Calculator
Enter values for one process. Unused fields can stay blank.
Formula Used
Constant pressure: W = P(V2 - V1).
Linear path: W = ((P1 + P2) / 2)(V2 - V1).
Isothermal ideal gas: W = nRT ln(V2 / V1). You may also use W = P1V1 ln(V2 / V1).
Polytropic process: W = (P2V2 - P1V1) / (1 - n). When n = 1, the isothermal form is used.
Tabular data: W is estimated with the trapezoidal rule over pressure-volume points.
Work by the gas is positive for expansion. Work on the gas is negative with this sign convention.
How to Use This Calculator
- Select the thermodynamic process type.
- Choose pressure, volume, and result units.
- Enter the required pressure and volume values.
- For isothermal work, enter moles and temperature, or use P1 and V1.
- For polytropic work, enter the exponent n.
- For PV data, enter one pressure-volume pair on each line.
- Use the correction factor if a calibration allowance is needed.
- Press Calculate Work. Then export the result if needed.
Example Data Table
| Case |
Inputs |
Formula |
Approximate work |
| Constant pressure |
P = 101.325 kPa, V1 = 10 L, V2 = 25 L |
W = PΔV |
1519.875 J |
| Linear path |
P1 = 100 kPa, P2 = 200 kPa, V1 = 0.02 m³, V2 = 0.06 m³ |
W = average P × ΔV |
6000 J |
| Isothermal |
n = 1 mol, T = 300 K, V1 = 0.02 m³, V2 = 0.05 m³ |
W = nRT ln(V2/V1) |
2285.76 J |
| Polytropic |
P1 = 300 kPa, P2 = 91.2 kPa, V1 = 0.02 m³, V2 = 0.05 m³, n = 1.3 |
W = (P2V2 - P1V1)/(1 - n) |
4800 J |
| PV data |
100 kPa 0.01 m³; 150 kPa 0.02 m³; 120 kPa 0.03 m³ |
Trapezoidal rule |
2600 J |
What Work Done by Gas Means
Work done by gas measures energy transferred during volume change. A gas pushes on a boundary as it expands. The boundary may be a piston, diaphragm, or flexible bag. When volume increases, work by the gas is positive. When volume decreases, work by the gas is negative. This sign convention matches many thermodynamics courses.
Why Pressure and Volume Matter
The area under a pressure volume curve gives boundary work. A constant pressure path uses one simple multiplication. A changing pressure path needs a process model. A linear path uses average pressure. A polytropic path uses an exponent. An isothermal ideal gas path uses a logarithm. Each model can fit a different experiment.
Using Units Correctly
Pressure must use absolute units for ideal gas and polytropic work. Gauge pressure can mislead the result. Volume should be converted before calculation. One pascal cubic meter equals one joule. This page converts common pressure and volume units. It also lets you choose the result unit. This reduces mistakes in lab reports.
Advanced Process Choices
The calculator supports isobaric, linear, isothermal, polytropic, and tabular data. Tabular data is useful when measured points are available. It estimates work with the trapezoidal rule. That method is practical for real pressure readings. Use more data points for a smoother curve. Use a correction factor when you need allowance for mechanical losses or measurement calibration.
Interpreting the Result
A positive answer means expansion work by the gas. A negative answer means work done on the gas. Magnitude shows the energy transfer across the moving boundary. Compare the value with heat and internal energy changes when solving the first law. Always state the path, because work is not a state property.
Good Calculation Practice
Record initial and final volumes. Choose a process type before entering data. Check whether pressure is absolute. Inspect the sign before exporting. Keep all decimal places while solving. Round only the final answer. The CSV file is useful for spreadsheets. The PDF file is useful for sharing a clean calculation summary.
Limits and Assumptions
The tool gives an estimate. It does not replace certified testing. Real gases can differ. Friction, leakage, and heat transfer can shift measured work inside devices.
FAQs
What is work done by gas?
It is energy transferred when gas changes volume against pressure. Expansion gives positive work by the gas. Compression gives negative work by the gas under this convention.
Which units should I use?
You can use many common pressure and volume units. The calculator converts them internally to pascals and cubic meters because one pascal cubic meter equals one joule.
Why is my answer negative?
A negative answer usually means the final volume is smaller than the initial volume. In that case, work is done on the gas during compression.
When should I use the isothermal option?
Use it when temperature stays constant and the gas behaves close to an ideal gas. You need moles and temperature, or initial pressure and volume.
What is a polytropic exponent?
The exponent n describes the process path in PV^n = constant. Different values can model expansion, compression, heat transfer, and special idealized cases.
How does the PV data option work?
It reads pressure and volume pairs line by line. Then it applies the trapezoidal rule to estimate the area under the pressure-volume path.
Should pressure be absolute or gauge?
Use absolute pressure for ideal gas and polytropic formulas. Gauge pressure may be acceptable only when your course or experiment defines work that way.
What does the correction factor do?
It multiplies the calculated work by a percentage. Use 100 for no change. Use another value for calibration, efficiency, or estimated measurement adjustment.