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# Use a computer to reproduce the table and graph in Figure ISBN: 9780201380279 40

## Solution for problem 9P Chapter 2

An Introduction to Thermal Physics | 1st Edition

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Problem 9P

Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six). Assuming that all microstates are equally likely, what is the most probable macrostate, and what is its probability? What is the least probable macrostate, and what is its probability?

Step-by-Step Solution:

Step 1</p>

we can model the two state paramagnet as an Einstein solid where the role of the oscillators is played by the dipoles, the energy quantum is the difference in energy between a parallel and antiparallel dipole. The antiparallel dipole has higher energy since a torque must be applied to twist the dipole against the field.

Step 2</p>

Using this model, we can picture two interacting paramagnets as toe interacting Einstein solids. As we know we have two solids A and B containing NA and NB  dipoles qA and qB quanta of energy with qA + qB.=q=constant.To any particular partition of the quanta that is for particular values and the total number of microstates available to the compound system is.

Step 3</p>  We take NA=NA=100 and q=80 using maple to calculate the binomial coefficient.       Step 4 of 5

Step 5 of 5

##### ISBN: 9780201380279

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