Ideal Gas (reversible Process)
The mathematical equation for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process is
where P is pressure, V is specific or molar volume, and
being the specific heat for constant pressure, being the specific heat for constant volume, is the adiabatic index, and is the number of degrees of freedom (3 for monatomic gas, 5 for diatomic gas).
For a monatomic ideal gas, and for a diatomic gas (such as nitrogen and oxygen, the main components of air) . Note that the above formula is only applicable to classical ideal gases and not Bose–Einstein or Fermi gases.
For reversible adiabatic processes, it is also true that
where T is an absolute temperature.
This can also be written as
Read more about this topic: Adiabatic Process
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