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Question:

A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is : (take γ=5/3)

64P

32P

16P

P/64

Solution:

The correct option is P/64
Isothermally PV = P₁2V
P₁ = P/2
Adiabatically, P₂(2V)^γ = P₁(16V)^γ
Pf = P₂(1/2)^(5/3)
Pf = P₂(1/2)^(5/3) = P(1/2)(1/2)^(5/3) = P(1/2)^(8/3)
Pf = P/64