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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.
The normalized density as a function of scale length for a wide range of polytropic indices. In astrophysics, a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form = (+) / = + /, where P is pressure, ρ is density and K is a constant of proportionality. [1]
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.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
Thermodynamic data is usually presented as a table or chart of function values for one mole of a substance (or in the case of the steam tables, one kg). A thermodynamic datafile is a set of equation parameters from which the numerical data values can be calculated.
A model of a four-phase Stirling cycle. Most thermodynamics textbooks describe a highly simplified form of Stirling cycle consisting of four processes. This is known as an "ideal Stirling cycle", because it is an "idealized" model, and not necessarily an optimized cycle.
Therefore, the heat capacity ratio in this example is 1.4. Another way of understanding the difference between C P and C V is that C P applies if work is done to the system, which causes a change in volume (such as by moving a piston so as to compress the contents of a cylinder), or if work is done by the system, which changes its temperature ...
One common class of barotropic model used in astrophysics is a polytropic fluid. Typically, the barotropic assumption is not very realistic. In meteorology, a barotropic atmosphere is one that for which the density of the air depends only on pressure, as a result isobaric surfaces (constant-pressure surfaces) are also constant-density surfaces.