The entropy of $4.0$ moles of an ideal gas increases by $\Delta S = 23 ext{ J/K}$ due to an isothe

Question

The entropy of $4.0$ moles of an ideal gas increases by $\Delta S = 23 	ext{ J/K}$ due to an isothermal expansion. The volume of the gas is increased by a factor of $x$. Find the nearest integer value of $x$. (Take $R = 8.314 	ext{ J/mol K}$ and $\ln 2 = 0.693$)

Professor PC Thomas Classes · Answer

For isothermal process, $\Delta S = n R \ln(V_2/V_1)$. $\Rightarrow \ln(x) = \frac{23}{4 	imes 8.314} \approx 0.691 \approx \ln 2$. Thus $x \approx 2$.