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

Given, density of gas at point A, {ρ}_{A} = {ρ}_{0}$</p><p>General equation for an ideal gas</p><p>$pV = nRT$</p><p>$⇒ 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 densityρ = $\dfrac{m}{V}$]$</p><p>Applying Equation. (i) at point A and B$, respectively.

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

From Equations. (ii)$and (iii), we get</p><p>\dfrac{1}{2} = \dfrac{ρA}{ρB} \cdot \dfrac{1}{3}$

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