Reversible adiabatic compression or expansion of a fixed mass of calorically perfect ideal gas keeps PV raised to the heat-capacity ratio 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. Made the ideal-gas, constant-γ, reversible-adiabatic assumptions explicit.
Reversible adiabatic compression or expansion of a fixed mass of calorically perfect ideal gas keeps PV raised to the heat-capacity ratio constant. The relation predicts the pressure change from a volume ratio without assuming the temperature stays constant.
| Symbol | Meaning | Units |
|---|---|---|
| Initial absolute pressure | ||
| Final absolute pressure | ||
| Initial gas volume | ||
| Final gas volume | ||
| Constant heat capacity ratio |
Estimate a pressure rise for a reversible adiabatic volume change.
Connect two idealized compression or expansion states.
A gas at 100000 Pa is compressed reversibly and adiabatically from 0.010 to 0.005 m³. Use constant γ = 1.4.
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. Made the ideal-gas, constant-γ, reversible-adiabatic assumptions explicit.
Assumptions
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