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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 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.
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]
(1) A Thermodynamic process is a process in which the thermodynamic state of a system is changed. A change in a system is defined by a passage from an initial to a final state of thermodynamic equilibrium. In classical thermodynamics, the actual course of the process is not the primary concern, and often is ignored.
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 ...
Additionally, the solution of the Cahn–Hilliard equation for a binary mixture is reasonably comparable with the solution of a Stefan problem. [11] In this comparison, the Stefan problem was solved using a front-tracking, moving-mesh method with homogeneous Neumann boundary conditions at the outer boundary. Also, Stefan problems can be applied ...
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.
The liquid stream from the gas–liquid separator flows through a valve and undergoes a throttling expansion from an absolute pressure of 62 bar to 21 bar (6.2 to 2.1 MPa), which is an isenthalpic process (i.e., a constant-enthalpy process) that results in lowering the temperature of the stream from about −51 °C to about −81 °C as the ...