Question

$1$ mole of ideal monoatomic gas is heated by supplying $5kJ$ heat from a reservoir maintained at $400K$ from $300K$ to $400K$. In the process volume of gas increased from $1L$ to $10L$. Find $\Delta S_{total}$ (in J/K-mol) in the process
Use: $\ln \left(\frac{4}{3}\right)=0.3\ln 10=2.3,R=8.3J/K-mol$ and $\ln x=2.3\log x$

Answer 1

$\Delta S_{reservoir}=\frac{q_{reversible}}{T}=\frac{-5000}{400}=-12.5$ $J{K}^{-1}$

$\Delta S_{sink}=nR\ln \frac{V_2}{V_1}+n{C}_V\ln \left(\frac{T_2}{T_1}\right)$

$⟹\Delta S_{sink}=R\ln 10+\frac{3}{2}R\ln \frac{4}{3}$

$⟹\Delta S_{sink}=19.1222+3.7413$

$⟹\Delta S_{sink}=22.8635$ $J{K}^{-1}$

$\Delta S_{total}=22.8635-12.5$

$⟹\Delta S_{total}=10.3$ $J{K}^{-1}$