Question

A closed tank has two compartments A and B, both filled with oxygen(assumed to be an ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator(Figure $1$). 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(in $m^3$) of the compartment A after the system attains equilibrium is _________.

Answer 1

$P_1=5$ $P_2=1$
$V_1=1$ $V_2=3$ $V_t=V_1+V_2=1+3=4$
$T_1=400K$ $T_2=300K$

$n_1=\frac{5}{400R}$ $n_2=\frac{3}{300R}$

Let volume $V_1\left(new\right)=x$ $V_2\left(new\right)=(4-x)$

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

$\Rightarrow \frac{n_1\times R}{V_1\left(new\right)}=\frac{n_2\times R}{V_2\left(new\right)}$

$\Rightarrow \frac{5}{400\left(x\right)}=\frac{3}{300(4-x)}$

$\Rightarrow 5(4-x)=4x$

$V_1\left(new\right)=\frac{20}{9}=2.22$.