12.11 Second law of thermodynamics

The First Law of Thermodynamics is the principle of conservation of energy. The Second Law of Thermodynamics gives a fundamental limitation to the efficiency of a heat engine and the coefficient of performance of a refrigerator. In simple terms, it says that the efficiency of a heat engine can never be unity. According to equation \(\eta=1-\frac{Q_2}{Q_1}\), this implies that heat released to the cold reservoir can never be made zero. For a refrigerator, the Second Law says that the co-efficient of performance can never be infinite.

According to equation \(\alpha=\frac{Q_2}{W}\), this implies that external work \((W)\) can never be zero. The following two statements, one due to Kelvin and Planck denying the possibility of a perfect heat engine, and another due to Clausius denying the possibility of a perfect refrigerator or heat pump, are a concise summary of these observations.

Kelvin-Planck statement

It is not possible to design a heat engine which works in a cyclic process and whose only result is to take heat from a body at a single temperature and convert it completely into mechanical work. This statement of the second law is called the Kelvin–Planck statement. One can convert mechanical work completely into heat but one cannot convert heat completely into mechanical work. In this respect, heat and work are not equivalent.

Clausius statement

No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.

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