Problems and Solutions on Thermodynamics and Statistical Mechanics

286 Problems €4 Solutiona on Thermodynamics d Statistical Mechanics

(c) F'rom the virial theorem, we have

($R3ne) :hc (2) 'I2 = i~ 3 GM2.

we obtain

M = -!!-. %/$ = 8.5 x lo3' kg = 4.1M, ,

128~ Gm,

where Ma is the mass of the sun.

2110

(a) Given that the mass of the sun is 2 x g, estimate the number

of electrons in the sun. Assume the sun is largely composed of atomic

hydrogen.

(b) In a white dwarf star of one solar mass the atoms are all ionized

and contained in a sphere of radius 2 x 109 cm. Find the Fermi energy of

the electrons in eV.

(c) If the temperature of the white dwarf is lo' K, discuss whether the

(d) If the above number of electrons were contained in a pulsar of one

solar mass and of radius 10 km, find the order of magnitude of their Fermi

energy.

(Columbia)

electrons and/or nucleons in the star are degenerate.

Solution:

(a) The number of electrons is

1.2 x lo5'.

2 x 1033

1.67 x 10-24

N=

(b) The Fermi energy of the electrons is

EJ 4 x lo4 eV.

EF'=%(GV) h2 3 N 2J3 xE(--) 9 N 2/3

2m, 32x2 R3