For a sample of perfect gas when its pressure is changed isothermally… | Entropy change in isothermal process

For a sample of perfect gas when its pressure is changed isothermally from pᵢ to p_f, the entropy change is…

34 2016 Phase II Thermodynamics Entropy change in isothermal process Medium

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

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

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

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

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

Explanation

$\Delta S = nR\ln(V_f/V_i) = nR\ln(p_i/p_f)$.

$\Delta S = nC_{p,m}\ln\frac{T_f}{T_i} + nR\ln\frac{P_i}{P_f}$
For isothermal change $T_i = T_f$, ln 1 = 0
$\Delta S = nR\ln\frac{P_i}{P_f}$