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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 ...
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.
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).
The index is the polytropic index that appears in the polytropic equation of state, = + where and are the pressure and density, respectively, and is a constant of proportionality. The standard boundary conditions are θ ( 0 ) = 1 {\displaystyle \theta (0)=1} and θ ′ ( 0 ) = 0 {\displaystyle \theta '(0)=0} .
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 ]
More generally, the process is not really adiabatic but involves cooling by radiation that is much faster than the contraction, so that the process can be modeled by an adiabatic index as low as 1 (which corresponds to the polytropic index of an isothermal gas). [citation needed] So the second case is the rule rather than an exception in stars ...