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# Starting with the result of 1, calculate the heat capacity

ISBN: 9780201380279 40

## Solution for problem 8P Chapter 3

An Introduction to Thermal Physics | 1st Edition

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Problem 8P

Starting with the result of Problem 1, calculate the heat capacity of an Einstein solid in the low-temperature limit. Sketch the predicted heat capacity as a function of temperature. (Note: Measurements of heat capacities of actual solids at low temperatures do not confirm the prediction that you will make in this problem. A more accurate model of solids at low temperatures is presented in Section 7.5.)

Problem 1:

Starting with the result of Problem 2, find a formula for the temperature of an Einstein solid in the limit q ≪ N. Solve for the energy as a function of temperature to obtain U = Nϵe−ϵ/kT(where ϵ is the size of an energy unit).

Problem 2:

Use the methods of this section to derive a formula, similar to below equation, for the multiplicity of an Einstein solid in the “low-temperature” limit, q ≪ N.

Equation:

Step-by-Step Solution:

Step 1 </p>

The value of U is given is

U = N

= The size of the energy unit

Step 2 </p>

To calculate the heat capacity of the einstein solid in the law temperature limit consider the thermodynamic equation.

CV =

CV =

N and are constants so Cv  become

CV = N

CV = N e-

CV = N e-

CV =  e-

Step 3 of 3

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Starting with the result of 1, calculate the heat capacity

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