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 7.2, Problem 16P
(a)
To determine
The dot diagram for all allowed system states.
(b)
To determine
The probability of each energy level being occupied for
(c)
To determine
The values of
(d)
To determine
To draw graph for entropy and energy.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1) Consider a system consisting of two particles, each of which can occupy any one of three
single-particle states, with energy 0, e and 2e.
a)
How many states are there if the particles are bosons? Write down the partition
function for this system?
b)
function for this system?
How many states are there if the particles are fermions? Write down the partition
Draw the Maxwell-Boltzmann, and Fermi-Dirac distributions for a temperature of 10K, 50K and 300K. Assume a Fermi energy of 2.0eV.
Please answer with explanation ASAP.
I will really upvote. Thanks
a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ- x
and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that
state B is unoccupied. In other words, show that the Fermi and Dirac distribution,
ƒ(E)
1
eß(E-μ) +1
is "symmetric" about the point E = μ.
b) Write simplified, approximate expressions for f(E) when
value of E is very close to μ.
(i) E < µ, (ii) E» µ
2
and (iii) the
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
- Show that the one-particle partition function Z₁ for a 2D ideal gas confined to area A is: A 2²/1 Z₁ = Sarrow_forwardHow "density of states" is defined and used in physics? Draw (schematically) the number of occupied energy levels for Fermi Dirac statistics, Maxwell Boltzmann statistics, and Bose Einstein statistics.arrow_forward4. (Kittel 7.4) Chemical potential versus temperature. Explain graphically why the initial curvature of u versus 7 is upward for a fermion gas in one dimension and downward in three dimensions (Figure 7.7). Hint: The D₁(e) and D, (e) curves are different, where D, is given in Problem 1. It will be found useful to set up the integral for N, the number of particles, and to consider from the graphs the behavior of the integrand between zero temperature and a finite temperature.arrow_forward
- Consider a 2D gas of free electrons confined to a square with area A = L a) Determine the state density g(e) of the gas. What is the energy dependence of this space density? b) Determine the fermi energy Ef of the gas given by the number of particles N and the surface area A. Show that at temperature T = 0 K the average energy of the electrons is EF/2.arrow_forwardGiven an Ising model containing two dipoles with interaction energy ±ɛ: enumerate the states of this system and write down their Boltzmann factors. determine the partition function and find the probabilities of the dipoles being parallel and antiparallel. C. plot the probability as a function of kT/ɛ. d. а. b. calculate the total average energy of this system. plot the total average energy normalized to ɛ as a function of kT/ɛ. f. е. Based on your observations from the above, at what temperatures are you more likely to find the dipoles aligned parallel than antiparallel?arrow_forwardProblem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system? (d) What are the quantum state vectors of the first excited state? (e) What is the degeneracy of the first excited state? (f) Discuss qualitatively how the excited-state energies change if we consider the particles to be interacting through the Coulomb potential.arrow_forward
- Consider a closed system with N noninteracting gaseous particles. Let the single particle nondegenerate energy levels be iЄ, i = 0,1,2,........ Evaluate the canonical partition function if the particles are (a) fermions (b) bosons. You are not expected to reach an answer here. This question is to illustrate the difficulty of using canonical ensembles.arrow_forwardTwo nonintercating gaseous particles form an open system. There are three nondegenerate single particle states of energies Є, 2Є, 3Є in the system. Find the canonical partition functions Z0, Zl, Z2 and the grand canonical partition function Z if the particles are (a) fermions (b) bosons What is the average number of particles per state in each case? Calculate the internal energy U? (related to statistical physics)arrow_forwardProblem 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?arrow_forward
- Determine the heat capacity of a two-dimensional layer of atoms in the Debye model. As in the lecture, start with the calculation of the phonon density of states in 2D and solve the integral for the inner energy thereafter. Demonstrate that the heat capacity in 2D scales with T?. You may use the following approximation: J x2 -dx = 2.404. ex-1arrow_forwardWhen developing the partition functions for each degree of freedom in a diatomic ideal gas, we made some approximations. Match the degree of freedom with the approximation(s) we made. Classical (energy levels are continuous) and the addition of one extra state. Classical (energy levels are continuous) no approximations excited states do not contribute significantly [Choose ] [Choose ] [Choose ] [Choose ] ♦arrow_forwardA particle of mass m is bound in a one-dimensional well with one impenetrable wall. The potential energy is given by the equation in the first provided image and the well is depticed in the second provided image. Solve the Shrodinger equation for E < 0 inside and outside the well. Apply the boundary conditions at x = 0 and x = a to obtain an equation that determines the allowed values of E.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning