Calculate energy from pressure × volume change (PΔV work) in joules, or solve for pressure or volume, using psi, bar, kPa, liters or cubic feet.
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Pressure Volume Energy Formula
- W = pressure-volume work done by the system (J), not a general change in internal energy
- P = constant resisting external pressure (Pa); pressure basis must match the physical boundary
- ΔV = change in volume (m³)
This formula is exact for isobaric (constant pressure) processes only. When pressure varies with volume, work equals the path integral of P dV and cannot be solved from endpoint values alone.
Work Formulas by Thermodynamic Process
| Process | Condition | Work Formula |
|---|---|---|
| Isobaric | Constant pressure | W = P · ΔV |
| Isothermal (ideal gas) | Reversible isothermal ideal gas | W = nRT · ln(V₂/V₁) |
| Adiabatic (ideal gas) | Reversible adiabatic ideal gas; constant γ | W = (P₁V₁ – P₂V₂) / (γ – 1) |
| Isochoric | Constant volume | W = 0 |
Near ordinary temperatures, approximate ideal-gas γ values are1.40 for air, N₂ and O₂,1.67 for monatomic gases such as Ar and He, and about1.30 for CO₂. γ varies with temperature and composition; the listed reversible adiabatic formula assumes a constant value.
Reference Values and Unit Conversions
| System | Pressure | Volume Change | Work Output |
|---|---|---|---|
| Balloon at sea level | 101,325 Pa (1 atm) | 1 L (0.001 m³) | 101.3 J |
| Pneumatic actuator (100 psi) | 689,476 Pa | 100 cm³ (0.0001 m³) | 68.9 J |
| Steam piston (15 bar) | 1,500,000 Pa | 1 L (0.001 m³) | 1,500 J |
| Car engine cylinder (9 bar) | 900,000 Pa | 400 cm³ (0.0004 m³) | 360 J |
The examples and reference table apply the listed constant resisting pressure throughout the volume change; they do not model an actual engine cycle or stored compressed-gas energy. Key unit conversion: 1 L·atm = 101.325 J. In chemistry, where pressures are often given in atm and volumes in liters, multiplying the product of liters and atm by 101.325 gives joules directly.
Sign Convention
When a gas expands (ΔV > 0), it does positive work on its surroundings. When compressed (ΔV < 0), work is done on the gas and W is negative. Chemistry commonly defines work as positive when done on the system, reversing the sign. This calculator follows the physics convention: expansion equals positive work output.
How to Calculate Pressure Volume Energy
Example 1: Pneumatic Cylinder
- Pressure: 550,000 Pa (approximately 80 psi)
- Stroke volume: 150 cm³ = 0.000150 m³
- W = 550,000 × 0.000150 = 82.5 J
Example 2: Balloon Expanding at Atmospheric Pressure
- Pressure: 101,325 Pa (1 atm at sea level)
- Volume change: 1.5 L = 0.0015 m³
- W = 101,325 × 0.0015 = 151.99 J (equivalently: 1.5 L·atm × 101.325 J/L·atm = 151.99 J)
