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 8P
(a)
To determine
The partition function of system for one particle in a box.
(b)
To determine
The partition function of system for two distinguishable particles in a box.
(c)
To determine
The partition function of system for two identical bosons in a box.
(d)
To determine
The partition function of system for two identical fermions in a box.
(e)
To determine
The partition function of system according to equation
(f)
To determine
The probability of finding of two distinguishable particles in a same single-state; the probability of finding of two identical bosons in a same single-state; the probability of finding of two identical fermions in a same single-state.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For simplicity, assume that each of these states has energy zero.
What is the partition function of this system if the box contains only one particle?
Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For simplicity, assume that each of these states has energy zero.
What is the partition function of this system if the box contains two distinguishable particles?
Draw an energy level diagram for a nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15· (h2/8mL2). Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?
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
- For a particle in a box of length L sketch the wavefunction corresponding to the state with the lowest energy and on the same graph sketch the corresponding probability density. Without evaluating any integrals, explain why the expectation value of x is equal to L/2.arrow_forwardFor a system of fermions at room temperature, compute the probability of a single-particle state being occupied if its energy is. 1 eV less than μarrow_forwardConsider both a finite potential well and an infinite potential well. When inside the boxes, may particles be stationary? Explain why.arrow_forward
- Use the fact that at the critical point the first and second partial derivatives of P with respect to Vm at constant T are zero (∂P/∂Vm=∂2P/∂V2m=0) to derive the expressions for the Van der Waals constants in terms of critical parameters. Show full and complete procedure, do not skip any steparrow_forwardSuppose there is a two state system with energies ε_0 = 0 and ε_1 = kT that follows the Boltzmann distribution. What is the partition function?arrow_forwardAt what displacements is the probability density a maximum for a state of a harmonic oscillator with v = 1? (Express your answers in terms of the coordinate y.)arrow_forward
- If you double the width of a one-dimensional infinite potential well, (a) is the energy of the ground state of the trapped electron multiplied by 4, 2, , , or some other number? (b) Are the energies of the higher energy states multiplied by this factor or by some other factor, depending on their quantum number?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_forwardI need help with this question. Can you show me step by step? Please and thank you! For a particle in a one-dimensional box in its ground state calculate the probability that theparticle is in the middle third of a box?arrow_forward
- 1. a. For a free particle, write the relations between the wave vector k and itsmomentum vector p and angular frequency ω and its energy E.b. What is the general form in one dimension of the wave function for a freeparticle of mass m and momentum p?c. Can this wave function ever be entirely real? If so, show how this ispossible. If not, explain why not.d. What can you say about the integral of the |Ψ (x; t)|^2 from - ∞ to + ∞ ?e. Is this a possible wave function for a real, physical particle? Explain whyor why not.arrow_forwardConsider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate the total probability of finding the particle between x = 0 and x = L/12? Provide your answer to three significant figures.arrow_forwardSuppose you have an ideal gas of fermions at room temperature (293 K). How large must E EF be for Fermi-Dirac and Maxwell-Boltzmann statistics to agree to within 1%? Do you think the agreement is within 1% for ideal gases under normal conditions?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 LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning