Kelvin-Planck and Clausius statement.

Considering relation between Kelvin-Planck and Clausius statement, if one statement between the two is violated then

a. other one may be or may not be violated
b. other one is also violated
c. other one must be correct
d. none of the above

Correct Answer : b. other one is also violated

Explanation :

Kelvin-Planck and Clausius statements look different but both are are the parallel statements of second law of thermodynamics. Consider, a heat pump absorbs heat Q1 from a cold reservoir which is at temperature T2 and transfers it to a hot reservoir which is at temperature T1 without expenditure of any work. This heat pump violates the Clausius statement.
Now consider, a heat engine absorbs same heat Q1 which is transferred by heat pump in the hot reservoir at temperature T1 and produces a new work W and rejects some heat energy Q2 to the cold reservoir at temperature T2. As heat engine absorbs heat Q1 which is the same heat absorbed by heat pump from the cold reservoir at T2. It shows that the heat engine is exchanging heat only with single reservoir at single fixed temperature T2. This violates the Kelvin-Planck statement.
Therefore, if one statement between the Kelvin-Planck and Clausius statement is violated, then the other one is also violated.
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