Problems and Solutions on Thermodynamics and Statistical Mechanics

2 74 Problem3 d Solutiow on Thermodylnmics d Statistical Mechanics

(c) Assume that the velocity distribution is D(v)dv, then the number
of the molecules which collide with a unit area of the walls of the container
in a unit time, with velocities between v and v + dv is nv,D(v)dv. The
force that the unit areas suffers due to the collisions is

dp = 2mv:nD(v)dv

Hence the pressure is

nD(v) .2mvgdv = nD(v). rnvgdv

= I,,,

1 2E

= 2 / nD(v) -mv2dv = --.

3 2 3v

For an electron gas

(d) The specific heat and the paramagnetic magnetization of metals

Superconductivity cannot be explained by the Fermi gas model.

can be qualitatively explained by the Fermi gas model.

2101

The free-electron model of the conduction electrons in metals seems

naive but is often successful. Among other things, it gives a reasonably

good account of the compressibility for certain metals. This prompts the

following question. You are given the number density n and the Fermi en-

ergy e of a non-interacting Fermi gas at zero absolute temperature, T =O K.

Find the isothermal compressibility

where V is volume, p is pressure.

Hint: Recall that pV = - E, where E is the total energy.

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(GUSPEA)