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Chapter 9: Q12CQ (page 403)

A. block has a cavity inside, occupied by a photon gas. Briefly explain what the characteristic of this gas should have to do with the temperature of the block.

Short Answer

Expert verified

Electromagnetic radiation is emitted from matter because it contains thermally oscillating charged particles. In our example, photon gas is produced by oscillating charged particles along the hollow walls of the block.

Step by step solution

01

Photon gas

A photon gas is a collection of photons that resembles a gas and has many of the same characteristics of a typical gas, such as hydrogen or neon, such as pressure, temperature, and entropy. The most prevalent illustration of an equilibrium photon gas is black-body radiation.

02

Average Energy of Oscillating Charges

The photon gas is in thermal equilibrium with the cavity in which it is contained. As a result, the gas's temperature can be assumed to be the same as the containers. Gas is present in it due to thermally oscillating charges. The quantity of energies and possible frequencies are determined by the average energy of oscillating charges.

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Most popular questions from this chapter

Defend or refuel the following claim: An energy distribution, such as the Boltzmann distribution. specifies the microstate of a thermodynamic system.

The exact probabilities of equation (9-9) rest on the claim that the number of ways of addingNdistinct non-negative integer to give a total ofM is (M+N-1)![M!(N-1)!] . One way to prove it involves the following trick. It represents two ways that Ndistinct integers can add toM-9 and5, respectively. In this special case.

The X's represent the total of the integers, M-each row has 5. The 1'srepresent "dividers" between the distinct integers of which there will of course be N-Ieach row has8 . The first row says thatn1 is3 (three X'sbefore the divider between it andn2 ), n2is0 (noX's between its left divider withn1 and its right divider withn3 ),n3 ) is1 . n4throughn6 are0 , n7is1 , and n8and n9are0 . The second row says that n2is 2. n6is 1, n9is2 , and all othern are0 . Further rows could account for all possible ways that the integers can add toM . Argue that properly applied, the binomial coefficient (discussed in AppendixJ ) can be invoked to give the correct total number of ways for anyN andM .

We claim that the famous exponential decrease of probability with energy is natural, the vastly most probable and disordered state given the constraints on total energy and number of particles. It should be a state of maximum entropy ! The proof involves mathematical techniques beyond the scope of the text, but finding support is good exercise and not difficult. Consider a system of11oscillators sharing a total energy of just5丑蝇0 . In the symbols of Section 9.3. N=11andM=5 .

  1. Using equation(9-9) , calculate the probabilities ofn , being0,1,2, and3 .
  2. How many particlesNn , would be expected in each level? Round each to the nearest integer. (Happily. the number is still 11. and the energy still5丑蝇0 .) What you have is a distribution of the energy that is as close to expectations is possible. given that numbers at each level in a real case are integers.
  3. Entropy is related to the number of microscopic ways the macro state can be obtained. and the number of ways of permuting particle labels withN0 ,N1,N2 , and N3fixed and totaling11 is11!(N0!N1!N2!N3!) . (See Appendix J for the proof.) Calculate the number of ways for your distribution.
  4. Calculate the number of ways if there were6 particles inn=0.5 inn=1 and none higher. Note that this also has the same total energy.
  5. Find at least one other distribution in which the 11 oscillators share the same energy, and calculate the number of ways.

  6. What do your finding suggests?

Suppose that in Figure 9.27, the level labelled E1, rather than the one labelledE2, were metastable. Might the material still function as a laser? Explain.

In Exercise 35, a simple two-state system is studied. Assume that the particles are distinguishable. Determine the molar specific heat Cvof this material and plot it versus T. Explain qualitatively why it should behave as it does.
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