Question

An ideal gas in a thermally insulated vessel at internal pressure $P_1$, volume$=V_1$ and absolute temperature $=T_1$ expands irreversiblly against zero external pressure, as shown in the diagram. The final external pressure, volume and absolute temperature of the gas are $P_2,V_2$ and $T_2$ respectively. For this expansion:

• A. $q=0$
• B. $T_2=T_1$
• C. $\Delta S_{Total}=nRIn\left(\frac{P_1}{P_2}\right)$
• D. $P_1{V}_2^{\gamma }=P_1{V}_1^{\gamma }$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $q=0$
B $T_2=T_1$
C $\Delta S_{Total}=nRIn\left(\frac{P_1}{P_2}\right)$

Since, the vessel is thermally insulated hence, $q=0$
Work done $(W=0)$ is zero for free expansion. $\Delta U$ is also zero for free expansion, so $T_1=T_2$ and $P_2{V}_2=P_1{V}_1$ (isothermal process)