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Isothermal Process Calculator

Work out isothermal process instantly with clear inputs, formula shown and shareable results.

About Isothermal Process Calculator

In an isothermal expansion the internal energy of an ideal gas does not change, so every joule of work done comes from heat absorbed: W = nRT ln(V2/V1). One mole tripling its volume at 300 K does 2741 J of work and takes in exactly that much heat, gaining 9.13 J/K of entropy while the surroundings lose the same.

Formulas

Isothermal work

W = n R T ln(V2 / V1)

Energy balance

dU = 0, so Q = W

Worked example

With the default values below, Isothermal Process Calculator returns Work Done By The Gas of 2,740.31. Change any input above and every figure here is recalculated in your browser.

Inputs used

Amount of gasminimum 0 mol
1 mol
Temperatureminimum 0 K
300 K
Initial volumeminimum 0 L
1 L
Final volumeminimum 0 L
3 L

Results

Work Done By The Gas
2,740.31 J
Heat Absorbed
2,740.31 J
Pressure Ratio P2/P1
0.3333
Entropy Change Of The Gas
9.1344 J/K

Step by step

  1. 1Values used
  2. 2Isothermal work
  3. 3Energy balance
  4. 4Work Done By The Gas= 2,740.31 J
  5. 5Heat Absorbed= 2,740.31 J
  6. 6Pressure Ratio P2/P1= 0.3333
  7. 7Entropy Change Of The Gas= 9.1344 J/K

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is the heat equal to the work?

Because internal energy depends only on temperature for an ideal gas. Hold temperature fixed and the first law reduces to Q = W.

How is an isothermal process achieved in practice?

Slowly, in good thermal contact with a reservoir. Fast changes are closer to adiabatic because heat has no time to flow.

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