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Adiabatic Process Calculator

Work out adiabatic process instantly with clear inputs, formula shown and shareable results.

About Adiabatic Process Calculator

In an adiabatic change no heat is exchanged, so PV^gamma stays constant and temperature changes with it: T2/T1 = (V1/V2)^(gamma-1). Compressing air fourfold at gamma = 1.4 raises pressure nearly sevenfold and temperature by 74%. This is why a bicycle pump warms up and why diesel engines ignite without a spark.

Formulas

Adiabatic relation

P1 V1^gamma = P2 V2^gamma

Temperature

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

Worked example

With the default values below, Adiabatic Process Calculator returns Final Pressure of 696.441. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial pressureminimum 0 kPa
100 kPa
Initial volumeminimum 0 L
2 L
Final volumeminimum 0 L
0.5 L
Heat capacity ratio gammaminimum 1
1.4

Results

Final Pressure
696.441 kPa
Temperature Ratio T2/T1
1.7411
Compression Ratio
4.000
Work Done By The Gas
-370.551 J

Step by step

  1. 1Values used
  2. 2Adiabatic relation
  3. 3Temperature
  4. 4Final Pressure= 696.441 kPa
  5. 5Temperature Ratio T2/T1= 1.7411
  6. 6Compression Ratio= 4.000
  7. 7Work Done By The Gas= -370.551 J

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is gamma for common gases?

1.67 for monatomic gases like helium, 1.4 for diatomic gases like air and nitrogen, and about 1.3 for triatomic gases such as carbon dioxide.

Why does adiabatic compression heat a gas?

Because all the work done on it goes into internal energy - none escapes as heat, since the process is by definition insulated.

Related Calculators

Adiabatic Process Calculator – Calculate Final Pressure