The First Law and Climate Change

Vincent J. Curtis

9 July 23

The First Law of Thermodynamics equates the system’s total internal energy E to the difference between heat, Q, and work, W.  In differential form the equation is:

                                                dE = dQ – dW

 You will notice the strike-throughs of the differential notations before the Q and W terms.  This indicates that these differentials are inexact; and the reason they’re inexact is that in the course of adding heat to the system some work can be done; and similarly some work being done by the system can be converted into heat.

We see an example of this when we heat a beaker of water on a hotplate.  As heat is added to the water at the bottom of the beaker, the water begins to move around and circulate.  This is work being done.  Similarly, when a solid is heated, it is subject to thermal expansion; and this expansion is work.  Some of the heat added to the solid was converted into the work of expansion.  That’s why the heat capacity of a solid or liquid at constant pressure, C_p , is different from the heat capacity at constant volume, C_v; the heat capacity at constant pressure takes into account the energy required to do the work of expansion. Just as in expansion, when a solid cools, it will be subject to thermal contraction, and this is negative work being done.

When the sun heats the earth, some of that heat energy gets converted into work in the atmosphere.  Air circulation patterns, wind, and weather in general is work being done by the atmosphere as it is alternately heated and cooled. 

Climate change is supposed to result in more intense storms.  Since a storm is work being done by the atmosphere, a more intense storm is one in which more work is being done.  Where is the energy to do this extra work to come from?  If E is constant, the only place is from Q.  Somehow, the atmosphere, as a result of climate change, is supposed to take more Q and convert it into more W.  The Second Law of thermodynamics says this is impossible.

The sun’s irradiation of the earth is constant, meaning the sun isn’t providing more energy to drive the earth’s weather systems.  That means that E is a constant.  More W requires less Q.  The Second Law of thermodynamics is:

                                                dS  -dQ/T

where S is entropy, Q is heat and T is absolute temperature.  The negative sign before the Q term is to account for the convention that heat is expressed as a negative number.  Entropy never spontaneous becomes smaller.  We never see a beaker of water spontaneously separating into hot and cold regions.  If the atmosphere spontaneously converted even more heat Q into work W at constant E, that would result in a smaller Q, meaning that S would become smaller; but this violates the Second Law.  Hence, climate change that allegedly produces more intense storms, or in general more work in the atmosphere, is impossible because it requires the Second Law of Thermodynamics to be violated.

Note, insulation doesn’t solve the problem for climate changers.  Insulating the solid that is being heated doesn’t change the amount of work done by thermal expansion, or make the solid expand more at the same T.  There is only so much internal energy available to drive the earth’s atmosphere, and to put more energy into the atmosphere so that it can do more work requires that heat to be taken from somewhere else.  But where?

The oceans are one place the atmosphere can gain additional energy, and El Nino is one such phenomenon.  Consistent with the First Law, the ocean releases heat into the atmosphere and cools itself.

If the sun isn’t putting more energy into the earth, where else can additional energy come from?

Energy in the earth’s atmosphere is reflected to a great extent by temperature.  If the global atmospheric temperature were higher, would that mean more heat in the atmosphere available to do work?  No, it wouldn’t, for at a constant E (regardless of what E is) the conversion problem remains; the conversion of heat into work spontaneously has an entropy problem.  If E is constant, it doesn’t matter at what T the conversion takes place.

The problem is resolved by recognizing that it is during the process of heating and cooling that the doing of work spontaneously is possible.  Hence if the sun were to heat the earth more intensely, then the spontaneous conversion of more E into W is possible without an entropy problem.  If Q remains constant, and all the additional energy E is converted to W, the system doesn’t have an entropy problem because S is not required to spontaneously get smaller.  Hence, it is only when the earth is being heated more intensely by the sun, putting in more energy, that weather patterns can produce more W.  If the sun were to decrease the energy it transferred to the earth, making E smaller, during the transition not only would the atmosphere cool, reflecting less Q, but work (technically, negative work) would be done.  (Just as a solid shrinks in size due to thermal contraction.  This is negative work.)  At a new level of solar irradiation, a new system would be established.

This analysis is T independent, meaning that the analysis holds regardless of what the underlying global average temperature is.  Whether the GAT is 287K or 291K, it is the input of energy from sources external to the atmosphere that causes weather, that is the doing of work W, in the atmosphere.  And somehow, climate change is supposed to alter the conversion ratio of input E into Q and W, emphasizing more W and less Q.  How tiny changes in atmospheric composition is supposed to effect this remains a mystery.

Global warming, within reasonable limits, does not impact the intensity of weather, or enable more work to the done by the atmosphere.

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