A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres

A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in final state is

T₁ = 273 + 27 = 300K
T₂ = 273 + 927 = 1200K
For adiabatic process, P^1–γ T^γ = constant
⇒ P₁^1–γ T₁^γ = P₂^1–γ T₂^γ

⇒		P₂		^1-γ	=		T₁		^γ
		P₁					T₂

⇒		P₁		^1-γ	=		T₂		^γ
		T₂					T₁

⇒		P₁		^1-1.4	=		1200		^1.4
		P₂					300

⇒		P₁		^-0.4	= (4)^1.4
		P₂

		P₂		^0.4	= (4)^1.4
		P₁

= P₁ (2⁷) = 2 × 128 = 256 atm