When exactly $n$ moles of an ideal gas undergo a perfectly reversible isothermal expansion from an i

Question

When exactly $n$ moles of an ideal gas undergo a perfectly reversible isothermal expansion from an initial volume $V_1$ to a final volume $V_2$, the corresponding the entropy change ($\Delta S$) is

Professor PC Thomas Classes · Answer

(c) : The general, fundamental thermodynamic equation for the entropy change of an ideal gas is $\Delta S = n C_v \ln(T_2 / T_1) + n R \ln(V_2 / V_1)$. Because the expansion is explicitly specified as isothermal, the temperature remains absolutely constant ($T_1 = T_2$). This renders the term $\ln(T_2/T_1) = \ln(1) = 0$. Consequently, the entire temperature-dependent term vanishes, leaving the exact formulation: $\Delta S = n R \ln(V_2 / V_1)$.