The pressure versus temperature graph of an ideal gas is shown in...

Given, density of gas at point $A, {ρ}_{A} = {ρ}_{0}$

General equation for an ideal gas

$pV = nRT$

$⇒ pV = \dfrac{m}{M}RT$ [$m \to$mass, $M \to$ molecular mass]

$⇒ p = \dfrac{m}{V} \cdot \dfrac{R}{M} \cdot T$

$⇒ p = ρ$\left(\dfrac{R}{M}\right)T . . . $\left(i\right)$ [where density $ρ = \dfrac{m}{V}$]

Applying Equation. (i) at point $A$ and $B$, respectively.

$p = {ρ}_{A}\left(\dfrac{R}{M}\right){T}_{0} . . . \left(ii\right)$

$2p = {ρ}_{B}\left(\dfrac{R}{M}\right)3{T}_{0} . . . \left(iii\right)$

From Equations. (ii) and (iii), we get

$\dfrac{1}{2} = \dfrac{{ρ}_{A}}{{ρ}_{B}} \cdot \dfrac{1}{3}$

$⇒ {ρ}_{B} = \dfrac{2}{3}{ρ}_{A} = \dfrac{2}{3}{ρ}_{0}$