Question

The entropy change involved in the isothermal reversible expansion of $1$ mole of an ideal gas from a volume of $20L$ to $200L$ at $300K$ is_____ $J{K}^{-1}$.

Answer 1

Answer: 19.15

$q_{\text{ rev }}=-w_{\max }=2.303\times nRT{\log }_{10}\frac{V_2}{V_1}$
$n=1,R=8.314J{K}^{-1}mo{l}^{-1},T=300K$
$V_1=20L,V_2=200L$
$\therefore q_{\text{rev }}=2.303\times 1\times 8.314\times 300\times {\log }_{10}\left(\frac{200}{20}\right)$
$=2.303\times 1\times 8.314\times 300\times {\log }_{10}(10)$
$=2.303\times 1\times 8.314\times 300$
$\Delta S=\frac{q_{\text{rev }}}{T}$
$\therefore \Delta S=\frac{2.303\times 1\times 8.314\times 300}{300}$
$=19.15J{K}^{-1}$