Adiabatic Process
An adiabatic process is a change of state in which no heat crosses the system boundary (Q = 0), so by the first law the work done changes the internal energy directly: compression heats the system and expansion cools it. For a reversible adiabatic process in an ideal gas, pVγ = constant and TVγ−1 = constant, where γ = Cp/Cv; such a process is also isentropic.
Curious
Pump up a bicycle tyre quickly and the pump barrel gets warm; release gas from a spray can and the can feels cold. These are near-adiabatic processes: they happen too fast, or with too little thermal contact, for heat to flow. The work done on or by the gas goes straight into or out of its internal energy.
Adiabatic processes shape the weather. Rising air expands as pressure drops with altitude, cooling by roughly 10 °C per kilometre if it stays dry; this is why mountain tops are cold and why clouds form when rising air cools to its dew point.
Exploring
| Process | Held constant | Ideal-gas results |
|---|---|---|
| Isothermal | T | Q = W = nRT ln(V2/V1), ΔU = 0 |
| Adiabatic | Q = 0 | pVγ = const, W = −ΔU |
| Isochoric | V | W = 0, Q = ΔU = nCvΔT |
| Isobaric | p | W = pΔV, Q = nCpΔT |
Deep Dive
Derivation. With δQ = 0, dU = −p dV; for an ideal gas nCvdT = −(nRT/V)dV, which integrates to TVR/Cv = const, i.e. TVγ−1 = const and pVγ = const (Poisson's relations). Work done by the gas is W = (p1V1 − p2V2)/(γ − 1). A reversible adiabatic process has dS = 0 (isentropic); irreversible adiabatic processes increase entropy (see Second Law).
Atmosphere. Hydrostatic balance plus the adiabatic relation gives the dry lapse rate g/cp. When water vapour condenses, released latent heat reduces the cooling to the moist adiabatic rate, typically 4–7 K/km (see Latent Heat). Comparing the actual temperature profile with these rates determines atmospheric stability and thunderstorm potential. The Earth average environmental lapse rate in the troposphere is about 6.5 K/km.
Quantum adiabatic. In quantum mechanics, “adiabatic” has a related but different meaning: a slowly changing Hamiltonian keeps a system in the same eigenstate (the adiabatic theorem, Born and Fock 1928). The two meanings share the idea of slowness relative to internal dynamics but should not be conflated.
Concept Relationship Map
Requires: first law, specific heat capacity
Enables: Carnot cycle, engine cycles, speed of sound, atmospheric stability
Commonly confused with: isothermal process
Sources
- Laplace, P.-S. (1816). Annales de Chimie et de Physique, 3, 238–241.
- Çengel, Y.A., Boles, M.A. (2015). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill.
- Wallace, J.M., Hobbs, P.V. (2006). Atmospheric Science: An Introductory Survey (2nd ed.). Academic Press.