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 which of the following relation(s) holds true?

• A. $q=0$
• B. $T_2=T_1$
• C. $P_2{V}_2=P_1{V}_1$
• D. $P_2{V}_2^{\gamma }$

Answer 1

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

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

This is free expansion.
Here $w,q,\Delta E$ are zero. $\Delta T$ is also zero.
$\to qiszero$
$\to T_2=T_1$
$\to P_1{V}_1=P_2{V}_2$
( $w=-P_{ext}△V=zeroas{P}_{ext}=zero.$ Similarly q is zero due to insulation. $\Delta E=n{C}_v\Delta T$ is also zero by 1st law.)