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(D) The general expression for entropy change of an ideal gas is $\Delta S = nC_{p,m} \ln \left( \frac{T_f}{T_i} \right) + nR \ln \left( \frac{p_i}{p_

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$\Delta S = nR \ln \left( \frac{p_i}{p_f} \right)$

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(D) The general expression for entropy change of an ideal gas is $\Delta S = nC_{p,m} \ln \left( \frac{T_f}{T_i} \right) + nR \ln \left( \frac{p_i}{p_f} \right)$.For an isothermal process,the temperature remains constant,so $T_i = T_f$,which implies $\ln \left( \frac{T_f}{T_i} \right) = \ln(1) = 0$.Substituting this into the equation,we get $\Delta S = 0 + nR \ln \left( \frac{p_i}{p_f} \right)$.Therefore,the entropy change is $\Delta S = nR \ln \left( \frac{p_i}{p_f} \right)$.

For a sample of a perfect gas,when its pressure is changed isothermally from $p_i$ to $p_f$,the entropy change is given by:

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