Consider a system of N identical free particles of mass m confined in a 3-dimensional box of volume V. (a) Show that the classical canonical partition function Z(V, N, ß) reads Z(V, N, B) and justify all steps. - WH (2mm) ² =
Consider a system of N identical free particles of mass m confined in a 3-dimensional box of volume V. (a) Show that the classical canonical partition function Z(V, N, ß) reads Z(V, N, B) and justify all steps. - WH (2mm) ² =
Related questions
Question
100%
Transcribed Image Text:Consider a system of N identical free particles of mass m confined in a
3-dimensional box of volume V.
(a) Show that the classical canonical partition function Z(V, N, ß) reads
3N
VN (2am\2
Z(V, N, B)
N! В
and justify all steps.
(b) In the isobaric-isothermal ensemble, the volume V is a random variable which
can vary from 0 to +∞. In this ensemble the probability density of getting a
particular volume reads
p(V) :
Z(V, N, B)
Π(Ρ, Ν,β)
exp(-BPV),
where P is a parameter setting the average volume in the ensemble and
П(P, N, ß) a real-valued function of P, N and B.
Given that the above probability density p(V) must be normalised, find an
integral expression for П(P, N, ß).
(c) Combining your results from (a) and (b) show that
3N
'2πm\ 2
1
TI(P, N, ß) = (²™m)
(BP)N+1*
(d) By using an appropriate derivative find the expression of the average volume
(V)B,P,N as a function of ß, N and P. Discuss your result in light of a familiar
thermodynamic equation of state.
=
=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
