- 4 The Equation Of State Of An Ideal Gas Of N Species Is Written As P 221ni Kot Where The Number Density Of The Spe 1 (176.4 KiB) Viewed 11 times
written as:
P =ΣNi=1nikBT, where the number density of the
species i is:
ni= Xi ρ, Ai mH
where Xi and Ai are the mass fraction and
mass number per particle of species i at a given point
inside a gas system, ρ is the mean density of the matter,
and kB and mH are the default physical
parameters. The matter inside a star can be regarded as an ideal
gas with each atom being fully ionised due to the high temperature
in its interior.
(a) Prove that the equation of state of stars can be written
as: P = RTρ,
μ
where R = kB/mH is the gas constant
and μ is the mean molecular
weight per particle. Find the formula for μ in terms
of Xi and Ai.
(b) If X and Y are the mass fractions
of H and He inside a star, find the mean molecular weight per
ion μI. You can assume that the mean atomic weight for metals
is 20.
(c) Using the fractional mass X only, find the
mean molecular weight per electron, μe.
(d) Prove that the three mean molecular weights for
different types of particles follow the relation:
μ1 = μ1 + μ1 . Ie
(e) If the composition of a star is X = 0.71
and Y = 0.28, calculate the values of the above three
mean molecular weights, μ, μe and μI
4. The equation of state of an ideal gas of N species is written as: P= (221ni) koT, where the number density of the species i is: X; ni = Am where X; and Aį are the mass fraction and mass number per particle of species i at a given point inside a gas system, p is the mean density of the matter, and kb and mh are the default physical parameters. The matter inside a star can be regarded as an ideal gas with each atom being fully ionised due to the high temperature in its interior. (a) Prove that the equation of state of stars can be written as: RTP P= д = where R = kb/mh is the gas constant and u is the mean molecular weight per particle. Find the formula for p in terms of Xi and Ai. (b) If X and Y are the mass fractions of H and He inside a star, find the mean molecular weight per ion Mr. You can assume that the mean atomic weight for metals is 20. (c) Using the fractional mass X only, find the mean molecular weight per electron, Me. (d) Prove that the three mean molecular weights for different types of particles follow the relation: 1 1 = 1 + MI μ Me (e) If the composition of a star is X = 0.71 and Y = 0.28, calculate the values of the above three mean molecular weights, H, Me and Mi.