Isothermal Process Calculator

Analyze ideal gas expansions and compressions confidently. Switch units, solve unknowns, and compare process states. Export neat reports with plots for faster physics decisions.

Calculator Inputs

Enter any three initial-state values. Leave one blank only when you want the calculator to solve it.

Initial Pressure P1

Initial Volume V1

Amount of Gas n

Temperature T

Final-State Input Mode

Decimal Places

Volume Ratio V2/V1

Final Volume V2

Final Pressure P2

Example Data Table

Case	P1	V1	n	T	V2/V1	P2	V2	Work	ΔS
Sample Expansion	101.325 kPa	24.617 L	1 mol	300 K	1.5	67.550 kPa	36.926 L	1011.93 J	3.37 J/K
Sample Compression	200 kPa	0.020 m3	1.6037 mol	300 K	0.6	333.333 kPa	0.012 m3	-2043.30 J	-6.81 J/K

Formula Used

Ideal-gas isothermal condition: P × V = constant = nRT

Final pressure: P2 = (P1 × V1) / V2

Final volume: V2 = (P1 × V1) / P2

Work by the gas: W = nRT ln(V2 / V1) = P1V1 ln(V2 / V1)

Heat transfer: Q = W

Internal-energy change for an ideal gas: ΔU = 0

Enthalpy change for an ideal gas: ΔH = 0

Entropy change: ΔS = nR ln(V2 / V1) = -nR ln(P2 / P1)

These relations assume an ideal gas and a truly constant temperature during the full process.

How to Use This Calculator

Enter any three initial-state values: pressure, volume, moles, and temperature.
Leave one initial field blank only if you want it solved automatically.
Select how you want to define the final state.
Enter either the final volume, final pressure, or the volume ratio.
Choose your preferred units for each field.
Set the number of decimal places for the results.
Press Calculate to show results above the form.
Use the CSV and PDF buttons to export the calculated report.

Frequently Asked Questions

1) What is an isothermal process?

An isothermal process keeps temperature constant throughout the change. For an ideal gas, pressure drops when volume rises, and pressure rises when volume falls.

2) Why is work nonzero when temperature stays constant?

The gas can still expand or compress against a boundary. Temperature remains unchanged, yet mechanical work happens because pressure acts through a changing volume.

3) Why are ΔU and ΔH zero here?

For an ideal gas, internal energy and enthalpy depend only on temperature. Since temperature stays constant in an isothermal ideal-gas process, both changes are zero.

4) Can this calculator solve a missing initial variable?

Yes. Enter any three initial values and leave one blank. The tool uses the ideal gas law to solve the missing pressure, volume, moles, or temperature.

5) Which final-state mode should I choose?

Use volume ratio for quick expansion or compression studies. Use final volume or final pressure when those values are known directly from measurements or design targets.

6) Which units are supported?

The calculator supports pressure in Pa, kPa, MPa, bar, atm, and psi. Volume supports m3, L, mL, cm3, and ft3. Temperature supports K, C, and F.

7) Why do I get an inconsistency warning?

If you enter all four initial values, they must satisfy PV = nRT. A warning appears when the entered values disagree beyond the allowed tolerance.

8) Does this work for real gases?

This page uses ideal-gas equations. It is excellent for education, screening, and many engineering approximations, but high-pressure real-gas behavior may need advanced equations of state.