Question

For a sample of perfect gas when its preesure is changed isothermally from $p_{i}to{p}_f$, the entropy change is given by

• A. $\Delta S=nRIn\left(\frac{p_f}{p_i}\right)$
• B. $\Delta S=nRIn\left(\frac{p_i}{p_f}\right)$
• C. $\Delta S=nRTIn\left(\frac{p_f}{p_i}\right)$
• D. $\Delta S=RTIn\left(\frac{p_i}{p_f}\right)$

Answer 1

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

For an ideal gas undergoing reversible expansion, when temperature changes from $T_{i}to{T}_f$ and pressure changes from $p_{i}to{p}_f$,
$\Delta S=n{C}_{p}In\frac{T_f}{T_i}+nRIn\frac{P_i}{P_f}$
For an isothermal process, $T_i=T_f$ so, In 1 = 0
$\therefore \Delta S=nRIn\frac{P_i}{P_f}$