Many of the issues discussed in this book can be understood in terms of the laws of thermodynamics. For example,


  • Energy neither be created nor destroyed (except through the use of nuclear reactions). Hence any proposal to “save energy” cannot work. Nor can energy be “renewed”. We can transform energy from one form to another. For example, we can burn gasoline in an automobile engine to create forward motion. But the total amount of energy involved remains the same.

  • Whenever energy is converted from one form to another the overall system entropy — a measure of disorder or randomness — always increases. For example, when we burn gasoline in the engine of an automobile some of the energy generated moves the vehicle forward. But more of the energy is discarded as waste heat from the automobile’s tail pipe. Nothing that we do is “sustainable” — every action leads to an increase in overall entropy. It also means that no machine can have “zero emissions”.

  • There is really no such thing as “clean energy”. Energy is simply energy. Some ways of transforming energy into useful work create generate less entropy than others. But none of them are “clean”.

A full discussion of the laws of thermodynamics, and their relevance to Age of Limits is available as a .pdf file here

Nicolas Carnot


Nicolas Carnot (1796-1832)

Nicolas Carnot, who served in the post-Napoleonic French army, developed the concepts that lie behind the discipline of thermodynamics. He recognized that, in the early 19th century, the French were falling behind the British both technically and in industrial capacity. His interest in thermodynamics was triggered by a desire to close the gap between the two countries. He explained thermodynamic basics with the concept of “thermal engine”.


The sketch  at the top of this page shows a modern concept of his thermal engine. On the left is a source of heat at high temperature, TH. (This could be steam from a boiler or it could be the explosive force created by the burning of gasoline in an internal combustion engine.) The heat source supplies energy in the form of a heat flow, QH, to an engine which creates useful work, W, defined as motion against an opposing force. Using the steam engine example, the thermal engine could be a piston moving up and down or it could be a spinning turbine wheel. That motion can then be used to drive the wheels of a locomotive or to generate electricity.

Not all of the heat, QH, is converted to work — some of it (actually most of it) is discarded to a “cold sink” which has a temperature TC. The quantity of discarded energy is QC. In the case of a steam engine, the cold sink could be a condenser that turns the exhaust steam into water that is then recycled back to the boiler; in the case of an automobile engine the cold sink is atmospheric air that cools the water in the radiator.


Carnot’s fundamental insight that the concept of a heat engine provides is that, whenever we use energy to create useful work (where the word ‘Work’ is used in its narrow, thermodynamic sense), then much of that energy that will be wasted. It is not possible to have perfectly efficient machines, nor is a perpetual motion machine possible, regardless of Lisa Simpson’s claim. Indeed, much of the work carried out by engineers is directed toward creating systems that minimize Qc — the amount of heat that is discarded.


There are four laws of thermodynamics, starting at Zero and finishing at Three. (The reason for this confusing numbering system is that the Zeroth law was developed after laws One through Three, but its logical position is to be ahead of them.)

Photovoltaic Efficiency

One of the basic equations based on Carnot’s insights is,

Ƞ  = 1 – (TC / TH)


where Ƞ is efficiency, Tc is the temperature of the cold sink, and TH  is the temperature of the heat source.


Let’s compare superheated steam with the sun. In both cases we assume that the cold sink temperature is 20C or 293K. The steam has a temperature of say 200C. The sun’s temperature is say 5500C. Converting temperatures to absolute (degrees Kelvin, K) we see that,


Efficiency steam = 1 – (293 / 473) = 38%

Efficiency solar = 1 – (293 / 5773) = 95%


All this assumes that there are no losses, which of course there are.


Solar energy creates waste heat, or entropy. But we see that it is fundamentally much more efficient than energy sources, such as steam, that are based on the burning of fossil fuels. Fossil fuel sources generally waste around 60% of the energy that they release.