An Introduction to Thermal Physics
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 7.6, Problem 66P

(a)

To determine

To calculate the value of ground state energy of rubidium-87.

(b)

To determine

To calculate the condensation temperature.

(c)

To determine

To find the number of atoms in ground state and first excited state.To find the difference of chemical potential with ground state energy for T=0.9Tc .

(d)

To determine

The condensation temperature, chemical potential, energy of atoms in ground state and first excited state for 106 atoms.

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For an Einstein solid with each of the following values of Nand q, list all of the possible microstates, count them, and verify formula 2.9. N = 4, q = 2
Problem 1: This problem concerns a collection of N identical harmonic oscillators (perhaps an Einstein solid) at temperature T. The allowed energies of each oscillator are 0, hf, 2hf, and so on. a) Prove =1+x + x² + x³ + .... Ignore Schroeder's comment about proving 1-x the formula by long division. Prove it by first multiplying both sides of the equation by (1 – x), and then thinking about the right-hand side of the resulting expression. b) Evaluate the partition function for a single harmonic oscillator. Use the result of (a) to simplify your answer as much as possible. c) Use E = - дz to find an expression for the average energy of a single oscillator. z aB Simplify as much as possible. d) What is the total energy of the system of N oscillators at temperature T?
For an Einstein solid with each of the following values of Nand q, list all of the possible microstates, count them, and verify formula 2.9. N = 1 , q = anything
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