In subsequent discussions we will consider gases with a particular behaviour in the way they change their thermodynamical quantities under quasi-statical processes. This gas, the so called polytropic gas was first introduced in thermodynamics by G. Zeuner (Chandrasekhar, 1958) and it is used extensively in Astrophysics.
A polytropic change on the thermodynamical quantities of a gas is said to occur if the change is done quasi-statical and is such that its specific heat remains constant during the entire process. From this definition it follows that (Chandrasekhar, 1958):
where the polytropic index is a constant
and has a very well known value of
for an adiabatic mono
atomic gas (Landau & Lifshitz, 1994b) in which relativistic effects are not taken
into account. In the case of an ultrarelativistic photon gas it has a
value of
. The first law of thermodynamics, eq.(9.3),
can be rewritten as (Stanyuokovich, 1960):
The speed of sound and the enthalpy per unit mass,
specific enthalpy,
of a polytropic gas can then be
written accordingly (Stanyuokovich, 1960):
In the case of an ultrarelativistic gas, that is, when
-for example, a photon gas in which
, it follows
that (Stanyuokovich, 1960):
For the case in which relativistic effects in the macroscopic motion of the gas are not considered, eqs.(12.3)-(12.4) become
according to eq.(10.1).
Sergio Mendoza Fri Apr 20, 2001