Single-stage adiabatic compression power, head, and discharge temperature for an ideal gas.
H_ad = Z R T₁/M · k/(k−1) · [(P₂/P₁)^((k−1)/k) − 1]; P = ṁ H_ad / η
How it works
For an ideal gas compressed adiabatically, the head depends only on suction temperature, pressure ratio, and the gas properties k and M. Multiplying by mass flow gives gas power; dividing by isentropic efficiency gives shaft power and an estimate of the actual discharge temperature.
Worked example
1000 kg/h of air from atmospheric pressure to 5 bar abs at 75% isentropic efficiency. ≈ 65 kW of shaft power, with discharge around 200 °C ideal — hot enough that real machines intercool at this ratio.
Inputs
Mass flow (kg/h)
Suction temperature (°C)
Suction pressure (abs) (kPa)
Discharge pressure (abs) (kPa)
Molecular weight (g/mol)
Cp/Cv ratio k — Air/N₂ ≈ 1.40, CH₄ ≈ 1.31, CO₂ ≈ 1.29.
Compressibility Z — Average of suction and discharge; 1.0 = ideal gas.
Isentropic efficiency (%)
Frequently asked questions
Why is my discharge temperature so high?
Adiabatic compression converts work into internal energy: T₂ = T₁·r^((k−1)/k). At a ratio of 5 with air that is already ~200 °C ideal, and inefficiency makes it hotter. This is why multi-stage machines intercool between stages.
When do I need multiple stages?
Common practice keeps the ratio per stage around 3–4, limited by discharge temperature (seals, lubricants, materials) and efficiency. The tool flags ratios above 4.
Is this valid for real (non-ideal) gases?
Approximately, via the average compressibility factor Z. For high pressures, gas mixtures near their dewpoint, or CO₂-rich streams, use an equation-of-state simulation — the ideal-gas path deviates significantly.
Assumptions
Ideal-gas adiabatic (isentropic) path with constant k; Z applied as a single average factor.
Single stage, no intercooling; mechanical losses (bearings, seals, gearbox) not included in shaft power.
Use absolute pressures for P₁ and P₂.
References
GPSA Engineering Data Book — Compressors (adiabatic head/power method).
Smith, Van Ness & Abbott, Introduction to Chemical Engineering Thermodynamics — ideal-gas compression work.
Related Thermodynamics tools
Vapor Pressure (Antoine) — Saturation pressure of a pure component from Antoine coefficients. Pick a preset or enter your own A, B, C.
Ideal Gas Law — Moles, mass, and density of an ideal gas from P, V, and T.
Steam Tables (IAPWS-IF97) — Saturated and single-phase water/steam properties — saturation pressure/temperature, enthalpy, entropy, and specific volume — from the IAPWS-IF97 standard.