Question

Two thermally insulated vessels of equal volume are filled with air at tempratures 2T, T and pressures P, 2P respectively. If the valves joining the three vessels is opened, then equilibrium temprature will be​

Answer 1

n1 = p1v1RT1n2 = p2v2RT2

Answer 2

Given info : Two thermally insulated vessels of equal volume are filled with air at tempratures 2T₀ , T₀ and pressures P₀ , 2P₀ respectively.

To find : if the valve joining the vessel is opened, the equilibrium temperature will be...

solution : no of moles of air in the first vessel, n₁ = P₁V₁/RT₁

here P₁ = P₀, V₁ = V₀ (let) and T₁ = 2T₀

so, n₁ = P₀V₀/2RT₀ ....(1)

similarly, no of moles of air in the 2nd vessel, n₂ = 2P₀V₀/RT₀ ....(2)

if the valve joining the vessel is opened, no of moles of air would be, n = n₁ + n₂

= P₀V₀/2RT₀ + 2P₀V₀/RT₀

= 5P₀V₀/2RT₀

final volume , V = 2V₀

according to Boyle's law,

P₁V₁ + P₂V₂ = P(V₁ + V₂)

so, P = (P₁V₁ + P₂V₂)/(V₁ + V₂) = (P₀V₀ + 2P₀V₀)/(2V₀) = 3P₀/2

so, equilibrium Temperature, T = PV/nR

= {3P₀/2}{2V₀}/{5P₀V₀/2RT₀)R

= 6T₀/5

Therefore the equilibrium temperature would be 6T₀/5.