Question

(a)
(i) In your own words, state Boltzmann’s two principles of statistical mechanics.
(ii) In the context of statistical mechanics, explain what is meant by a phase cell, and explain
how such cells may be used in the specification of the configuration of a classical gas.
(iii) In your own words, state Boltzmann’s distribution law for a gas in equilibrium.
(iv) Two phase cells in a gas in equilibrium are labelled X and Y. The probability of finding a
given molecule in cell X relative to the probability of finding the molecule in cell Y is 125
and the temperature of the gas is 300 K. If the energy of cell X is 1.00 × 10−20 J, what is
the energy of cell Y?
(b) A sealed container of volume V = 0.10m3 holds a sample of N = 3.0 × 1024 atoms of
helium gas in equilibrium. The distribution of speeds of the helium atoms shows a peak at
1.1 × 103 ms−1.
(i) Calculate the temperature and pressure of the helium gas.
(ii) What is the average kinetic energy of the helium atoms?
(Take the mass of each helium atom to be 4.0 amu.)

Answer 1

I am using the boltzman statistical distribution concept