Question

An ideal gas is originally confined to a volume $v_A$ in an insulated container of volume $v_A+v_B$. The remaining of the container is evacuated. The portion is then removed and the gas expands to fill the entire container as shown in figure.
If $T_1$ is the initial pressure, then which of the following is/are correct?

• A. $\Delta S_{\text{surrounding}}=0$
• B. The final temperature $T_2>T_1$
• C. $\Delta S_{\text{system}}>0$
• D. The final temperature $T_2=T_1$

Answer 1

Answer: (A), (C), (D)

The final temperature $T_2=T_1$

It is a free expansion adiabatic process in which internal energy remains constant, i.e., temperature does not change.
Hence, final temperature $T_2=T_1$
$\Delta S_{\text{system}}=nR\ln \frac{v_A+v_B}{v_A}>0$ since $v_A+v_B>v_A$
$\Delta S_{\text{surr}}=0$
$\Delta S_{\text{univ}}=\Delta S_{\text{system}}+\Delta S_{\text{surr}}>0$