Arun
Last Activity: 4 Years ago
Volume of the two parts is = Vo P1^1/γ / P1^1/γ + P2^1/γ, heat given to the gas in the left part is 0, final common pressure of the gases is P = ( P1/γ1 + P1/γ2/2 )^γo
Explanation:
For Adiabatic process:
PV^γ = constant
(a) P1V1 = P2V2
V1 + V2 = Vo
V2 = Vo - V1
P1V1^γ = P2( Vo - V1)^γ
(P1/P2)^1/γ = Vo - V1/ V1
V1P1^1/γ = Vo P2^1/γ - V1P2^1/γ
V1( P1^1/γ + P2^1/γ) = VoP2^1/γ
V1 = VoP2^1/γ / P1^1/γ + P2^1/γ
V2 = Vo - V1 = Vo P1^1/γ / P1^1/γ + P2^1/γ
(b) Adiabatic Wall + Adiabatic separator
Heat given to the left part is 0
(c) P1V1^γ + P2V2^γ = PVo^γ
For equilibrium:
V1 = V2 = Vo/2
P1 (Vo/2)^γ + P2 (Vo/2)^γ = PVo^γ
P = P1/2^γ + P2/2^γ
= ( P1/γ1 + P1/γ2/2 )^γo