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Chapter 7: Quantum Statistics

An Introduction to Thermal Physics
Pages: 257 - 326
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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83 Questions for Chapter 7: Quantum Statistics

  1. Although the integrals (7.53and 7.54) forNand Ucannot be

    Found on Page 285
  2. Use the formula P=-(∂U/∂V)S,N to show that the pressure of a photon gas is 1/3 times the energy density (U/V). Compute the pressure exerted by the radiation inside a kiln at 1500 K, and compare to the ordinary gas pressure exerted by the air. Then compute the pressure of the radiation at the centre of the sun, where the temperature is 15 million K. Compare to the gas pressure of the ionised hydrogen, whose density is approximately 105 kg/m3.

    Found on Page 297
  3. d

    Found on Page 323
  4. Near the cells where oxygen is used, its chemical potential is significantly lower than near the lungs. Even though there is no gaseous oxygen near these cells, it is customary to express the abundance of oxygen in terms of the partial pressure of gaseous oxygen that would be in equilibrium with the blood. Using the independent-site model just presented, with only oxygen present, calculate and plot the fraction of occupied heme sites as a function of the partial pressure of oxygen. This curve is called the Langmuir adsorption isotherm ("isotherm" because it's for a fixed temperature). Experiments show that adsorption by myosin follows the shape of this curve quite accurately.

    Found on Page 260
  5. Consider a system of five particles, inside a container where the allowed energy levels are nondegenerate and evenly spaced. For instance, the particles could be trapped in a one-dimensional harmonic oscillator potential. In this problem you will consider the allowed states for this system, depending on whether the particles are identical fermions, identical bosons, or distinguishable particles.

    Found on Page 265
  6. For a system of fermions at room temperature, compute the probability of a single-particle state being occupied if its energy is

    Found on Page 269
  7. Consider two single-particle states, A and B, in a system of fermions, where ϵA=μ-xand ϵB=μ+x; that is, level A lies below μ by the same amount that level B lies above μ. Prove that the probability of level B being occupied is the same as the probability of level A being unoccupied. In other words, the Fermi-Dirac distribution is "symmetrical" about the point where ϵ=μ.

    Found on Page 269
  8. For a system of bosons at room temperature, compute the average occupancy of a single-particle state and the probability of the state containing 0,1,2,3bosons, if the energy of the state is

    Found on Page 269
  9. For a system of particles at room temperature, how large must ϵ-μbe before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1%? Is this condition ever violated for the gases in our atmosphere? Explain.

    Found on Page 270
  10. For a system obeying Boltzmann statistics, we know what μis from Chapter 6. Suppose, though, that you knew the distribution function (equation 7.31) but didn't know μ. You could still determine μ by requiring that the total number of particles, summed over all single-particle states, equal N. Carry out this calculation, to rederive the formula μ=-kTlnZ1/N. (This is normally how μ is determined in quantum statistics, although the math is usually more difficult.)

    Found on Page 270

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