An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 7.4, Problem 40P
To determine
The expression for the density of states of a photon gas and plot for the function.
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Starting from equation 7.83 attached, derive a formula for the density of states of a photon gas (or any other gas of ultrarelativistic particles having two polarization states). Sketch this function.
For Problem 9.18, how do I determine part A & B? This is from a chapter titled, "Electron Spin." This chapter is part of quantum mechanics.
8.5 Calculate the grand partition function for a system of N noninteracting quantum
mechanical harmonic oscillators, all of which have the same natural frequency wn. Do this
for the following two cases:
(a) Boltzmann statistics
(b) Bose statistics.
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
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Similar questions
- 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?arrow_forwardLiquid He (consisting of just a single isotope He-4, which is a boson) undergoes a super- fluid transition at temperature T = 2.16K. At this temperature, it has a mass density of 0.145g/cm³. Make an assumption that liquid helium behaves like an ideal gas and compute the critical temperature for Bose-Einstein condensation. Express your answer in Kelvins. What is the mass density of He atoms at excited states at this temperature? Express your answer in g/cm³ units. What can be said about the chemical potential of He-4 atoms at this point?arrow_forward8.8 Calculate by direct integration the expectation values (r) and (1/r) of the radial position for the ground state of hydrogen. Compare your results to the quoted expressions in Eq. (8.89) and discuss your results. Did you expect that (1/r) # 1/(r)? Use your result for (1/r) to find the expectation value of the kinetic energy of the ground state of hydrogen and discuss your result. 8.9 Calculate by direct integration the expectation value of the radial position for each of thearrow_forward
- Problem # 2. In the two-level system, estimate the emission line full width at half maximum (FWHM) for spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about 3,000 nanoseconds.arrow_forwardPROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (x2), (p²), and the product (r2)(p²).arrow_forwardConsider 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_forward
- 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?arrow_forwardConsider a hypothetical star of radius R, with density rho that is constant,i.e., independent of radius. The star is composed of a classical, nonrelativistic, ideal gas of fully ionized hydrogen. Solve the equations of stellar structure for the pressure profile, P(r), with the boundary condition P(R)=0 An image of the stellar structure equations is attached.arrow_forwardConsider a system of two Einstein solids, A and B, each containing10 oscillators, sharing a total of 20 units of energy. Assume that the solids areweakly coupled, and that the total energy is fixed. What is the probability of finding exactly half of the energy in solid A?arrow_forward
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