Gas Work Calculator

Calculator Inputs

Process type

Pressure unit

Volume unit

Temperature unit

Sign convention

Decimal places

Initial pressure P₁

Needed for isobaric, polytropic, and adiabatic.

Final pressure P₂

Used directly for isochoric.

Initial volume V₁

Final volume V₂

Ignored for isochoric; V₂ = V₁.

Gas temperature

Directly required for isothermal.

Amount of gas (mol)

Needed for ideal-gas temperature and isothermal work.

Heat capacity ratio γ

Used for the adiabatic model.

Polytropic exponent n

Used for the polytropic model.

Example data table

Case	Process	Given values	Expected focus
Example 1	Isothermal	n = 1 mol, T = 300 K, V₁ = 10 L, V₂ = 25 L	Reversible work from volume ratio
Example 2	Isobaric	P = 200 kPa, V₁ = 0.02 m³, V₂ = 0.05 m³	Constant-pressure rectangular P-V area
Example 3	Polytropic	P₁ = 300 kPa, V₁ = 12 L, V₂ = 6 L, n = 1.3	Pressure rise during compression path
Example 4	Adiabatic	P₁ = 150 kPa, V₁ = 18 L, V₂ = 9 L, γ = 1.4	Work without heat-transfer assumption

Formula used

This calculator focuses on boundary work for idealized quasi-static gas processes. The P-V area represents the mechanical work transfer between the gas and its surroundings.

1) Isobaric process

W = P(V₂ − V₁)

Pressure stays constant. Expansion gives positive work by the gas, while compression gives negative work by the gas.

2) Isochoric process

W = 0

Because volume does not change, the gas does no boundary work even if pressure rises or falls.

3) Isothermal reversible process

W = nRT ln(V₂ / V₁)

Temperature remains constant. The ideal gas law is used to determine pressure along the path.

4) Polytropic process

PVⁿ = constant

W = (P₂V₂ − P₁V₁) / (1 − n), for n ≠ 1

If n = 1, the path becomes isothermal and the logarithmic formula is used.

5) Reversible adiabatic process

PVᵞ = constant

W = (P₂V₂ − P₁V₁) / (1 − γ)

This model assumes no heat transfer and uses the heat capacity ratio γ.

How to use this calculator

Select the thermodynamic process that matches your problem statement.
Choose pressure, volume, and temperature units before entering values.
Enter the known state variables. Use P₂ only for isochoric cases.
Enter moles for ideal-gas temperature outputs and isothermal work.
Provide γ for adiabatic paths or n for polytropic paths.
Pick the sign convention that matches your textbook or course notes.
Press Calculate Gas Work to show the result above the form.
Use the CSV button for tabular export or PDF for a shareable report.

FAQs

1) What does gas work mean in thermodynamics?

Gas work is the mechanical energy transfer caused by volume change against external pressure. On a P-V diagram, it equals the area under the process curve for a quasi-static path.

2) Why is work zero in an isochoric process?

Boundary work depends on volume change. If volume remains constant, then dV is zero everywhere, so the integral of P dV is also zero.

3) Why does the isothermal formula use a logarithm?

For a reversible isothermal ideal gas, pressure varies as 1/V. Integrating that inverse-volume relationship produces the natural logarithm term in the work expression.

4) What is the difference between adiabatic and polytropic processes?

Adiabatic means no heat transfer and commonly uses γ. Polytropic is broader and uses a general exponent n, which can represent many real compression or expansion behaviors.

5) Which sign convention should I choose?

Use the same convention as your class, textbook, or engineering standard. Physics often treats work done by the gas as positive, while some engineering contexts track work on the gas as positive.

6) Can this calculator handle real-gas behavior?

No. This version uses idealized process relations and ideal-gas assumptions where needed. Real-gas corrections require an equation of state or experimentally fitted property data.

7) Why are some temperatures shown as dashes?

If the amount of gas is not provided, the calculator cannot infer temperature from pressure and volume. Add moles to enable ideal-gas temperature estimates.

8) What does the plotted graph represent?

The plot shows the pressure-volume path for the selected process. Its shape helps explain why different thermodynamic paths can produce different work values between similar states.