Adiabatic Expansion – Adiabatic Compression

Adiabatic Process

An adiabatic process is a thermodynamic process, in which there is no heat transfer into or out of the system (Q = 0). The system can be considered to be perfectly insulated. In an adiabatic process, energy is transferred only as work. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes. In these rapid processes, there is not enough time for the transfer of energy as heat to take place to or from the system.

In real devices (such as turbines, pumps, and compressors) heat losses and losses in the combustion process occur, but these losses are usually low in comparison to overall energy flow and we can approximate some thermodynamic processes by the adiabatic process.

Main characteristics of adiabatic process
Main characteristics of adiabatic process

See also: First Law of Thermodynamics

See also: Ideal Gas Law

See also: What is Enthalpy

Adiabatic Expansion – Adiabatic Compression

See also: What is an Ideal Gas


pV = nRT


  • p is the absolute pressure of the gas
  • n is the amount of substance
  • T is the absolute temperature
  • V is the volume


The adiabatic process can be expressed with the ideal gas law as:

pVκ = constant


p1V1κ = p2V2κ

in which κ = cp/cv is the ratio of the specific heats (or heat capacities) for the gas. One for constant pressure (cp) and one for constant volume (cv). Note that, this ratio κ  = cp/cv is a factor in determining the speed of sound in a gas and other adiabatic processes.

Other p, V, T Relation

p,V,T relation - isentropic process

On a p-V diagram, the process occurs along a line (called an adiabat) that has the equation p = constant / VκFor an ideal gas and a polytropic process, the case n = κ  corresponds to an adiabatic process.

Example of Adiabatic Expansion

P-V diagram - adiabatic process
Assume an adiabatic expansion of helium (3 → 4) in a gas turbine (Brayton cycle).

Assume an adiabatic expansion of helium (3 → 4) in a gas turbine. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate outlet temperature of the gas (T4,real). In this turbines the high-pressure stage receives gas (point 3 at the figure; p3 = 6.7 MPa; T3 = 1190 K (917°C)) from a heat exchanger and exhaust it to another heat exchanger, where the outlet pressure is p4 = 2.78 MPa (point 4).


The outlet temperature of the gas, T4,real, can be calculated using p, V, T Relation for adiabatic process. Note that, it is the same relation as for the isentropic process, therefore results must be identical. It this case, we calculate the expansion for different gas turbine (less efficient) as in case of Isentropic Expansion in Gas Turbine.

p,V,T relation - isentropic process

In this equation the factor for helium is equal to κ=cp/cv=1.66. From the previous equation follows that the outlet temperature of the gas, T4,real, is:

adiabatic process - example

See also: Mayer’s relation

Nuclear and Reactor Physics:

Advanced Reactor Physics:


See above:

Adiabatic Process