Eduard-Job-Stiftung für Thermo- und Stoffdynamik

Entropieerzeugung in einem Entropiestrom

Adiabatic Compression

A process is called adiabatic, if the entropy content of the system does not change. It is therefore possible to use the following simplification of the main equation (equation 1)

=    since dS = 0 by definition

It is now possible to substitute p on the left side using the ideal gas law (pv=nRT).

 


To simplify the following calculations we define the adiabatic exponent = first and use = for the integration (from V0 to V and from T0 to T).


The expression = is the adiabatic analogue of GAY-LUSSACS law. The corresponding expression for BOYLE's law can be obtained by substituting the temperatures T and T0 with the ideal gas law ( T=(pV)(nR)-1).

    and therefore

The exponents and depend on the heat capacity cV of the gas and describe the influence of the temperature change on the compression.

   since    for ideal gases