A certain amount of an ideal gas is initially at a pressure

A certain amount of an ideal gas is initially at a pressure p₁ and temperature T₁ First, it undergoes a constant pressure process 1-2 such that T₂ = 3T₁ /4. Then, it undergoes a constant volume process 2-3 such that T₃ = T₁ /2. The ratio of the final volume to the initial volume of the ideal gas is

For (1 – 2) process: Constant pressure process {P₂ = P₁}

	T₁	=	T₂	⇒ V₂ =	T₂	× V₁
	V₁		V₂		T₁

For (2 – 3) process: Constant volume process {V₃ = V₂}

Given T₂ =	3T₁
	4

V₂ =	3T₁	× V₁ =	3	V₁
	4T₁		4

⇒	V₃	=	V₂	=	3	= 0.75
	V₁		V₁		4