A researcher compresses one mole of an ideal gas from state A to state B in a single rapid (irreversible) step while the gas is in thermal contact with a large 300K reservoir. Measurements show that 1500J of heat leave the gas during the compression and that the entropy change of the gas for this step is ΔSgas(irr)=−20JK−1. Immediately afterward, the gas is returned from state B to the original state A by a sequence of reversible processes that are also carried out while in contact with the same 300K reservoir.
(1) For the irreversible compression A → B, calculate the entropy change of the reservoir and the total entropy change of the universe.
(2) For the reversible path B → A, determine (i) the entropy change of the gas, (ii) the entropy change of the reservoir, and (iii) the total entropy change of the universe.
(3) Combine your results to find the net entropy changes of (i) the gas and (ii) the universe for the complete cycle A → B → A.
(4) Using your answers, evaluate whether the researcher’s procedure violates the second law of thermodynamics. Provide a clear justification.