Question

$1$ mole of an ideal gas is allowed to expand isothermally at ${27}^{o}C$ until its volume is tripled. Calculate $\Delta S_{sys}$ and $\Delta S_{univ}$ under the following conditions:
(a) the expansion is carried out reversibly.
(b) the expansion is a free expansion

Answer 1

(a) $\Delta S_{sys}=9.135J{K}^{-1}{mol}^{-1}$
$\Delta S_{surr}=-9.135J{K}^{-1}{mol}^{-1}$
$\Delta S_{univ}=0$
(b) $\Delta S_{univ}=\Delta S_{sys}=9.135J{K}^{-1}{mol}^{-1}$
(a) In isothermal reversible process
$\Delta S=\frac{q_{rev}}{T}$
$q=-W=2.303RT\log \frac{V_2}{V_1}$
$=2740.6kJ{mol}^{-1}$
$\Delta S_{sys}=\frac{q_{rev}}{T}=9.135J{K}^{-1}{mol}^{-1}$
(b) In the case of free expansion
$\Delta S=2.303nR\log \frac{V_2}{V_1}$