A monoatomic gas at a pressure P, having a volume V expands

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

For isothermal process P₁V₁ = P₂V₂

⇒ PV = P₂(2V) ⇒ P₂ =	P
	2

For adiabatic process
P₂V₂^γ = P₃V₃^γ

⇒		P		(2v)^γ = (P₃16v)^γ
		2

⇒ P₃ =	3		1		^{5 / 3}	=	P
	2		8				64

then adiabatically to a volume 16V. The final pressure of the gas is : (take γ =	5	)
	3