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

The correct option is A P1P2(m1+m2)(P2m1+P1m2)
According to Boyle's law, PV=k (a constant)
or P/mρ = k or ρ = P/mk (∵V = mρ) or ρ = Pk (∵km = K a constant)
So, ρ1 = P1/K and V1 = m1ρ1 = m1P1/K = Km1P1
Similarly, V2 = Km2P2
∴Total number = V1 + V2 = K(m1P1 + m2P2)
Let P be the common pressure and ρ be the common density of mixture. Then
ρ = m1 + m2/V1 + V2 = m1 + m2/K(m1P1 + m2P2)
∴P = Kρ = m1 + m2/m1P2 + m2P2 = P1P2(m1+m2)/(m1P2 + m2P1)