Question

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

Answer 1

$q _{\text{ rev }}=- w _{\max }=2.303 \times nRT \log _{10} \frac{ V _{2}}{ V _{1}}$
$n =1, R =8.314\, J\, K ^{-1} mol ^{-1}, T =300\, K$
$V _{1}=20\, L , V _{2}=200\, L$
$\therefore q _{ \text{rev }} =2.303 \times 1 \times 8.314 \times 300 \times \log _{10}\left(\frac{200}{20}\right)$
$=2.303 \times 1 \times 8.314 \times 300 \times \log _{10}(10)$
$=2.303 \times 1 \times 8.314 \times 300$
$\Delta S =\frac{ q _{ \text{rev }}}{ T }$
$\therefore \Delta S =\frac{2.303 \times 1 \times 8.314 \times 300}{300}$
$=19.15\, J\, K ^{-1}$