Exploring the second law

using the kelvin–planck statement of the second law of thermodynamics, demonstrate the following corollaries:

(a) the coefficient of performance of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when both exchange energy by heat transfer with the same two reservoirs.

(b) all reversible refrigeration cycles operating between the same two reservoirs have the same coefficient of performance.

(c) the coefficient of performance of an irreversible heat pump cycle is always less than the coefficient of performance of a reversible heat pump cycle when both exchange energy by heat transfer with the same two reservoirs.

(d) all reversible heat pump cycles operating between the same two reservoirs have the same coefficient of performance.

(a) The coefficient of performance of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when both exchange energy by heat transfer with the same two reservoirs.

Explanation:

According to the  Kelvin–Planck statement of the second law of thermodynamics ,it is not possible to construct a device which operates in cycle and does not produce effect on the environment than the production of work.

We know that

Coefficient of performance is the ratio of desired effect to the work input in a cycle.

Given all option is correct but most appropriate option is a.

So the option a is correct

(a) The coefficient of performance of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when both exchange energy by heat transfer with the same two reservoirs.

first one is the correct answer