irreversible adiabatic changes in state, expansion (left) and compression (right) in the Ts diagram

Adiabatic machine is a term from technical thermodynamics . It describes heat engines and work machines in which an adiabatic change of state takes place, i.e. which are neither cooled nor heated (i.e. without heat transfer ).

An adiabatic change of state is not always isentropic , since entropy can be produced on the way from the inlet through the blade rings to the outlet through friction , impact and throttling processes ( dissipation ) . As a result, the technical work done by an expansion machine ( turbine ) is less than with lossless isentropic expansion, and the work to be done increases when compressing in a compressor .

For both cases, the figure shows the basic course of the change in state in the Ts diagram, which does not differ qualitatively from the hs diagram for the gas phase of the working medium .

The first law of thermodynamics for the open system is :

${\ displaystyle {\ dot {Q}} + {\ dot {W _ {\ mathrm {t}}}} = {\ dot {H}} _ {\ mathrm {2}} - {\ dot {H}} _ {\ mathrm {1}} + \ underbrace {{\ dot {m}} \ cdot g \ cdot \ left (z _ {\ mathrm {2}} -z _ {\ mathrm {1}} \ right) + {{\ dot {m}} \ over 2} \ cdot \ left (c _ {\ mathrm {2}} ^ {2} -c _ {\ mathrm {1}} ^ {2} \ right)} _ {\ Delta E_ {a }}}$

By dividing by the mass flow , neglecting the heat transfer ( ) and the external energies ( ), one obtains the simple equation for the specific quantities : ${\ displaystyle {\ dot {m}}}$${\ displaystyle q = 0}$${\ displaystyle \ Delta E_ {a} = 0}$

${\ displaystyle w_ {t} = h_ {2} -h_ {1}}$

The technical work is therefore equal to the enthalpy difference (according to the convention valid in thermodynamics , the work removed from the system, i.e., gained, is negative). ${\ displaystyle w_ {t}}$

This results in  the turbine grade ν:

${\ displaystyle \ nu _ {\ rm {T}} = {\ frac {h_ {1} -h_ {2}} {h_ {1} -h _ {\ rm {2is}}}}}$

and the compressor:

${\ displaystyle \ nu _ {\ rm {V}} = {\ frac {h _ {\ rm {2is}} - h_ {1}} {h_ {2} -h_ {1}}}}$

## Dissipated work and loss of exergy

One form of the second law of thermodynamics is the equation:

${\ displaystyle \ Tds = \ delta {q} + \ delta {w _ {\ rm {diss}}}}$

Since no heat is transferred ( ), it can be seen from this equation that the area in the Ts diagram under the state curve (red area in the figure) represents the dissipated work. ${\ displaystyle \ delta {q} = 0}$

The specific exergy that is lost or converted into anergy results from

${\ displaystyle ex _ {\ rm {verl}} = T_ {U} \ cdot \ Delta {s _ {\ rm {irr}}}}$

as the part of the area which is below the line of the ambient temperature.