Calculator inputs
Pick a process model, enter state values, choose units, then calculate work. Large screens use three columns, smaller screens use two, and mobile uses one.
Formula used
General definition
Boundary work is the area under the pressure-volume curve: W = ∫ P dV.
Isobaric
W = P(V₂ − V₁). Pressure stays constant, so work equals constant pressure multiplied by volume change.
Isothermal ideal gas
W = P₁V₁ ln(V₂ / V₁). This form assumes constant temperature for an ideal gas and uses P₁V₁ = P₂V₂.
Polytropic
W = (P₂V₂ − P₁V₁) / (1 − n), with P₁V₁ⁿ = P₂V₂ⁿ. When n = 1, the model becomes the isothermal logarithmic form.
Linear path
W = [(P₁ + P₂) / 2](V₂ − V₁). This is the trapezoid area under a straight pressure-volume line between two states.
How to use this calculator
- Select the process model that best matches the physical path.
- Choose one pressure unit and one volume unit for all inputs.
- Enter initial and final state values. Provide
P₂for the linear path. - Enter the polytropic index only when using the polytropic model.
- Choose your preferred work display unit and decimal precision.
- Press Calculate work to show the result above the form.
- Review the P-V graph, summary metrics, and formula statement.
- Use the CSV or PDF buttons to save the calculated results.
Example data table
| Process | Pressure inputs | Volume inputs | Extra input | Work by gas |
|---|---|---|---|---|
| Isobaric | 150 kPa | 0.020 m³ → 0.050 m³ | — | 4,500 J |
| Isothermal | 100 kPa initial | 0.020 m³ → 0.050 m³ | Ideal-gas assumption | 1,832.58 J |
| Polytropic | 200 kPa initial | 0.010 m³ → 0.030 m³ | n = 1.3 | 1,866.67 J |
| Linear P-V path | 300 kPa → 120 kPa | 0.010 m³ → 0.040 m³ | Straight-line path | 6,300 J |
FAQs
1) What does positive work mean here?
Positive work means the gas expands and does work on its surroundings. The calculator uses the common thermodynamics sign convention for work done by the system.
2) Why can work become negative?
Work becomes negative during compression because the surroundings push inward on the gas. In that case, the system receives work instead of delivering it.
3) Which formula should I choose?
Use isobaric for constant pressure, isothermal for constant-temperature ideal-gas behavior, polytropic for paths following PVⁿ = constant, and linear when pressure changes uniformly between two endpoints.
4) Does unit selection affect accuracy?
No. The calculator converts all inputs to SI units internally, performs the calculation in joules, and then converts results back to your preferred display units.
5) Why is the isothermal formula logarithmic?
For an ideal gas at constant temperature, pressure varies inversely with volume. Integrating that curved relation over volume produces the natural logarithm term.
6) What does the graph represent?
The graph shows the selected pressure-volume path. The shaded area under the curve represents boundary work, which is why graph shape changes with the chosen process model.
7) Can I use this for real gases?
It is best for simplified engineering and classroom estimates. Real gases may deviate from ideal or assumed path behavior, especially at high pressure or near phase change.
8) What do the CSV and PDF buttons save?
They save the current result summary, including state values, volume change, work outputs, direction, and the formula label used for the calculation.
Notes
In SI units, pressure in pascals multiplied by volume in cubic meters gives work in joules.