Global Warming and the Second Law of Thermodynamics

copyright 2017 Jennifer Coopersmith

The Second Law of Thermodynamics tells us that the efficiency of a ‘heat engine’ decreases if the temperature of the environment, the ‘heat sink’, is raised (even if the temperature of the heat source is raised by the same amount). Now the Second Law is a universal law, and every (macroscopic) physical process is a heat engine of sorts. (For example, the internal combustion engine, while it is described by the ‘Otto Cycle’, a pressure cycle, nevertheless it ultimately relates to the heat flowing between two temperatures.)

With Global Warming, the average temperature of the sink of heat is raised, and so the efficiency of every physical process on Earth is potentially compromised. (The temperature of the heat sink – of the atmosphere, of oceans, etc. – has local variations, and so some heat engines will actually run more efficiently; but, overall, the efficiency of running planet Earth is reduced.)

What does this mean? Here are some examples.

On a warmer planet, plants will need more water to grow. The purpose of the water is two-fold: 1) it is one of the ingredients in the manufacture of plant material, and (2) it is lost to the environment as water vapour in order to ensure that there is a net increase in entropy. What is astounding is the scale of (2) – over 500 times more water is required for entropy production (plant-cooling) than is required just to make plant material. The hotter (and wetter) the atmosphere, the more cooling water will be required.

In France, in the heat wave of 2003, some nuclear power stations had to be shut down as the temperature of the heat sink (nearby rivers) was too high.

Cars will run less efficiently on hot days. Actually, I have never seen a study of this, but my gifted mechanic informs me that his car uses noticeably more fuel to drive from Bendigo to Sydney (some 840 km) at night than on a hot summer’s day, over 40 degrees C (note that, as the journey is mostly through empty landscape, the traffic conditions are not very different between night and day).

Efficiency is defined as 1- T_sink/T_source. As these temperatures are measured in Kelvin, then the reduction in efficiency for, say, a 2 degree temperature rise is tiny (typically, just 0.2 % worse). However, over a whole planet, it will add up.

There is just one process that is guaranteed to run more efficiently after Global Warming: the loss of heat energy to ‘Outer Space’ (as, in this bigger system, T_source  is now T_Earth while  T_sink is now T_OuterSpace).