Question

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. $\Delta S=nRTln\left(\frac{p_f}{p_i}\right)$
• B. $\Delta S=RTln\left(\frac{p_i}{p_f}\right)$
• C. $\Delta S=nRln\left(\frac{p_f}{p_i}\right)$
• D. $\Delta S=nRln\left(\frac{p_i}{p_f}\right)$

Answer 1

The correct option is D $\Delta S=nRln\left(\frac{p_i}{p_f}\right)$

$\Delta S=n{C}_{p,m}ln\frac{T_f}{T_i}+nRln\frac{P_i}{P_f}$
For isothermal $T_i=T_f\Rightarrow ln1=0$
$\Delta S=nRln\frac{P_i}{P_f}$