An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 7.3, Problem 32P
(a)
To determine
The value of the integral of the total number of electrons in the density of states for Fermi energy equal to
(b)
To determine
The value of the integral of the total number of electrons in the density of states for
(c)
To determine
The values and the plot of the integral for the energy as a function of temperature and
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
1-5. In a strictly steady state situation, both the ions and the electrons will follow
the Boltzmann relation
n; = no exp (-4,6/KT,)
For the case of an infinite, transparent grid charged to a potential 6, show that
the shielding distance is then given approximately by
ne 1
AD
€o KT, KT,.
Show that Ap is determined by the temperature of the colder species.
Start by defining
1(1) = N1 sin(7r/a)
(1)
b2(x) = N2 sin(2ñr/a)
(2)
for the infinite square well. Fix N1 and N2 so that
%3D
2)
You should find that p(r) is periodic in time. That is p(x, t + T) = p(x,t). Find
that T, and draw p(x) for at t = 0, t = T/4, t = T/2, and T = 3T/4.
Consider N identical harmonic oscillators (as in the Einstein floor). Permissible Energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on.
A) Calculating the selection function of a single harmonic oscillator. What is the division of N oscillators?
B) Obtain the average energy of N oscillators at temperature T from the partition function.
C) Calculate this capacity and T-> 0 and At T-> infinity limits, what will the heat capacity be? Are these results consistent with the experiment? Why? What is the correct theory about this?
D) Find the Helmholtz free energy from this system.
E) Derive the expression that gives the entropy of this system for the temperature.
Chapter 7 Solutions
An Introduction to Thermal Physics
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Show that when a system is in thermal and...Ch. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13P
Ch. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.4 - Prob. 37PCh. 7.4 - Prob. 38PCh. 7.4 - Prob. 39PCh. 7.4 - Prob. 40PCh. 7.4 - Prob. 41PCh. 7.4 - Prob. 42PCh. 7.4 - Prob. 43PCh. 7.4 - Prob. 44PCh. 7.4 - Prob. 45PCh. 7.4 - Prob. 46PCh. 7.4 - Prob. 47PCh. 7.4 - Prob. 48PCh. 7.4 - Prob. 49PCh. 7.4 - Prob. 50PCh. 7.4 - Prob. 51PCh. 7.4 - Prob. 52PCh. 7.4 - Prob. 53PCh. 7.4 - Prob. 54PCh. 7.4 - Prob. 55PCh. 7.4 - Prob. 56PCh. 7.5 - Prob. 57PCh. 7.5 - Prob. 58PCh. 7.5 - Prob. 59PCh. 7.5 - Prob. 60PCh. 7.5 - The heat capacity of liquid 4He below 0.6 K is...Ch. 7.5 - Prob. 62PCh. 7.5 - Prob. 63PCh. 7.5 - Prob. 64PCh. 7.6 - Prob. 65PCh. 7.6 - Prob. 66PCh. 7.6 - Prob. 67PCh. 7.6 - Prob. 68PCh. 7.6 - If you have a computer system that can do...Ch. 7.6 - Prob. 70PCh. 7.6 - Prob. 71PCh. 7.6 - Prob. 72PCh. 7.6 - Prob. 73PCh. 7.6 - Prob. 75P
Knowledge Booster
Similar questions
- In free spoce, E (2,t) = 10. sin (wt - 82) ox, (V/m) %3D Show that the overage power po ssing through circular disk with a radius of 15.5 m in the Constant plane z= is IW. (Please write down , explaining all the Steps)arrow_forward(a) Fun fact about factorials: (N - 1)! = N! / N , since dividing by N cancels the final factor in N! and leaves just the first N-1 factors. Use this to show that the multiplicity of an Einstein solid can be expressed as: (g + N)! q! N! N q+ N Then apply Stirling's Approximation to each of the factorials, to express the multiplicity as approximately (g + N)o+N N qª NN 2nq(q+ N)' (b) When N and q are both large, we can set the entire square-root in the above multiplicity expression to 1, leaving just: (q + N)N+q N(N,q) = Using this formula, find an expression for the total entropy of the Einstein solid. (c) Use your result from part (b) to find the solid's temperature as a function of its energy. (d) Invert your answer from part (c) to find the energy as a function of temperature, then use it to find a formula for the solid's heat capacity C.arrow_forwardFind an explicit relation for the chemical potential u of a 2DEG at a finite temperature.arrow_forward
- The Einstein model for a solid assumes the system consists of 3N independent simple harmonic oscillators with frequencies &. Within these assumptions, the heat capacity at constant volume as: Cv=3Nk() (-1)² ² Complete the table for the molar heat capacity at various temperatures under either the Einstein model or high-temperature limit. You might like to use the Wolfram Alpha calculator to do the numerical calculations more easily. Use k-0.695 cm /K. High temperature limit value of molar heat capacity of metal is T 1 K 10 K 50 K -1 Einstein, = 100 cm Einstein, : = 500 cm 1.4021 3.8991 100 K 500 K 2.434E-4 1000 K 6.1499 2434E-4 kJ/mol.arrow_forwardFor 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 = 2arrow_forwarda formula was generated for the velocity of an electron that generates a stable waveform. To use that equation you need a constant k. This constant is 2.307×10-28 and the charges are entered as unitless as positive. (That is, if one charge be4ing entered into the formula is a proton, it is entered into the formula as +1.) The mass must be in kg and the distance must be in meters. If all these are entered correctly, the velocity comes out in meters per second. The radius of the orbit of an electron in the Bohr atom of hydrogen is 52.9 pm. What is the velocity of that electron?arrow_forward
- Give only typing answer with explanation and conclusion The Einstein-A coefficient for a particular rovibrational transition of CO2 is 220 s−1. In the absence of collisions, what is the characteristic lifetime of the upper state? Compare this with the Na transition near 589.6nm which has an Einstein-A coefficient of 6.14×10^7 s−1.arrow_forwardHow might I be able to answer Problem 11.1? I could some kind of integral in order to find the average P for part B, but I'm not sure. This section is in a chapter named "Atomic Transitions and Radiation," and is under quantum mechanics.arrow_forwardCalculate the radiative equilibrium temperature of the satellite immedi-ately after it emerges from the earth’s shadow (i.e., when the satelliteis sunlit but the earth, as viewed from the satellite, is still entirely inshadow). Givens: the Earth radiates as a blackbody at an equivalent blackbody temperature TE 255 K, the subtended angle is 2.21 steradians, and the radiative equilibrium temperature of the satellite is 166 K when it is in the Earth's shadowarrow_forward
- write the solution step by step and clearly.arrow_forwardThe E-k relation of a simple cubic lattice given by (4.79) is derived from the tight-binding approximation. Show that near k≈ 0 this relation can be expressed by :-ħ²/26₁a². Ek = Eno + where m* = n²/2ßna². And for kπ/a, show that the E-k relation is given by ħ²k² 2m* where m* = Ek ħ²k² 2m* = Eno +arrow_forwardConsider an object containing 6 one-dimensional oscillators (this object could represent a model of 2 atoms in an Einstein solid). There are 4 quanta of vibrational energy in the object. (a) How many microstates are there, all with the same energy? (b) If you examined a collection of 38000 objects of this kind, each containing 4 quanta of energy, about how many of these objects would you expect to find in the microstate 000004?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON