What is polytropic exponent?
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 can describe multiple expansion and compression processes which include heat transfer.
Is the sun a Polytrope?
An index n = 0 polytrope is often used to model rocky planets as well. A polytrope with index n = 3 is usually also used to model main-sequence stars like our Sun, at least in the radiation zone, corresponding to the Eddington standard model of stellar structure. A polytrope with index n = 5 has an infinite radius.
What is polytropic process example?
the case < n < ∞, in this process heat and work flows go in the same direction, This process occurs, for example, in an internal combustion engine (e.g. Otto cycle), in which there are heat loses through the cylinder walls during gas expansion (power stroke).
What is CP and CV?
CV and CP are two terms used in thermodynamics. CV is the specific heat at constant volume, and CP is the specific heat at constant pressure. Specific heat is the heat energy required to raise the temperature of a substance (per unit mass) by one degree Celsius.
Why are Polytropes useful?
Polytropes are self-gravitating gaseous spheres that were, and still are, very useful as crude approximation to more realistic stellar models. Properties of polytropes are thoroughly described in a classical, and very old, textbook: An Introduction to the Study of Stellar Structure by S.
What do Polytropes do?
Polytropes are models of stars and planets that use the equation of state P = Kρ1+1/n to derive hydrostatic configurations of the pressure P and mass density ρ. The polytropic equation of state (EOS) relates P to ρ with a constant K and the polytropic index n.
What is a polytropic process used for?
The term “polytropic” was originally coined to describe any reversible process on any open or closed system of gas or vapor which involves both heat and work transfer, such that a specified combination of properties were maintained constant throughout the process.
Why is Polytropic process called Polytropic?
What is the polytropic exponent equivalent to?
The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus where its relation to the Murnaghan equation of state has also been demonstrated.
What does polytrope mean in physics?
Polytrope. 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. The constant n is known as the polytropic index; note however that the polytropic index has an…
What is the index of a good polytrope?
An index n = 0 polytrope is often used to model rocky planets as well. 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 (like those of red giants ), brown dwarfs, giant gaseous planets (like Jupiter ).
What is the constant n in polytropic index?
where P is pressure, ρ is density and K is a constant of proportionality. The constant n is known as the polytropic index; note however that the polytropic index has an alternative definition as with n as the exponent.