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Ben-Gurion University of the Negev
Department of Physics
Thermodynamics & Statistical Mechanics 1
‫גוריון בנגב‬-‫אוניברסיטת בן‬
‫המחלקה לפיסיקה‬
1 ‫תרמודינמיקה ומכניקה סטטיסטית‬
Tutorial 6 – Ideal Gas
1.
Diatomic molecules
a. Find the partition function of an ideal gas of N diatomic molecules in which the two
atoms don't interact with each other
b. What is the energy of the gas? What is the heat capacity?
c. How would the above change if the two atoms of each molecule interact with each
other? Consider the interaction as a spring connecting the two atoms
d. Derive the equation of state
2.
Energy of gas of extreme relativistic particles
Extreme relativistic particles have momenta p such that pc  Mc 2 , where M is the rest
mass of the particle. The de-Broglie relation   h / p for the quantum wavelength
continues to apply.
a. Show directly that the mean energy per particle of an extreme relativistic ideal gas is
3 if   pc . In contrast to 32  for the nonrelativistic problem
b. Get the same result using the equipartition relation
can be any coordinate (momentum or spatial)
xm
H
  mn k BT , where xi
xn