A quasi-equilibrium polytropic path follows PVⁿ = constant.
Difficulty
Intermediate
Read time
4 min
Prerequisites
Consistent SI units, algebra, and the physical assumptions listed below
Source
Teng-Jui Lin — Equation SheetsAdapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Integrated the source's general polytropic relation with work-by-positive convention. Did not reuse its incorrect isothermal work expression in the adiabatic section.
A quasi-equilibrium polytropic path follows PVⁿ = constant. Integrating pressure with respect to volume gives the boundary work done by the gas, with positive work for expansion under the convention used here.
| Symbol | Meaning | Units |
|---|---|---|
| Boundary work done by the system | ||
| Initial absolute pressure | ||
| Final absolute pressure | ||
| Initial volume | ||
| Final volume | ||
| Polytropic exponent |
Evaluate boundary work for a specified polytropic path.
Compare compression work under different exponents and conventions.
A gas expands from P₁ = 200000 Pa and V₁ = 0.10 m³ to V₂ = 0.20 m³ along PV^1.3 = constant. P₂ = 81225.24 Pa follows from that path.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Integrated the source's general polytropic relation with work-by-positive convention. Did not reuse its incorrect isothermal work expression in the adiabatic section.
Assumptions
FormuLab is a study reference. Verify formulas, units, assumptions, and course-specific conventions before relying on them.
© 2026 FormuLab. All rights reserved.