Adiabatic Compression Calculator
Calculate temperature and pressure after adiabatic compression or expansion.
Covers diesel engine ignition, turbocharger heating, and bicycle pump compression.
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 of a bicycle pump compress air noticeably. The pump barrel gets warm — not from friction but from adiabatic heating. At a compression ratio of 5:1, air temperature rises from 25°C to about 125°C.
Turbocharger: Air is compressed before entering the engine. A 2:1 pressure ratio heats the intake air by about 75°C, which is why turbocharged engines use intercoolers between the turbocharger and engine intake.