Question

One molelse of an ideal gas expand isothermally to five times its volume. Calculate the entropy change in terms of R , the gas constant.

Answer 1

Answer on Question #66754– Physics – Molecular Physics – Thermodynamics

One molele of an ideal gas expand isothermally to five times its volume. Calculate the entropy change in terms of $R$, the gas constant.

Solution

The entropy of one mole an ideal gas is

$$S(T, V) = C_V \ln T + R \ln V + S_0.$$

Entropy change is given by

$$\Delta S = S(T_2, V_2) - S(T_1, V_1) = C_V \ln T - C_V \ln T + R \ln V_2 - R \ln V_1 = R \ln \frac{V_2}{V_1}.$$ $$\Delta S = R \ln 5 \approx 13.37 \frac{\mathrm{J}}{\mathrm{K}}.$$

**Answers**: $\Delta S = 13.37 \frac{\mathrm{J}}{\mathrm{K}}$.

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