Polytropic change of state

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In thermodynamics , a change of state of a system in which the equation applies to pressure and specific volume is called polytropic . The exponent is called the polytropic exponent . In technical processes, the polytropic exponent can be viewed as constant. In the pv diagram, a polytrope takes the form of a power function with a negative slope.

Special cases of the polytropic change of state are:

Special cases of the polytropic change of state

The heat supplied to a gas during this change of state is given by:

Here referred to the mass , and start and end temperature of the process. The polytropy is characterized by a fixed heat capacity , which is from , and results.

One also speaks of a polytropic equation of state :

with the pressure p, the density , the polytropic constant K and the polytropic index m in . It is used, for example, in astrophysics ( Lane-Emden equation ).

Ideal gases

For ideal gases with isentropic changes of state, the following relationships also apply:



: absolute temperature
: Pressure
: Volume.

For the isentropic change of state of an ideal gas, the following applies . With the isobaric heat capacity and the isochoric heat capacity . In the case of diatomic gases (for example air as a gas mixture ) and monatomic gases ( noble gases ) can be used.


Individual evidence

  1. Fran Bosniakovic, "Technical Thermodynamics", 7th edition, Steinkopf-Verlag Darmstadt; Chapter 4.5 "Polytropic state change"
  2. Peter Stephan u. a .: Thermodynamics. Basics and technical applications, Vol. 1: One-component systems . 18th edition Springer, Berlin 2013, p. 115, ISBN 3-642-30097-9 .

See also

Wiktionary: polytropic  - explanations of meanings, word origins, synonyms, translations