Guest essay by Jan Kjetil Andersen
As Willis describes in his article on December 21, the atmosphere can be seen as a gigantic heat engine, i.e. a machine which convert thermal energy, namely temperature, into mechanical energy, namely wind.
It may seem a bit strange to view the weather system as a kind of machine and compare it with engineered constructs like an automobile engine, but it is sound physics because all such systems are bound by the same fundamental physical laws and they utilizes the same basic phenomena to create movement from heat.
A heat engine cannot convert heat directly to mechanical energy since that would break the second law of thermodynamics. What are needed are temperature differences. The greater temperature difference the greater effect of the machine. The amount of the energy in the temperature difference that is converted to mechanical energy is called the machines efficiency.
And here we have a very interesting, but less known fact of heat engines; the maximum theoretical efficiency decreases with increasing temperatures. This is interesting because it negates the conventional wisdom and often cited myth that a warmer climate leads to
more storminess, like the claim in the Guardian “a warmer planet has more energy to power stronger storms”, see http://www.theguardian.com/environment/2011/jun/27/climate-change-extreme-weather-2010.
Let us therefore take a look at the theoretical foundation of this effect. This is described by Carnot’s theorem.
Carnot’s Theorem says that the maximum efficiency drawn from a heat engine is the temperature difference between the warmest element and the coldest element divided by the temperature of the highest element.
Expressed as a formula it says: Emax = (Th-Tc)/Th.
Emax is the maximum efficiency
Th is the high temperature element measured in Kelvin
Tc is the cold temperature element measured in Kelvin.
The Carnot cycle is an ideal reversible cyclic process involving the expansion and compression of an ideal gas, which enables us to evaluate the efficiency of an engine utilizing this cycle.
For an interactive demonstration of the Carnot heat engine cycle, courtesy of the University of Virginia, click on the image:
Three important effects can be seen from Carnot’s theorem. The first is that a temperature difference is a necessary condition for converting heat energy to mechanical energy such as wind.
The second effect is that even if we had a perfect heat engine with zero internal friction; it would not achieve anything close to 100% efficiency. The maximum theoretical efficiency for a heat engine operating between 300 K and 600K is for example 50%. The efficiency of a real machine would of cause be considerably lower.
This is why our car engines only operate at about 25% efficiency. The warm element for a car engine is the exploding fuel inside the cylinders and the cold element is the air intake.
The best coal fired power plants have about 40% efficiency and the best gas powered about 55%. The cold elements for those plants are the coolant water, and those with highest efficiency utilize cold seawater as coolant.
Warming gives less efficiency
The third effect is as mentioned above, that, for a given temperature difference between the warm element and the cold element, the efficiency will decrease if both elements heat equally much. On cold days one can see a discernible effect of this in car engines; because the air intake is colder, the engine gives somewhat more power and higher efficiency.
This is also why some turbo charged engines have intercoolers. The turbo gives higher effect, but a non-intentional side effect is that it also increases the temperature in the air intake which will reduce the efficiency. The intercooler reduces the temperature increase introduced by the turbo.
The same effect applies to the wind formations in the atmosphere. Consider the summer temperature in the northern hemisphere; the cold element is the Arctic with a temperature of approximately 0 Celsius and the warm element is in the tropics with approximately 35 Celsius.
The Carnot theorem gives a maximum efficiency in this temperature range of 11.36%. If the temperature increased with 1 Celsius all over the globe, i.e. the difference changed to 1 Celsius in the Arctic and 36 Celsius in the tropic, the maximum efficiency would sink to 11.32%.
This is a minuscule difference, but the point is that it is a decrease, not an increase as the conventional wisdom will have it.
Less temperature differences on the surface
In addition to the effect of higher overall temperatures, the temperature differences will also be smaller. It is quite uncontroversial that the largest effect of global warming is on the cold polar winters and the smallest on the hot tropical summers.This means that both the overall heating and the reduced temperature differences should contribute to less storminess.
However, to be fair, this is not all there is to this. Some climate models tell that the temperature differences in the upper troposphere will increase and this may have larger effect than both the reduced differences on the surface and the higher temperatures.
No settled science there.