Adiabatic Process Calculator

An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings (Q = 0). This means all energy changes come from work done on or by the gas. It occurs when the system is perfectly insulated or when the process happens so rapidly that heat transfer has no time to take place.

For an ideal gas undergoing an adiabatic process, the governing relation is PV^γ = constant, where γ (gamma) is the heat capacity ratio Cp/Cv. This leads to the relations p₁V₁^γ = p₂V₂^γ and T₁V₁^(γ−1) = T₂V₂^(γ−1), which connect the initial and final states.

In an isothermal process the temperature stays constant (ΔT = 0) and heat flows freely, following PV = constant. In an adiabatic process no heat is exchanged (Q = 0), so the temperature changes as the gas expands or compresses, following PV^γ = constant. Because γ > 1, the pressure drops faster in an adiabatic expansion than in an isothermal one.

The work done by the gas is W = (p₁V₁ − p₂V₂) / (γ − 1). Because Q = 0, the first law gives ΔU = −W, so the change in internal energy equals the negative of the work done. A positive W means the gas expanded and did work on its surroundings; a negative W means the surroundings did work on the gas.

γ = Cp/Cv is the ratio of specific heat at constant pressure to specific heat at constant volume. Monatomic gases like helium and argon have γ ≈ 1.667, while diatomic gases like nitrogen, oxygen, and air have γ ≈ 1.4. A higher γ means a steeper pressure–volume curve, so the same compression produces a larger temperature rise.

This calculator assumes ideal gas behaviour, where molecules have no intermolecular forces and negligible volume. Real gases deviate from ideal behaviour at very high pressures or very low temperatures. For such conditions you would need the van der Waals equation or another equation of state to get accurate results.

Common examples include the compression stroke in a diesel engine (air heats up enough to ignite fuel without a spark), rising air parcels in the atmosphere cooling as they expand (responsible for cloud formation), and the compression inside a bicycle pump becoming warm. Refrigeration cycles also involve adiabatic compression and expansion stages.

This calculator uses SI units throughout. For pressure: 1 atm = 101 325 Pa, 1 bar = 100 000 Pa, 1 psi ≈ 6 895 Pa. For volume: 1 litre = 0.001 m³, 1 cm³ = 1 × 10⁻⁶ m³. For temperature: K = °C + 273.15. Always convert to Pa, m³, and K before entering values.