What is an isothermal process?

An isothermal process is a thermodynamic change in which the temperature of the system remains constant throughout. For an ideal gas this means PV = constant (Boyle's Law), so pressure and volume change inversely.

Why does heat equal work in an isothermal process?

For an ideal gas, internal energy depends only on temperature. At constant temperature ΔU = 0, so from the first law (ΔU = Q − W) we get Q = W. All energy added as heat leaves as work (expansion), or all work done on the gas leaves as heat (compression).

What units does this calculator use?

Temperature must be in Kelvin, volume in liters, and moles as a dimensionless count. Pressure is displayed in atmospheres (atm). Work and heat are in Joules (J) or kilojoules (kJ).

What is the gas constant R used here?

R = 8.314 J/(mol·K), the universal gas constant. This gives work directly in Joules.

How do I convert Celsius to Kelvin?

Add 273.15 to the Celsius value. For example, 25 °C = 298.15 K. The calculator accepts Kelvin only because thermodynamic equations require absolute temperature.

Can I use pressure inputs instead of volume?

Yes. Switch to "Pressure mode" and enter P₁ and P₂ in atm. Boyle's Law gives V₂/V₁ = P₁/P₂, so the work formula becomes W = nRT ln(P₁/P₂).

Isothermal Process Calculator

Name: Isothermal Process Calculator
Availability: InStock
Author: Nham Vu

Enter initial and final volumes (or pressures) plus temperature and moles to compute work done and heat exchanged in an isothermal ideal-gas process.

Process Inputs

Moles of gas (n) mol

Temperature (T) K

Kelvin only. 25 °C = 298.15 K.

V₁ L

V₂ L

Enter values on the left to see results.

Summary

Enter initial and final volumes (or pressures) plus temperature and moles to compute work done and heat exchanged in an isothermal ideal-gas process.

How it works

Enter the amount of gas in moles (n) and the absolute temperature in Kelvin (T).
Provide initial volume V₁ and final volume V₂ (in liters), or switch to pressure mode.
The calculator derives the pressure ratio from Boyle's Law (P₁V₁ = P₂V₂).
Work done W = nRT ln(V₂/V₁) is computed using the universal gas constant R = 8.314 J/(mol·K).
Heat transferred Q equals W because ΔU = 0 for an isothermal ideal-gas process.
Results update instantly as you type.

Use cases

Thermodynamics homework on isothermal expansion and compression problems.
Checking PV diagram areas for ideal gas cycles (Carnot, etc.).
Engineering calculations for compressed-gas systems held at constant temperature.
Teaching or demonstrating Boyle's Law and the first law of thermodynamics.
Verifying hand calculations for isothermal work done on or by a gas.
Comparing expansion ratios and their effect on work and heat exchange.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu