Question

A closed tank has two compartments $A$ and $B$, both filled with oxygen (assume to be 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 leak across ( figure 2), the volume ( in $m^3$) of the compartments $A$ after the system attains equilibrium is

Answer 1

Given,

P₁ = 5 bar ; P₂ = 1 bar

V₁ = 1 m³ ; V₂ = 3 m³

V(t) = V₁ +V₂ = 1+3 = 4 m³

T₁ = 400 K ; T₂ = 300 K

n₁ = $\frac{5}{400R}$ ; n₂ = $\frac{3}{300R}$

Let volume, V₁' = x and V₂' = (4-x)

Now, $\frac{P_1}{V_1}$ = $\frac{P_2}{V_2}$

⇒ $\frac{n_{1}R}{V_1^{\prime }}$ = $\frac{n_{2}R}{V_2^{\prime }}$

⇒ $\frac{5}{400x}$ = $\frac{3}{300(4-x)}$

⇒ 5 (4-x) = 4x

⇒ V₁' = x = $\frac{20}{9}$ = 2.22 m³