×
Log in to StudySoup
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 7 - Problem 70p
Join StudySoup for FREE
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 7 - Problem 70p

Already have an account? Login here
×
Reset your password

Figure shows the heat capacity of a Bose gas as a function

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 70P Chapter 7

An Introduction to Thermal Physics | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

4 5 1 289 Reviews
13
2
Problem 70P

Problem 70P

Figure shows the heat capacity of a Bose gas as a function of temperature. In this problem you will calculate the shape of this unusual graph.

(a) Write down an expression for the total energy of a gas of N bosons confined to a volume V, in terms of an integral (analogous to equation 7.122).

(b) For T < Tc you can set µ = 0. Evaluate the integral numerically in this case, then differentiate the result with respect to T to obtain the heat capacity. Compare to Figure.

(c) Explain why the heat capacity must approach  Nk in the high-T limit.

(d) For T > Tc you can evaluate the integral using the values of µ calculated in Problem. Do this to obtain the energy as a function of temperature, then numerically differentiate the result to obtain the heat. capacity. Plot the heat capacity, and check that your graph agrees with Figure.

Figure: Heat capacity of an ideal Bose gas in a three-dimensional box.

Problem:

If You have a computer system that can do numerical integrals, It’s not particularly difficult to evaluate μ for T > Tc.

(a) As usual when solving a problem on a computer, it’s best to start by putting everything m terms of dimensionless variables. So define t == T /Tc , c = μ/kTc, and x = ϵ/kTc. Express the integral that defines μ, equation , in terms of these variables. You should obtain the equation

(b) According to Figure 7.33, the correct value of c when T = 2Tc is approximately –0.8. Plug in these values and check that the equation above is approximately satisfied.

(c) Now vary μ, holding T fixed, to find the precise value of μ for T = 2Tc Repeat for values of T/Tc ranging from 1.2 up to 3.0, in increments of 0.2. Plot a graph of μ as a function of temperature.

Step-by-Step Solution:
Step 1 of 3

. Day 1 Wednesday, January 11, 2017 11:31 AM Day 2 Friday, January 13, 2011:05 AM Day 2 Friday, January 13, 2011:27 AM Day 2 Friday, January 13, 2011:47 AM Day 2 Friday, January 13, 2012:06 PM Day 3 Wednesday, January 18, 20111:13 AM Day 3 Wednesday, January 18, 201711:28 AM Day 3 Wednesday, January 18, 2017 11:37 AM Day 3 Wednesday, January 18, 201711:52 AM Day 3 Wednesday, January 18, 2017 12:04 PM Day 4 Friday, January 20, 2011:10 AM Day 4 Friday, January 20, 2011:10 AM Day 4 Friday, January 20, 2011:10 AM Day 4 Friday, January 20, 2011:10 AM

Step 2 of 3

Chapter 7, Problem 70P is Solved
Step 3 of 3

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Figure shows the heat capacity of a Bose gas as a function