Question

An ideal gas in a thermally insulated vessel at internal pressure $=P_1$, volume $=V_1$ and absolute temperature $=T_1$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal 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. $P_2{V}_2^{\gamma }=P_1{V}_1^{\gamma }$
• D. $P_2{V}_2=P_1{V}_1$

Answer 1

Answer: (A), (B), (D)

$P_2{V}_2=P_1{V}_1$

Work against zero external pressure is zero $q=0$ due to insulated boundary
So, $q=0$
$\Delta U=0$
$\Delta T=0$
$\therefore T_2=T_1$
and $P_2{V}_2=P_1{V}_1$