Adiabatic Compression Calculator

An adiabatic process is one where no heat is exchanged with the surroundings. Compress a gas quickly enough and it heats up entirely from the work done on it. The temperature rise can be dramatic, enough to ignite diesel fuel without a spark plug.

The relations

For an ideal gas compressed or expanded adiabatically:

T2 = T1 x (V1/V2)^(gamma - 1)

P2 = P1 x (V1/V2)^gamma

Or in terms of pressure and temperature:

T2 = T1 x (P2/P1)^((gamma-1)/gamma)

Where gamma (the heat capacity ratio Cp/Cv) depends on the gas.

Gamma values

Monatomic gases (He, Ar): gamma = 5/3 ≈ 1.667. Only translational degrees of freedom.

Diatomic gases (air, N2, O2, H2): gamma = 7/5 = 1.40. Translational + rotational modes.

Triatomic and polyatomic (CO2, H2O vapor): gamma ≈ 1.30. More vibrational modes absorb energy.

Real-world examples

Diesel ignition: A diesel engine compresses air at a ratio of 14-22:1. Starting from 25°C (298 K) at compression ratio 18:1: T2 = 298 x 18^0.4 ≈ 298 x 3.18 ≈ 948 K = 675°C. Diesel fuel ignites at around 250°C, so compression alone provides more than enough heat. No spark plug needed.

Bicycle pump: a few strokes and the barrel gets noticeably warm, and that is adiabatic heating rather than friction. Compress 5:1 and the ideal figure is 298 K × 5^0.4 = 567 K, or 294°C. You will never measure that, because a pump barrel is thin steel with a large surface area and it dumps heat to your hand and the air as fast as it makes it. The ideal number is the ceiling, not the prediction. That gap is the whole difference between an adiabatic process and a real one.

Turbocharger: air is compressed before it enters the engine. Careful with the ratio here: a turbo is rated by its pressure ratio, not the volume ratio this calculator takes. For pressure use T2 = T1 × (P2/P1)^((γ−1)/γ), so a 2:1 pressure ratio gives 298 × 2^0.286 = 363 K, a rise of 65°C. Real compressors run at 70 to 80% isentropic efficiency, so the measured rise is more like 80 to 95°C. Either way it is why turbocharged engines need an intercooler between the compressor and the intake.

Enter 2 into the calculator below and you get 120°C, not 65, because it reads 2 as a volume ratio of 2:1. Both answers are right for their own question. Feed it the compression ratio stamped on the engine, not the boost pressure.