What is an adiabatic process?

An adiabatic process is one in which no heat enters or leaves the system (Q = 0). All energy exchange occurs as mechanical work. Rapid compressions and expansions are often approximately adiabatic because there is not enough time for heat to transfer.

What is the adiabatic index γ (gamma)?

Gamma (γ) is the ratio of the heat capacity at constant pressure (Cp) to the heat capacity at constant volume (Cv). It determines how steeply pressure changes with volume. Diatomic gases (air, N₂, O₂) have γ ≈ 1.4; monatomic gases (Ar, He) have γ ≈ 1.67; polyatomic gases (CO₂) have γ ≈ 1.3.

What formulas does this calculator use?

For the pressure-volume relation: P₁V₁^γ = P₂V₂^γ. For temperature-volume: T₁V₁^(γ−1) = T₂V₂^(γ−1). For temperature-pressure: T₁P₁^((1−γ)/γ) = T₂P₂^((1−γ)/γ). Work done: W = (P₁V₁ − P₂V₂)/(γ − 1), with volumes in liters and pressures in atm converted to Joules (1 L·atm = 101.325 J).

How is adiabatic work different from isothermal work?

In an isothermal process, temperature is constant and W = nRT ln(V₂/V₁). In an adiabatic process, temperature changes and W = (P₁V₁ − P₂V₂)/(γ − 1). Adiabatic expansion does less work than isothermal expansion from the same initial state because the gas cools as it expands.

Why does temperature change in an adiabatic process?

Because Q = 0, all work done by the gas comes from its internal energy. When the gas expands and does positive work, internal energy falls and temperature drops. When compressed, work is done on the gas, internal energy rises, and temperature increases — this is why diesel engines can ignite fuel by compression alone.

What units does this calculator use?

Pressure in atm, volume in liters (L), temperature in Kelvin (K). Work and internal energy change are reported in Joules (J) and kilojoules (kJ). To convert Celsius to Kelvin, add 273.15.

Adiabatic Process Calculator

Name: Adiabatic Process Calculator
Availability: InStock
Author: Nham Vu

Enter initial pressure, volume, and temperature plus the adiabatic index to find the final state after an adiabatic expansion or compression.

Initial State & Parameters

Initial Pressure (P₁) atm

Initial Volume (V₁) L

Initial Temperature (T₁) K

Kelvin only. 25 °C = 298.15 K.

Adiabatic Index (γ)

Final state — solve for:

Final Volume V₂ L

Enter initial state values on the left to see results.

Summary

Enter initial pressure, volume, and temperature plus the adiabatic index to find the final state after an adiabatic expansion or compression.

How it works

Enter the initial pressure P₁ (in atm), volume V₁ (in liters), and temperature T₁ (in Kelvin).
Set the adiabatic index γ (gamma). Common values: 1.4 for diatomic gases like air, N₂, O₂; 1.67 for monatomic gases like Ar, He; 1.3 for polyatomic gases like CO₂.
Choose what you know about the final state: final volume V₂, final pressure P₂, or final temperature T₂.
Enter the known final value. The calculator solves for all remaining unknowns using PV^γ = constant and the ideal gas law.
Work done W, change in internal energy ΔU, and the process direction are computed from the results.
Results update instantly. Switch the "Solve for" mode to explore different scenarios.

Use cases

Thermodynamics homework on adiabatic expansion and compression.
Engine cycle analysis — the power stroke of an Otto or Diesel cycle is approximately adiabatic.
Calculating temperature rise in rapid gas compression (e.g., diesel ignition).
Atmospheric science: estimating temperature change as air masses rise or descend adiabatically.
Checking PV diagram work areas for ideal gas cycles.
Teaching the relationship between heat capacity ratio and thermodynamic behavior.
Verifying hand calculations for adiabatic work done on or by a gas.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu