Question

In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box 1 and $2$, respectively, are ($1$ atm, V.T) and $0.5$ atm, $4V$. T). When the valve is opened, the final pressure of the system is approximately

• A. $0.5atm$
• B. $0.6atm$
• C. $0.75atm$
• D. $1.0atm$

Answer 1

Answer: (B)

$0.6atm$

After opening of at equilibrium temperature and pressure of whole gas be $T_1,P_1$

$n_1=\frac{1\times V}{RT}$

$n_2=\frac{0.5\times V\times 4}{RT}$

$n_1+n_2=n$

$\frac{V}{RT}+\frac{V\times 4}{2RT}=\frac{5V{P}_1}{R{T}_1}$

$\frac{P_1}{T_1}=\frac{0.6}{T}$

No heat exchange and no work is done (since molecules do not push anything against which it moves)

$\Delta Q=0,\Delta W=0$

$\therefore \delta U=0$

$n_1{C}_{v}T+n_2{C}_{v}T=(n_1+n_2)C_v{T}_1$

$T_1=T$

Hence , $\frac{P_1}{T_1}=\frac{0.6}{T}$

$P_1=0.6atm$