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. $P_2{V}_2=P_1{V}_1$
• D. $P_2{V}_2^{\gamma }=P_1{V}_1^{\gamma }$

Answer 1

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

The correct options are
A $T_2=T_1$
B $q=0$
C $P_2{V}_2=P_1{V}_1$

Since container is thermally insulated. So, q $=$ 0, and it is a case of free expansion, therefore, W $=$ 0 and $\Delta$E $=$ 0
So, $T_1=T_2$.
Also, $P_1{V}_1=P_2{V}_2$.