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A polytropic process is a thermodynamic process that obeys the relation: = where p is the pressure , V is volume , n is the polytropic index , and C is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer.
Neutron stars are well modeled by polytropes with index between n = 0.5 and n = 1. A polytrope with index n = 1.5 is a good model for fully convective star cores [5] [6] (like those of red giants), brown dwarfs, giant gaseous planets (like Jupiter). With this index, the polytropic exponent is 5/3, which is the heat capacity ratio (γ) for ...
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (C P) to heat capacity at constant volume (C V).
A polytropic process is a thermodynamic process that obeys the relation: P V n = C , {\displaystyle PV^{\,n}=C,} where P is the pressure, V is volume, n is any real number (the "polytropic index"), and C is a constant.
A polytropic process, in particular, causes changes to the system so that the quantity is constant (where is pressure, is volume, and is the polytropic index, a constant). Note that for specific polytropic indexes, a polytropic process will be equivalent to a constant-property process.
The most important polytropic processes run between the adiabatic and the isotherm functions, the polytropic index is between 1 and the adiabatic exponent (γ or κ). Dimensionless heat capacity [ edit ]
The particular choice of a polytropic gas as given above makes the mathematical statement of the problem particularly succinct and leads to the Lane–Emden equation. The equation is a useful approximation for self-gravitating spheres of plasma such as stars, but typically it is a rather limiting assumption.
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