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Chapter 9: Q77E (page 409)
At what wavelength does the human body emit the maximum electromagnetic radiation? Use Wien's law from Exercise 79 and assume a skin temperature of.
The wavelength at which human body emits maximum electromagnetic radiation .
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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 -axis?
Heat capacity (at constant volume) is defined as. (a) Using a result derived in Example 9.6. obtain an expression for the heat capacity per unit volume, in, of a photon gas. (b) What is its value at?
The exact probabilities of equation (9-9) rest on the claim that the number of ways of addingdistinct non-negative integer to give a total of is . One way to prove it involves the following trick. It represents two ways that distinct integers can add to and, respectively. In this special case.
The X's represent the total of the integers, -each row has . The represent "dividers" between the distinct integers of which there will of course be each row has . The first row says that is (three before the divider between it and ), is (no between its left divider with and its right divider with ), ) is . through are , is , and and are . The second row says that is . is , is , and all other are . Further rows could account for all possible ways that the integers can add to . Argue that properly applied, the binomial coefficient (discussed in Appendix ) can be invoked to give the correct total number of ways for any and .
The temperature of our Sun鈥檚 surface is .(a) At what wavelength is the spectral emission of the Sun is maximum? (Refer to Exercise 79.) (b) Is there something conspicuous about this wavelength?
Figure 9.8 cannot do justice to values at the very highspeed end of the plot. This exercise investigates how small it really gets. However, although integrating the Maxwell speed distribution over the full range of speeds from 0 to infinity can be carried out (the so-called Gaussian integrals of Appendix K), over any restricted range, it is one of those integrals that. unfortunately. cannot be done in closed form. Using a computational aid of your choice. show that the fraction of molecules moving faster thanis; faster thanis; and faster thanis. where" from Exercise 41, is. (Exercise 48 uses these values in an interesting application.)
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