An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter A.3, Problem 17P
To determine
A formula for the allowed energies of a system of two-dimensional harmonic oscillator which can be considered as a system of two independent one-dimensional oscillators.
To draw:An energy level diagram showing the degeneracy of each level.
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Draw a typical dispersion relation curve (w-k curve ) for Vp=Vg and Vp not equal to Vg where Vp is the phase velocity and Vg the group velocity .
Also the image for the delta w and delta k values are attached in a photo below . There are 9 values .
Given an Ising model containing two dipoles with interaction energy ±ɛ:
enumerate the states of this system and write down their Boltzmann factors.
determine the partition function and find the probabilities of the dipoles being parallel and
antiparallel.
C. plot the probability as a function of kT/ɛ.
d.
а.
b.
calculate the total average energy of this system.
plot the total average energy normalized to ɛ as a function of kT/ɛ.
f.
е.
Based on your observations from the above, at what temperatures are you more likely to find the
dipoles aligned parallel than antiparallel?
Problem 3: Harmonic oscillator. Canonical ensemble.
Consider a system of N harmonic oscillators. We assume that the oscillators are
distinguishable, one-dimensional, practically independent and having the same
angular frequency w.
1) Compute the partition function Z, for one subsystem (i.e. harmonic
oscillator).
2) Compute the partition function Z for the system.
3) Deduce the free energy.
4) Deduce the entropy.
5) Deduce the internal energy.
Chapter A Solutions
An Introduction to Thermal Physics
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