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Ideal-Gas Thermodynamic Process Calculator — result sheet
Compare final state, boundary work, internal-energy change, and heat transfer for an ideal-gas isothermal, isobaric, isochoric, or adiabatic process.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Use PV=nRT and the selected path: isothermal P2=P1/rV, W=P1V1 ln(rV); isobaric T2=T1rV, W=P1(V2−V1); isochoric V2=V1 and P2/P1=T2/T1; reversible adiabatic P2/P1=rV^(−γ), T2/T1=rV^(1−γ). In every mode ΔU=nR(T2−T1)/(γ−1) and Q=ΔU+W.
The same two end states can carry different work and heat depending on the path. This page keeps the path choice explicit and uses SI internally: pressure in pascals, volume in cubic metres, temperature in kelvins, and the ideal-gas constant R. Isothermal and isobaric modes use the entered final volume ratio; isochoric mode uses the entered final temperature ratio; reversible adiabatic mode uses the volume ratio and heat-capacity ratio.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Process model — 4 choices
- Initial absolute pressure — kPa; minimum 1.0E-6; maximum 1000000000
- Initial gas volume — L; minimum 1.0E-6; maximum 1000000000000
- Initial absolute temperature — K; minimum 1.0E-6; maximum 1000000
- Final volume ratio V2/V1 — ratio; Used by isothermal, isobaric, and adiabatic modes.; minimum 1.0E-6; maximum 1000000
- Final temperature ratio T2/T1 — ratio; Used by isochoric mode.; minimum 1.0E-6; maximum 1000000
- Heat-capacity ratio γ — γ; For an ideal diatomic-gas approximation, γ is often near 1.4.; minimum 1.000001; maximum 10
Worked example
| Input | Value |
|---|---|
| Process model | isothermal |
| Initial absolute pressure | 101.325 |
| Initial gas volume | 10 |
| Initial absolute temperature | 300 |
| Final volume ratio V2/V1 | 2 |
| Final temperature ratio T2/T1 | 1.1 |
| Heat-capacity ratio γ | 1.4 |
A reversible isothermal doubling from 10 L at 101.325 kPa ends at 50.663 kPa and 20 L; work and heat are both about 702.33 J and ΔU = 0.
Assumptions and limits
- The gas amount is fixed and the ideal-gas equation of state is used for both states.
- Pressure and temperature are absolute; the returned boundary work is work done by the gas, positive during expansion.
- Isothermal and isobaric paths are treated as quasistatic; adiabatic mode is reversible and uses PV^γ constant.
- The heat-capacity relation Cv=R/(γ−1) is used, so γ must be greater than one and is treated as constant.
- Real-gas effects, phase change, friction, irreversible losses, heat leaks, and a detailed engine or refrigeration cycle are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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