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For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change in entropy \(\Delta s\) from state 1 to 2?

1. \(\Delta s = C_p \ln(T_2/T_1) - R \ln(P_2/P_1)\)
2. \(\Delta s = C_v \ln(T_2/T_1) - C_p \ln(V_2/V_1)\)
3. \(\Delta s = C_p \ln(T_2/T_1) - C_v \ln(P_2/P_1)\)
4. \(\Delta s = C_v \ln(T_2/T_1) + R \ln(V_1/V_2)\)

Correct answer: \(\Delta s = C_p \ln(T_2/T_1) - R \ln(P_2/P_1)\)

Solution

For an ideal gas with constant specific heats, the entropy change between two states can be written as \(\Delta s = C_p \ln(T_2/T_1) - R \ln(P_2/P_1)\). This is one of the standard forms derived from the Gibbs relation.

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