Two chambers containing m₁ ~g and m₂ ~g of a gas at pressures P₁ and P₂ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

Step-by-step solution

According to Boyle'slaw, P V=k (a constant) or P m =k or = P m k ( V= m ) = P K ( k m =K . a constant ) So, ₁= P₁ K and V₁= m₁ ₁ = m₁ P₁ / K = K m₁ P₁ Similarly, V₂= K m₂ P₂ Total volume =V₁+V₂=K ( m₁ P₁ + m₂ P₂ ) Let P be the common pressure and be the common density of mixture. Then aligned & = m₁+m₂ V₁+V₂ = m₁+m₂ K ( m₁ P₁ + m₂ P₂ ) P & =K = m₁+m₂ m₁ P₁ + m₂ P₂ = P₁ P₂ (m₁+m₂ ) (m₁ P₂+m₂ P₁ ) aligned