For a sample of perfect gas when its pressure is changed isothermally from pi to pf, the entropy change is given by
$\triangle S = RT \ln \left(\dfrac{p_{i}}{p_{f}}\right)$
$\triangle S = nR \ln \left(\dfrac{p_{f}}{p_{i}}\right)$
$\triangle S = nR \ln \left(\dfrac{p_{i}}{p_{f}}\right)$
$\triangle S = nRT \ln \left(\dfrac{p_{f}}{p_{i}}\right)$
Explanation:
$\triangle S_{sys} = nR \ ln\dfrac{P_1}{P_2} \ + \ nCP\ ln\dfrac{T_2}{T_1}$
In isothermal process T1 = T2
$\triangle S_{sys} = nR \ln\dfrac{P_i}{P_f}$