2.3 (a) A classical harmonic oscillator p? Kq? + 2 H 2m is in thermal contact with a heat bath at temperature T. Calculate the partition function for the oscillator in the canonical ensemble and show explicitly that (E) = kgT, ((E – (E))²) = kỷT² %3D |
2.3 (a) A classical harmonic oscillator p? Kq? + 2 H 2m is in thermal contact with a heat bath at temperature T. Calculate the partition function for the oscillator in the canonical ensemble and show explicitly that (E) = kgT, ((E – (E))²) = kỷT² %3D |
Related questions
Question
100%
Transcribed Image Text:2.3 (a)
A classical harmonic oscillator
p?, Kq?
H
+
2m
2
is in thermal contact with a heat bath at temperature T. Calculate the
partition function for the oscillator in the canonical ensemble and
show explicitly that
• (E) = kgT, ((E – (E))²) = k¿T²
Transcribed Image Text:2.6 (a), (b)
(a) Show that, if the kinetic energy of a particle with mass m, momentum p
is E = p²/2m, the single particle partition function can be written Z1 =
V/23, where 1 = /h²/2nmkgT is the thermal wavelength. The canonical
partition function for the ideal gas will then be
VN
ZN
N!23N
(b) Use Stirling's approximation to show that in the thermodynamic limit
the Helmholtz free energy of an ideal
gas
is
V
A = -NkgT |In
N23
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
