- #1
mamela
- 6
- 0
The question is:
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(-ax2)dx = SQRT(PI/a)
and
[integral from -infinity to infinity]x2exp(-ax2)dx = (1/2)SQRT(PI/a3)
I've taken the average energy as [integral from -infinity to infinity]E.Aexp(-E/KBT)dE which gives:
[integral from -infinity to infinity]2b2z3exp(-bz2/KBT)dz by changing variable to z (dE/dz=2bz)
But this is not the standard result so I can't proceed!
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(-ax2)dx = SQRT(PI/a)
and
[integral from -infinity to infinity]x2exp(-ax2)dx = (1/2)SQRT(PI/a3)
I've taken the average energy as [integral from -infinity to infinity]E.Aexp(-E/KBT)dE which gives:
[integral from -infinity to infinity]2b2z3exp(-bz2/KBT)dz by changing variable to z (dE/dz=2bz)
But this is not the standard result so I can't proceed!