The question is:(adsbygoogle = window.adsbygoogle || []).push({});

Write an expression for the average energy of a set of particles obeying Boltz-

mann statistics and each having energy E = bz2, where b is a constant and

z is a variable. Hence, show that the average energy per degree of freedom

for each particle is 1

2kBT; where kB is Boltzmann's constant. You should use

the standard integrals shown at the end of the question.

You are given:

[integral from -infinity to infinity]exp(-ax^{2})dx = SQRT(PI/a)

and

[integral from -infinity to infinity]x^{2}exp(-ax^{2})dx = (1/2)SQRT(PI/a^{3})

I've taken the average energy as [integral from -infinity to infinity]E.Aexp(-E/K_{B}T)dE which gives:

[integral from -infinity to infinity]2b^{2}z^{3}exp(-bz^{2}/K_{B}T)dz by changing variable to z (dE/dz=2bz)

But this is not the standard result so I can't proceed!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Average Energy of Boltzmann Distribution

**Physics Forums | Science Articles, Homework Help, Discussion**