Suppose that the system described by the T-S diagram in Fig....

Suppose that the system described by the $T-S$ diagram in Fig. 12.25 is returned to its original state, state 1 , by a reversible process depicted by a straight line from state 3 to state $1 .$ (a) The change in entropy of the system for this overall cyclic process is (1) positive, (2) zero, (3) negative. Explain. (b) How much heat is transferred in the cyclic process? [Hint: See Example $12.6 .]$

Suppose that the system described by the $T-S$ diagram in Fig. 12.25 is returned to its original state, state 1 , by a reversible process depicted by a straight line from state 3 to state $1 .$ (a) The change in entropy of the system for this overall cyclic process is (1) positive,
(2) zero,
(3) negative. Explain. (b) How much heat is transferred in the cyclic process? [Hint: See Example $12.6 .]$

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Key Concepts

T-S Diagram and Heat Transfer

A Temperature–Entropy (T-S) diagram provides a graphical representation of thermodynamic processes. For a reversible process, the heat transferred is given by the integral of temperature with respect to entropy (Q = ?T?dS). In a closed cycle, even though the net change in entropy is zero, the area enclosed by the cycle on the T-S diagram represents the net heat transfer (which equals the net work done) during the cyclic process.

First Law of Thermodynamics in Cyclic Processes

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added minus the work done by the system. In a cyclic process where the system returns to its original state, the net change in internal energy is zero, which means that the total heat transferred into the system must equal the total work done by the system over the cycle.

Entropy as a State Function

Entropy is a property that depends only on the state of a system and not on how that state was reached. In any cyclic process, if the system is returned to its original state, the net change in entropy is zero. This holds true regardless of the details of the process as long as the paths are reversible, because the initial and final states have the same entropy.

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