book_cover_big.gifI know that it is sometimes really difficult to get a good feeling of what it is that entropy can tell us. Hopefully the following gives you some more insight.

As I mentioned earlier one of the prime questions around 1800 was why heat only streams from warm to cold places. Another question that came up was caused by the growing popularity of the steam engines. Steam engines can also be called heat engines because it converts heat into work. Another example of a heat engines is a car engine. Steam engines where used in England to pump water out of the coal mines, a job that was done by manually by many workers day and night before steam engines became available. To keep the steam engine running, fuel (such as wood or coal) was burned to generate the steam. While the steam engine was gaining ground, many improvements (for instance 25% by James Watt) were done that increased the efficiency of the steam engines considerably. Therefore much more work was obtained from a given amount of fuel.

While this went on there was a young French military engineer, Sadi Carnot, who asked himself the question whether there was perhaps an upper limit to this efficiency. To answer that question he carried out a careful analysis around 1825 using a simplified model of the steam engines. The result of his analysis was that the upper limit of the efficiency was only determined by two factors: the temperatures of the heat source (the steam) and the temperature of the heat sink (the location where the steam was condensed, for all practical matters the outside air). More precisely he found that the heat, Qh, taken from the heat source at temperature , Th, is related to the heat given up at the heat sink, Qc, at temperature Tc, as: Qh/Th = Qc/Tc. Although he did not coined the factor Q/T as entropy ( as you can read in “What is Entropy (2)”)  he clearly laid the foundation for scientists such as Clausius who came to the conclusion that “something was missing” . That something became later the Second Law of thermodynamics. The best possible efficiency of the steam engine was then shown by Carnot to be equal to (Th-Tc)/Th (an atmospheric steam engine efficiency is therefore limited to about 25% efficiency).

The work of Carnot showed very clearly that in order for a heat engine to work you MUST have a heat source at high temperature and a heat sink at colder temperature and that the heat disposed at the heat sink can NEVER generate any work anymore unless you have another heat sink available at an even lower temperature. Also, from Qh/Th = Qc/Tc, it becomes clear that in an heat engine you MUST give up an amount of heat, Qc, no escape. That is the fundamental reason for having the efficiency of the heat engines less than 100%! Much more about all this in the book!

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© Copyright 2007, John E.J. Schmitz