Two containers of equal volume contain the same gas at pressure p1 and p2 and absolute temperatures T1 and T2 …..

Q: Two containers of equal volume contain the same gas at pressure p1 and p2 and absolute temperatures T₁ and T₂ respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T. The ratio p/T is equal to
(a)p₁/T₁ + p₂/T₂

(b)½ [p₁/T₁ + p₂/T₂]

(c)[p₁T₂ + p₂T₁]/(T₁+T₂)

(d)[p₁T₂ – p₂T₁]/(T₁-T₂)

Solution : (b)
For a closed system, the total mass of gas or the number of moles remains constant.

P₁V = n₁RT₁ ,
 
  p₂V = n₂RT₂

p(2V) = (n₁ + n₂)RT

p(2V) = (p₁V/RT₁ + p₂V/RT₂)RT

p/T =1/2[p₁/T₁ + p₂/T₂]