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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

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 just5hω0 . 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 still5hω0 .) 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?

:In a certain design of helium-neon laser, the chamber containing these gases has a perfect mirror at one end. as usual, but only a window at the other, Beyond the window, is a region of free air space and then the second mirror, which is partially reflecting, allowing the beam to exit. The resonant cavity between the mirrors thus has a region free of the helium-neon gas-the "lasing material"-in which you can insert something. If you insert a sheet of clear plastic at any orientation in this region between the mirrors, the laser beam disappears. If the same sheet is placed in the beam outside the partially reflecting mirror, the beam passes through it, regardless of the orientation. Why?

Classically, what would be the average energy of a particle in a system of particles fine to move in the xy-plane while rotating about the i-axis?

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.

The entropy of an ideal monatomic gas is(3/2)NkBlnE+,NkBlnV-NkBlnN to within an additive constant. Show that this implies the correct relationship between internal energy Eand temperature.
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