Question

A closed tank has two compartment A and B, both filled with oxygen (assumed to be ideal gas).The partition separating the two compartments is fixed and is a perfect heat insulator (Figure1.). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume $\left(in{m}^3\right)$ of the compartment After the system attains equilibrium is____.

Answer 1

Solution:-

As we know that, ideal gas equation is-

$PV=nRT$

$\Rightarrow n=\frac{PV}{RT}$

Given:-

$P_A=5$

$V_A=1$

$T_A=400$

$\Rightarrow n_A=\frac{5\times 1}{400\times R}=\frac{1}{80R}$

$P_B=1$

$V_B=3$

$T_B=300$

$\Rightarrow n_B=\frac{1\times 3}{300\times R}=\frac{1}{100R}$

After the system attains equillibrium;

$\frac{P_A}{T_A}=\frac{P_B}{T_B}$

$\Rightarrow \frac{n_A\times R}{V_A}=\frac{n_B\times R}{V_B}$

$\Rightarrow \frac{\left(\frac{1}{80R}\right)\times R}{V_A}=\frac{\left(\frac{1}{100R}\right)\times R}{V_B}$

$\Rightarrow V_B=\frac{4}{5}{V}_A⟶\left(i\right)$

Now, total volume of container-

$\left(V\right)=V_A+V_B=1+3=4$

$\Rightarrow V_A+V_B=4⟶\left(ii\right)$

Now, form ${eq}^n\left(i\right)\&\left(ii\right)$, we have

$V_A+\frac{4}{5}{V}_A=4$

$\Rightarrow \frac{9}{5}{V}_A=4$

$\Rightarrow V_A=2.22m^3$