Question

Equal masses of air are sealed in two vessels, one of volume V₀ and the other of volume 2V₀. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels.

Use R = 8.31 JK^-1 mol^-1

Answer 1

Let the pressure and temperature for the vessels of volume V₀ and 2V₀ be P₁, T₁ and P₂ , T₂, respectively.
Since the two vessels have the same mass of gas, n₁ = n₂ = n.

$$T_1=300K$$ 

$$T_2=600K$$ 

$$\text{ Using the equation of state for perfect gas, we get }$$ $$PV=nRT$$ 

$${\text{ For the vessel of volume V}}_o:$$ 

$$P_1{V}_o=nR{T}_1...\left(1\right)$$ 

$${\text{ For the vessel of volume 2 V}}_o:$$ 

$$P_2\left(2V_o\right)=nR{T}_2...\left(2\right)$$ 

$$\text{ Dividing eq . }\left(2\right)\text{ by eq . }\left(1\right),\text{ we get }$$ 

$$\frac{2P_2}{P_1}=\frac{T_2}{T_1}=\frac{600}{300}=2$$ 

$$\Rightarrow \frac{P_2}{P_1}=1$$ 

$$\Rightarrow P_2:P_1=1:1$$