Adiabatic Compression and Expansion Calculator (Ideal Gas)
Final temperature, pressure and work when an ideal gas is compressed or expanded so quickly that no heat flows in or out, with the isothermal result for comparison.
Results
The dashed line marks the value you entered.
What this tool does
In an adiabatic change no heat moves, so all the work goes into or out of the gas's internal energy: squeeze it and it heats up, let it expand and it cools. Compressing air tenfold, from 10 L to 1 L, raises it from 20 °C to about 460 °C and the pressure to about 25 times — the heating a diesel engine uses to ignite fuel without a spark. A bicycle pump warming up and an aerosol can chilling as it sprays are the same effect. The relations assume an ideal gas and a reversible, frictionless process; the real change is somewhat different.
Formula
T₂ = T₁ (V₁ ÷ V₂)^(γ−1) · P₂ = P₁ (V₁ ÷ V₂)^γ · W = (P₂V₂ − P₁V₁) ÷ (γ − 1)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
gs | Type of gas | — |
p1 | Starting pressure | kPa |
t1 | Starting temperature | °C |
v1 | Starting volume | L |
v2 | Volume after the change | L |
T2 | Final temperature | °C |
P2 | Final pressure | kPa |
W | Work done on the gas (negative when it expands) | J |
PI | Pressure if the temperature had stayed the same | kPa |
N | Amount of gas | mol |
Worked example
- Type of gas2
- Starting pressure101.325 kPa
- Starting temperature20 °C
- Starting volume10 L
- Volume after the change1 L
- Final temperature463.2 °C
- Final pressure2545.2 kPa
- Work done on the gas (negative when it expands)3829.8 J
- Pressure if the temperature had stayed the same1013.3 kPa
- Amount of gas0.4157 mol
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.