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Chapter 9: Statistical Mechanics

Expert-verified
Modern Physics
Pages: 347 - 412
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Illustration

89 Questions for Chapter 9: Statistical Mechanics

  1. Show that the rms speed of a gas molecule, defined as vrms≡v2, is given by3kBTm.

    Found on Page 405

  2. Found on Page 405

  3. Found on Page 405

  4. Determine the relative probability of a gas molecule being within a small range of speeds around 2vrmsto being in the same range of speeds around vrms.

    Found on Page 405

  5. (a) From equation (9.34) and the Fermi-Dirac distribution given in Exercise 53, obtain an expression for EF(T), the Fermi temperature for a collection of fermion oscillators, (b) Show that EFo=ε. (c) Plot EF(T)versuskBTεfrom 0tokBT6=1.5. (d) By what percent does the Fermi energy drop from its maximum T=0value when kBTrises to 25%ofε?

    Found on Page 407

  6. The electromagnetic intensity thermally radiated by a body of temperature Tis given by I=σT4whereσ=5.67×10−8W/m2⋅K4

    Found on Page 409

  7. The fact that a laser's resonant cavity so effectively sharpens the wavelength can lead to the output of several closely spaced laser wavelengths, called longitudinal modes. Here we see how. Suppose the spontaneous emission serving as the seed for stimulated emission is of wavelength , but somewhat fuzzy, with a line width of roughly0.001nm either side of the central value. The resonant cavity is exactly60cm long. (a) How many wavelengths fit the standing-wave condition'? (b) If only u single wavelength were desired, would change the length of the cavity help? Explain.

    Found on Page 347

  8. Somehow you have a two-dimensional solid, a sheet of atoms in a square lattice, each atom linked to its four closest neighbors by four springs oriented along the two perpendicular axes. (a) What would you expect the molar heat capacity to be at very low temperatures and at very high temperatures? (b) What quantity would determine, roughly, the line between low and high?

    Found on Page 347

  9. Discusses the energy balance in a white dwarf. The tendency to contract due to gravitational attraction is balanced by a kind of incompressibility of the electrons due to the exclusion principle.

    Found on Page 347

  10. There are more permutations of particle labels when two particles have energy0 and two have energy1 than when three particles have energy 0and one has energy . 2(The total energiesarethe same.) From this observation alone argue that the Boltzmann distribution should be lower than the Bose-Einstein at the lower energy level.

    Found on Page 403

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