Analyze isothermal, adiabatic, isobaric, and polytropic gas expansion cases. Enter known values with quick validation. Export reports for labs, classes, maintenance, and design reviews.
Select a process path. Fill the known values. Leave nonrequired boxes empty. The calculator supports isothermal, isobaric, adiabatic, and polytropic expansion.
| Process | Inputs | Calculated Final State | Work Done by Gas |
|---|---|---|---|
| Isothermal | P1 = 200 kPa, V1 = 0.10 m3, T1 = 300 K, V2 = 0.18 m3 | P2 = 111.111 kPa | 11.755 kJ |
| Isobaric | P = 150 kPa, V1 = 0.05 m3, V2 = 0.09 m3 | P2 = 150 kPa | 6 kJ |
| Adiabatic | P1 = 300 kPa, V1 = 0.08 m3, V2 = 0.14 m3, γ = 1.4 | P2 = 137.047 kPa | 12.034 kJ |
| Polytropic | P1 = 250 kPa, V1 = 0.06 m3, V2 = 0.11 m3, n = 1.2 | P2 = 120.795 kPa | 8.563 kJ |
The calculator uses the ideal gas model. Work is positive when the gas expands and does work on the surroundings.
| Path | Work Equation | Useful State Relation |
|---|---|---|
| Isothermal | W = nRT ln(V2 / V1) | P1V1 = P2V2 |
| Isobaric | W = P(V2 - V1) | T is proportional to V |
| Adiabatic | W = (P1V1 - P2V2) / (γ - 1) | PV^γ = constant |
| Polytropic | W = (P2V2 - P1V1) / (1 - n) | PV^n = constant |
For ideal gases, the calculator can also estimate temperature change, internal energy change, and heat transfer when enough data is provided.
Gas expansion work is a core topic in physics and thermodynamics. It explains how pressure and volume changes create useful mechanical output. This matters in engines, compressors, turbines, pistons, pipelines, and lab systems. A clear work calculation helps students learn energy transfer. It also helps engineers check system behavior before testing hardware.
Different process paths create different work values. In an isothermal process, temperature stays constant. The gas exchanges heat with its surroundings while it expands. In an isobaric process, pressure stays constant. The work then depends directly on volume change. In a reversible adiabatic process, no heat enters or leaves the gas. The gas cools during expansion, and internal energy falls. In a polytropic process, pressure and volume follow a general power relation. This path is useful when real equipment does not match ideal textbook limits.
The main variables are pressure, volume, temperature, amount of gas, and process index values. Unit handling is important because inconsistent values can produce wrong work output. This calculator converts common pressure, volume, and temperature units before solving. It also estimates final pressure, final volume, and thermal quantities when enough information is available. That saves time during design review, homework checking, and maintenance analysis.
You can compare several process paths for the same gas sample. That makes it easier to see how assumptions change work, heat transfer, and energy storage. The result section also shows expansion ratio and pressure ratio. These extra values help with reporting and troubleshooting. The export options support documentation, class records, and field notes.
Always verify the process type before trusting the answer. Real gases may deviate from the ideal model at extreme conditions. Use the calculator for fast estimates, learning, and routine checks.
Positive work means the gas expands and does work on the surroundings. Negative work means compression, where work is done on the gas.
Work depends on the pressure-volume path, not only the starting and ending states. Each thermodynamic process follows a different relation between pressure and volume.
Use it when the gas temperature remains constant during expansion. This usually implies heat exchange with the surroundings keeps the gas at one temperature.
Gamma is the heat capacity ratio, Cp/Cv. It controls how strongly pressure and temperature change during reversible adiabatic expansion.
The polytropic index n describes a general process where PV^n stays constant. It is useful for real compression and expansion paths that are neither perfectly isothermal nor perfectly adiabatic.
Yes. Enter only the values required for the chosen process. The calculator derives missing final values when the selected equations allow it.
It is mainly for ideal gas estimates. For high pressure or very low temperature work, real gas behavior may need a more advanced equation of state.
Exporting helps you keep a clean record for reports, design checks, assignments, maintenance logs, and repeat comparisons across multiple cases.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.