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GATE 2018 ME (ME2) – Question 20

Thermodynamics · Entropy changes, closed and open systems · 1 mark · Multiple choice

An ideal gas with constant properties undergoes a quasi-static process from state 1 to 2. Which gives its entropy change?

  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. $\Delta s=C_v\ln(T_2/T_1)+R\ln(V_1/V_2)$

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

Explanation

For an ideal gas, $ds=C_p\,dT/T-R\,dP/P$. Integrate with constant properties: $$\Delta s=C_p\ln(T_2/T_1)-R\ln(P_2/P_1).$$ Answer **A**. The volume form uses $+R\ln(V_2/V_1)$, the reverse of option D’s ratio.