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Entropy and The Second Law of Thermodynamics


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Entropy and Performance of Refrigerators:

Refrigerator is a heat engine which operates in reverse manner as that of the usual heat engine.
The efficiency of a refrigerator is defined as:



There is no upper limit on this quantity yet, since this can be greater than 1 in accordance the first
law of thermodynamics. However, the second law of thermodynamics says that the entropy
dumped into the hot reservoir must be at least as much as the entropy absorbed from cold
reservoir:



In this case, the entropy is flowing in the reverse manner as that of the heat engine and thus, the
performance of the refrigerator is given as:


 
This implies that the efficiency of the household refrigerator is ~ 5 and the air conditioners have an
efficiency of 2-3. This is because the efficiency cannot be made infinitely large because of the
consequence of second law.

The Efficiencies of Real Engines:

The efficiency of a real engine is given as:

 

This value for all of the real engines would be well below 100%. All real engines are less efficient
than the Carnot engine because they do not operate through a reversible cycle. The efficiency of a
real engine is further reduced by practical difficulties like friction and energy loss due to
conduction. The efficiency of a typical real engine is 15-25%.
        Any real engine cycle will result in more entropy given to the environment than was taken from
it, leading to an overall net increase in entropy  





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