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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.
Gibbs free energy G The first derivatives of the internal energy with respect to its (extensive) natural variables S and V yields the intensive parameters of the system - The pressure P and the temperature T .
A thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. [1]
Residential drug treatment co-opted the language of Alcoholics Anonymous, using the Big Book not as a spiritual guide but as a mandatory text — contradicting AA’s voluntary essence. AA’s meetings, with their folding chairs and donated coffee, were intended as a judgment-free space for addicts to talk about their problems.
Smooth solutions of the free (in the sense of without source term: g=0) equations satisfy the conservation of specific kinetic energy: + (+) = In the one-dimensional case without the source term (both pressure gradient and external force), the momentum equation becomes the inviscid Burgers' equation : ∂ u ∂ t + u ∂ u ∂ x = 0 ...
Bryan Yeshion Schneps, a 21‑year‑old Temple University student, tried to prevent his attackers from gaining entry. He pressed his hands, his shoulders, his knees, his feet, the full weight of his 6'1", 180‑pound body against the door. But his stamina wore thin, and the door swung free. Bryan cried for help.