Adiabatic Process Calculator

An adiabatic process is one with no heat transfer across the system boundary: Q = 0. This occurs in perfectly insulated systems, or when the process is so rapid that negligible heat flows in or out (e.g. sound waves, quick compression in a diesel engine). The first law reduces to ΔU = −W.

For a reversible quasistatic adiabatic process of an ideal gas with constant heat capacities, the process equations are: PV^γ = constant, TV^(γ−1) = constant, and TP^((1−γ)/γ) = constant, where γ = C_p/C_v is the heat capacity ratio (adiabatic index).

During adiabatic expansion, the gas does positive work on the surroundings, internal energy decreases, and temperature falls — this is why expanding spray cans feel cold. Adiabatic compression does work on the gas, raising T (bicycle pump heating). On a P–V diagram, an adiabat is steeper than an isotherm because γ > 1.

Typical γ values: monatomic ideal gas γ = 5/3 ≈ 1.67; diatomic (N₂, O₂, air at room T) γ ≈ 1.4; polyatomic and water vapor γ closer to 1.33. For ideal gas, Mayer's relation gives C_p − C_v = R and γ = 1 + R/C_v.

Reversible adiabatic work between states 1 and 2: W = (P₁V₁ − P₂V₂)/(γ − 1) = nR(T₁ − T₂)/(γ − 1). For γ = 1.4 and volume doubling (V₂ = 2V₁), P₂/P₁ = 2^(−γ) ≈ 0.38 and T₂/T₁ = 2^(1−γ) ≈ 0.76.

Adiabatic is not the same as isentropic for irreversible processes, but reversible adiabatic ideal gas processes are isentropic (ΔS = 0). Real irreversible adiabatic expansions (e.g. Joule–Thomson throttling) may not follow PV^γ relations exactly.