Reversible Isothermal Ideal-Gas Work
Calculate work done by an ideal gas during a reversible isothermal volume change.
Try this formula
Calculate boundary work done by the gas or choose another supported quantity.
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Try this formula
Calculate boundary work done by the gas or choose another supported quantity.
Constants used
- = 8.31446261815 J/(mol·K)
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Boundary work done by the gas
Enter the known values to see the result.
Use a fixed amount of ideal gas undergoing a reversible, quasi-equilibrium process. Temperature is constant and strictly positive in kelvins; both volumes are positive. Work done by the gas is positive for expansion and negative for compression.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra and introductory thermodynamics
Source
Teng-Jui Lin — CHEM E 326 — Chemical Engineering ThermodynamicsReference equation: Isothermal/Isoenergetic process — Work (changing volume). FormuLab wrote new explanations, assumptions, applications, and numerical examples. Changed the source work-on-system sign to explicitly positive work done by the gas. Used total molar work and the universal gas constant.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Changed the source work-on-system sign to explicitly positive work done by the gas. Used total molar work and the universal gas constant.
Definition
At fixed temperature, ideal-gas pressure falls as the gas expands. Integrating pressure over volume produces a logarithm, so equal volume ratios produce equal work at the same amount and temperature.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Boundary work done by the gas | ||
| Amount of gas | ||
| Universal gas constant | ||
| Constant absolute temperature | ||
| Final gas volume | ||
| Initial gas volume |
Real-World Applications
Piston expansion
Estimate reversible isothermal expansion work.
Compression comparison
Calculate the corresponding work input for a reversed path.
Worked Example
Problem
One mole of ideal gas expands reversibly at 300 K from 0.01 m³ to 0.02 m³. Find work done by the gas using R = 8.31446261815324 J/(mol·K).
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Isothermal/Isoenergetic process — Work (changing volume). FormuLab wrote new explanations, assumptions, applications, and numerical examples. Changed the source work-on-system sign to explicitly positive work done by the gas. Used total molar work and the universal gas constant.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Changed the source work-on-system sign to explicitly positive work done by the gas. Used total molar work and the universal gas constant.
Assumptions
- • Use a fixed amount of ideal gas undergoing a reversible, quasi-equilibrium process.
- • Temperature is constant and strictly positive in kelvins; both volumes are positive.
- • Work done by the gas is positive for expansion and negative for compression.
Languages
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