M = near-surface atmospheric mean molar mass gm/mol⁻¹

Now, I agree with all of that. Well, other than the strange form of the last equation, Equation 5. I’d simplify it to

T =P M / (ρ R) (5)

But that’s just mathematical nitpicking. The underlying math is correct. That’s not the problem. The problem is where it goes from there. The author makes the following claim:

In short, the hypothesis being put forward here, is that in the case of Earth, solar insolation provides the ‘first’ 255 Kelvin – in accordance with the black body law [11]. Then adiabatic auto-compression provides the ‘other’ 33 Kelvin, to arrive at the known and measured average global temperature of 288 Kelvin. The ‘other’ 33 Kelvin cannot be provided by the greenhouse effect, because if it was, the molar mass version of the ideal gas law could not then work to accurately calculate planetary temperatures, as it clearly does here.

I’m sorry, but the author has not demonstrated what he claims.

All that Robert Holmes has shown is that the atmospheres of various planets obey, to a good approximation, the Ideal Gas Law.

… So what?

I mean that quite seriously. So what? In fact, it would be a huge shock if planetary atmospheres did NOT generally obey the Ideal Gas Law. After all, they’re gases, and it’s not just a good idea. It’s a Law …

But that says exactly NOTHING about the trajectory or the inputs that got those planetary atmospheres to their final condition. Whether the planet is warmed by the sun or by internal radioactivity or whether the warming is increased by GHGs is NOT determinable from the fact that the atmospheres obey the Ideal Gas Law. They will ALWAYS generally obey the Ideal Gas Law, no matter how they are heated.

And more to the point, this does NOT show that greenhouse gases don’t do anything, as he incorrectly claims in the above quote.

Look, we could start up ten million nuclear reactors and vent all their heat to the atmosphere. The planet would assuredly get warmer … but the atmosphere wouldn’t stop obeying the Ideal Gas Law. The variables of density and temperature and mean near-surface atmospheric molar mass would simply readjust to the new reality and the Ideal Gas Law would still be satisfied. You could still use his Equation 5 version of the Ideal Gas Law to calculate the temperature from the other variables, regardless of whether or not the atmosphere is heated by nuclear reactors.

So I’m sorry, but the underlying premise of this paper is wrong. Yes, planetary atmospheres generally obey the Ideal Gas Law, duh, why wouldn’t they … and no, that doesn’t mean that you can diagnose or rule out heating processes simply because the atmosphere obeys the Ideal Gas Law. They will always obey the law regardless of how they are heated, so you can’t rule out anything.

Best of another sunny day to everyone,

w.

MY USUAL POLITE REQUEST: When you comment, please QUOTE THE EXACT WORDS YOU ARE TALKING ABOUT so we can all understand what you have an issue with.