GATE 2025 CH – Question 33

Thermodynamics · Laws of thermodynamics, open and closed systems, entropy and chemical potential · 1 mark · Numerical answer

Ideal nonreacting gases $A$ and $B$ are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is ____ J/K (rounded off to 1 decimal place).

GIVEN: Universal gas constant $R = 8.314$ J/(mol K)

an insulated chamber divided by a partition into gas A on the left (larger part) and gas B on the right (smaller part). Both gases are at $T_A = T_B = 273$ K and $P_A = P_B = 1$ atm, with $V_B = 22.4$ L and $V_A = 3V_B$.

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Correct answer: 18.61 to 18.79

Explanation

At 273 K and 1 atm one mole occupies 22.4 L, so $n_B = 1$ mol and $n_A = \frac{3 \times 22.4}{22.4} = 3$ mol. The two gases are at the same temperature and pressure, so the temperature and the total pressure do not change on mixing, and the entropy change is the entropy of mixing: $\Delta S = -R(n_A\ln x_A + n_B\ln x_B)$ with $x_A = 0.75$ and $x_B = 0.25$. This is $8.314 \times (3 \times 0.2877 + 1 \times 1.3863) = 8.314 \times 2.2494 = 18.7$ J/K.