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

PVγ=constant
T1 = 273 + 27 = 300 K
T2 = 273 + 927 = 1200 K
For adiabatic process:
P1⁻γTγ = constant ⇒ P1⁻γ1Tγ1 = P2⁻γ2Tγ2
⇒ (P2/P1)^(1-γ) = (T2/T1)^γ
⇒ P2/P1 = (T2/T1)^γ/(1-γ)
(P1/P2)^(1-γ) = (T2/T1)^γ
(P1/P2)^0.4 = (1200/300)^1.4
(P1/P2)^0.4 = 4^1.4
P2 = P1 * 4^(1.4/0.4) = P1 * 4^(7/2) = P1 * 2^7 = P1 * 128
P2 = 2 × 128 = 256 atm