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, then the final pressure of the system is approximately

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

Answer 1

Answer: (B)

Given situation is

Let final temperature after opening the valve is $T_f$,
then $\Delta W_{\text{ext }}-0$ and $\Delta Q_{\text{ext }}-0$
So, from first law of thermodynamics,
$\Delta U=0$
$\Rightarrow n_1{C}_{V}T+n_2{C}_{V}T=\left(n_1+n_2\right)C_V{T}_f$
$\Rightarrow T_f=T$
Now, by gas equation, we have
As, $n_1+n_2=n$
$\Rightarrow \frac{V}{RT}+\frac{4V\times 0.5}{RT}=\frac{5V\times p_1}{RT}$
$\Rightarrow p=0.6atm$