Isothermal Work (W = nRT ln(V₂/V₁))
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W = nRT ln(V₂/V₁)
What each symbol means
| Symbol | What it stands for |
|---|---|
| R | Universal gas constant = 8.314 J/(mol·K) |
| T | Absolute temperature of gas (K) — constant throughout process |
| W | Work done by gas during isothermal process (J) |
| n | Number of moles of gas (mol) |
| V₁ | Initial volume of gas (m³ or L, consistent units) |
| V₂ | Final volume of gas (m³ or L, consistent units) |
When to use this
Applies to ideal gas undergoing a reversible isothermal (constant temperature) process. W > 0 for expansion (V₂ > V₁), W < 0 for compression (V₂ < V₁). Can also be written as W = nRT ln(P₁/P₂) using Boyle's law. For irreversible isothermal process against constant external pressure, use W = P_ext × ΔV instead.