Boltzmann statistics

Problem:

Neutrons are released into an evacuated cubical chamber and lowered to a very cold T = 1 mK temperature.  What is their mean height above the floor of the chamber, once their gravitational energy has reached an equilibrium distribution?  (Show work!  Derive a formula and quote a number.)

Solution:

Problem:

Consider ideal gas particles of mass m at temperature T.  What is the average speed <v> (not the rms <v2>½ ) of the particle in terms of m, T and the Boltzmann constant kB?

Solution:

Problem:

Suppose a small meteorite makes a hole of area A = 1 mm2 in the wall of a spaceship.  The habitable volume of the spaceship is V = 10 m3.  The temperature of the air in the spaceship is T = 27o C and the pressure P = 105 kPa.  The molar mass of air is M = 29 g /mole.  Estimate, how much time will be available to astronauts to put on spacesuit, if the pressure should not drop by more than to 50% of its initial value.

Maxwell-Boltzmann speed distribution:  f(v) = (m/(2πkT))3/2 4πv2exp(-mv2/(2kT)

Solution:


Quantized energies