Library / Thermodynamics / THE-03
Thermodynamics
Boundary work at constant pressure
Work done by a gas expanding against a constant pressure.
- Ref
- THE-03
- Rev
- v1
- Field
- Thermodynamics
- Result
- Wb [kJ]
For a quasi-equilibrium process with a moving boundary, V is total volume. Expansion gives positive work by the system. The second form applies at constant p; use absolute or gauge pressure consistently with the surroundings.
A gas that pushes a piston out at constant pressure does work equal to the pressure times the volume change.
Calculator
- Volume change0.25 m³
- Work per cubic metre swept200 kJ/m³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- kPa × m³ gives kJ directly.
- Compression gives negative work by the system.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kJ) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V₁ Initial volume | 0.001 to 10 m³ | −1,930 | 69.8 | 2,000 | +10% | −4 % |
| V₂ Final volume | 0.001 to 10 m³ | −19.8 | 1,980 | 2,000 | +10% | +14 % |
| p Pressure | 10 to 5,000 kPa | 2.5 | 1,250 | 1,247 | +10% | +10 % |
Sweep of Final volume
| Final volume (m³) | Boundary work (kJ) |
|---|---|
| 0.001 | −19.8 |
| 0.003162 | −19.37 |
| 0.01 | −18 |
| 0.03162 | −13.68 |
| 0.1 | 0 |
| 0.3162 | 43.25 |
| 1 | 180 |
| 3.162 | 612.5 |
| 10 | 1,980 |
Sweep one variable
Variables and how each one contributes
Boundary work
What the equation gives you. Everything else feeds it.
Pressure
Constant pressure on the boundary. Directly proportional.
Initial volume
Initial volume. Lowers the work.
Final volume
Final volume. Raises the work.
Worked example with the values above
- Volume change: 0.35 − 0.1 = 0.25 m³.
- Multiply by p = 200 kPa.
- Wb = 50 kJ.
Assumptions and limits
- Quasi-equilibrium process.
- Constant pressure.
Common mistakes
- Using the wrong pressure (gauge vs absolute) against ambient.
- Forgetting the sign.
Statistics and uncertainty
Volume changes come from small differences between large readings, so a ±2% error in V can mean a larger error in ΔV.
Where it is used
- Piston and cylinder energy balances.
- Expansion of gases against a constant load.
Maths you need
- Pressure and volume: kPa and m³
- Work: force × distance