Question

1 mole of an ideal gas at 20 atm pressure and 15 L volume expands such that the final pressure becomes 10 atm and the final volume becomes 60 L. Calculate the change in entropy for the process.
$(C_{p.m}=30{\text{J mole}}^{-1}{\text{K}}^{-1},R=\frac{25}{3}\text{J/mol K, ln 2 = 0.7, ln 3 = 1.1})$.

• A. $80.2{\text{JK}}^{-1}{\text{mole}}^{-1}$
• B. $15.17{\text{JK}}^{-1}{\text{mol}}^{-1}$
• C. $120\times {10}^2{\text{JK}}^{-1}{\text{mol}}^{-1}$
• D. $26.83{\text{JK}}^{-1}{\text{mol}}^{-1}$

Answer 1

The correct option is D $26.83{\text{JK}}^{-1}{\text{mol}}^{-1}$

$\Delta S$ for irreversible system:
$\Delta S=C_{p}ln\frac{T_f}{T_i}-nRln\frac{P_f}{P_i}\left(i\right)$
Given Data:
$n=1$
$P_i=20atm$ $P_f=10atm$
$V_i=15L$ $V_f=60L$
number of moles of gas is constant so
$\frac{P_i{V}_i}{T_i}=\frac{P_f{V}_f}{T_f}$
$\frac{T_f}{T_i}=\frac{P_f{V}_f}{P_i{V}_i}=2$
On substituting in $\left(i\right)$ we get
$21+\frac{25}{3}\times 0.7=26.83J{K}^{-1}mo{l}^{-1}$