Which of the following statements about entropy (S) is true?

Question

A. Entropy is not a state property, but molar entropy is.
B. The change in entropy for an adiabatic process occurring in a closed system is always zero.
C. For a reversible process occurring in a steady state system, the entropy of the entering stream is always equal to the entropy of the exiting stream.
D. The change in entropy of a heat reservoir is always positive.
E. None of the above is true.

Answer 1

A. Incorrect. Entropy is definitely a state property (review Section 4.3.1), consequently so is molar entropy and specific entropy.
B. Incorrect. Since there is no heat (Q), it appears there is no change of entropy according to Equation 4.14; however, the entropy balance (Equation 4.37) shows that entropy can be generated in this not-reversible system. The system has no mass flows (m) and no heat (Q), but it could expand and contract (WEC) or be stirred (WS), which could in turn generate entropy. Do not mix up the definitions of “change in entropy” (Equation 4.17) with the “generation of entropy” term in the balance.
C. Incorrect. The change in entropy OF THE SYSTEM is zero at steady state, but this question is asking about the entropy of the entering and exiting streams, not the entropy of the system itself. The process could be condensing a vapor to a liquid, lowering the entropy of the fluid. Examine Equation 4.37: if Q is negative (leaving the system), then the change in entropy of the material moving through the system is negative—Sout will be lower than Sin.
D. Incorrect. If a heat reservoir loses heat (Q is negative), Equation 4.37 shows that the entropy will decrease.
E. Correct. Each statement has clear flaws.