Question

$1$ mole of an ideal gas at $25^{\circ} C$ is subjected to expand reversibly and adiabatically to ten times of its initial volume. Calculate the change in entropy during expansion (in $J k ^{-1} mol ^{-1}$ )

Answer 1

$\Delta S=n C_{v} \ln \frac{T_{2}}{T_{1}}+n R \ln \frac{V_{2}}{V_{1}}$
For adiabatic process $(Q=0)$
$\Delta E = W $
$n C _{ v } \ln \frac{ T _{2}}{ T _{1}}=- nR \ln \frac{ V _{2}}{ V _{1}} $
$\therefore \Delta S =0$