An adiabatic process is a change in a thermodynamic system during which no heat crosses the boundary separating the system from its surroundings. In thermodynamics, this condition is expressed as (Q=0). It does not mean that the system’s temperature remains constant or that no energy is exchanged: energy may still be transferred through work. Adiabatic processes are important idealizations in the analysis of gases, engines, and atmospheric motion. (ocw.mit.edu)
Physical meaning and realization
The defining feature is the absence of heat transfer throughout the process, rather than merely a zero net heat transfer after heating and cooling cancel. An adiabatic boundary prevents thermal exchange but may permit mechanical interaction, such as the movement of a piston. A thermally insulated cylinder containing gas therefore provides a standard model. Adiabatic should not be confused with isolated: an isolated system exchanges neither matter nor energy with its surroundings. (ocw.mit.edu)
Actual processes approximate this condition when insulation makes heat transfer sufficiently small, or when a change occurs too rapidly for appreciable heat exchange. Rapid compression inside an internal combustion engine is one example. Speed alone does not establish an exact adiabatic condition; the approximation concerns the importance of heat transfer during the interval being studied. Conversely, a well-insulated process need not be rapid. (openstax.org)
Energy balance
For a closed system whose changes in bulk kinetic and gravitational potential energy are negligible, the first law of thermodynamics gives
[ \Delta U=Q-W, ]
where (U) is internal energy, (Q) is heat supplied to the system, and (W) is work done by the system. Consequently, an adiabatic process satisfies
[ \Delta U=-W. ]
Positive work output reduces internal energy; work input increases it. An alternative convention takes work done on the system as positive, giving (\Delta U=W_{\mathrm{on}}). These conventions express the same physical balance. (openstax.org)
For an ideal gas, internal energy depends only on temperature. Adiabatic compression with work input therefore raises its temperature, while expansion with work output lowers it. This differs from an isothermal process, which maintains constant temperature and generally requires heat exchange to balance work. (openstax.org)
Reversible ideal-gas relations
Consider a fixed amount of ideal gas undergoing a reversible process with no heat transfer and only pressure–volume work. Its states remain arbitrarily close to thermodynamic equilibrium. With constant molar heat capacities, the energy balance and ideal-gas equation of state give
[ nC_V,dT=-p,dV, \qquad pV=nRT, ]
where (n) is the amount of gas, (R) the gas constant, (p) pressure, and (V) volume. Defining (\gamma=C_p/C_V), integration yields
[ pV^\gamma=\text{constant}, \qquad TV^{\gamma-1}=\text{constant}. ]
Thus,
[ \frac{T_2}{T_1} =\left(\frac{V_1}{V_2}\right)^{\gamma-1} =\left(\frac{p_2}{p_1}\right)^{(\gamma-1)/\gamma}. ]
Temperatures in these relations are absolute temperatures, ordinarily expressed in kelvin. (openstax.org)
The work output between the endpoints is
[ W=\frac{p_1V_1-p_2V_2}{\gamma-1} =nC_V(T_1-T_2). ]
On a pressure–volume diagram, the reversible adiabat has slope (-\gamma p/V), making it steeper than an isotherm through the same state. These power-law relations are not general equations for every adiabatic process: they require the stated assumptions, including reversibility and constant heat capacities. (openstax.org)
Entropy and irreversible changes
Adiabatic and isentropic are distinct concepts. An isentropic process preserves entropy, whereas an adiabatic process prevents heat transfer. According to the second law of thermodynamics, a closed adiabatic system satisfies
[ \Delta S=S_{\mathrm{gen}}\geq0, ]
where (S_{\mathrm{gen}}) is entropy generated internally. Reversible adiabatic changes generate no entropy and are therefore isentropic. Irreversible changes involving friction or other dissipative effects can increase entropy despite the absence of heat exchange. (ocw.mit.edu)
An important counterexample to the claim that adiabatic expansion always cools a gas is free expansion into a vacuum inside an insulated, rigid vessel. There is no external boundary work and no heat transfer, so (\Delta U=0). An ideal gas consequently has the same initial and final temperature, although its volume increases. Its entropy increases, and the reversible relation (pV^\gamma=\text{constant}) does not describe this process. (ocw.mit.edu)
Engineering applications
Adiabatic models occur throughout heat-engine theory. The Carnot cycle contains two reversible adiabatic stages connecting two isothermal stages. During these adiabatic stages, compression and expansion change the working substance’s temperature without heat exchange with a reservoir. (openstax.org)
Flowing systems require a different energy balance from a fixed quantity of gas. For a steady, adiabatic turbine with negligible changes in kinetic energy and potential energy, specific shaft-work output is
[ w_{\mathrm{out}}=h_{\mathrm{in}}-h_{\mathrm{out}}, ]
where (h) is specific enthalpy. For a compressor under corresponding assumptions, work input equals the enthalpy increase. Adiabatic operation does not imply reversible operation; real devices can generate entropy while remaining approximately thermally insulated. (live.ocw.mit.edu)
Atmospheric processes
In the Earth’s atmosphere, a rising air parcel encounters lower pressure and expands, cooling approximately adiabatically; a descending parcel is compressed and warms. Unsaturated air follows the dry adiabatic lapse rate, approximately (10^\circ\mathrm{C}) per kilometre. This describes a moving parcel, not necessarily the temperature gradient of the surrounding atmosphere. (weather.gov)
Once rising air becomes saturated, condensation releases latent heat, reducing its cooling rate. The moist adiabatic lapse rate varies with temperature and pressure. Such internal phase changes can occur without heat crossing the parcel boundary, although mixing and precipitation complicate the idealized parcel model. (weather.gov)