Thermodynamics, Statistical Physics, and Quantum Mechanics

98

The integral required here may befound by differentiating(S.4.13.7) once
with respect to

Using (S.4.13.8) in (S.4.13.3),where gives

so

b) The most likely speed occurs when (S.4.13.11) is a maximum. This
may be found by setting its derivative or, simply the derivative of In
equal to 0:

c) The average speed is given by

SOLUTIONS