Adiabatic processes

What Are Adiabatic Processes?

Adiabatic processes are thermodynamic changes of state in which no heat crosses the boundary of the system, so that any change in internal energy is accounted for entirely by work. The condition is expressed as zero heat transfer in the first law of thermodynamics, which reduces the energy balance to the statement that the change in internal energy equals the negative of the work done by the system. In practice a process is treated as adiabatic when it is either well insulated or fast enough that heat conduction has no time to act, which is why rapid compression in a cylinder and the slow ascent of an insulated air parcel are both modeled the same way. The concept sits alongside isothermal, isobaric, and isochoric processes as one of the idealized paths used to construct thermodynamic cycles.

An adiabatic process is not automatically reversible. Reversible adiabatic processes hold entropy constant and are called isentropic, while irreversible adiabatic processes such as throttling and free expansion generate entropy internally even though no heat crosses the boundary.

Isentropic Relations for an Ideal Gas

For an ideal gas undergoing a reversible adiabatic change, pressure and volume are linked by the relation that pressure multiplied by volume raised to the specific heat ratio remains constant, with companion expressions relating temperature to pressure and to volume. The specific heat ratio is approximately 1.4 for diatomic gases such as air at moderate temperature and 1.67 for monatomic gases. NASA's Glenn Research Center presents the derivation and the resulting formulas in its treatment of isentropic compression, which is the standard reference form used in gas dynamics. The same relations follow directly from setting the entropy change to zero, as set out in the companion discussion of the entropy of a gas.

Adiabatic Processes in Engines and the Atmosphere

Every standard air-standard cycle contains adiabatic legs. The Otto and Diesel cycles model compression and power strokes as isentropic, the Brayton cycle used for gas turbines does the same for its compressor and turbine, and the Carnot cycle joins its two isothermal legs with two adiabatic ones. Real compressors and turbines depart from the ideal, and the departure is quantified by isentropic efficiency, which compares the work of the ideal process with the work of the actual one. In meteorology, a rising parcel of unsaturated air expands and cools at the dry adiabatic lapse rate of approximately 9.8 kelvin per kilometer, and comparing that rate with the observed environmental lapse rate determines whether the atmosphere is stable or convectively unstable.

Adiabatic Demagnetization and Cryogenics

Adiabatic processes also underpin magnetic refrigeration. In adiabatic demagnetization, a paramagnetic salt is magnetized while thermally connected to a heat bath, then isolated, and the field is slowly reduced. Because spin entropy depends on the ratio of magnetic field to temperature, lowering the field while holding entropy fixed forces the temperature down. NIST has applied the method in millikelvin cryostats, with one instrument reaching roughly 23 millikelvin by staging a mechanical cryocooler, a helium-3 sorption stage, and an adiabatic demagnetization refrigerator. NASA has developed continuous-duty demagnetization refrigerators to hold detector arrays for space-based astronomy at stable sub-kelvin temperatures without the duty-cycle gaps of single-stage designs.

Applications

Adiabatic processes have applications in a wide range of fields, including: