schroeder introduction to thermal physics solutions 2.42

These are the problems that I would recommendworking in a first course, or when reading through the book for thefirst time. Schroeder, Department of Physics, Weber State Universityīecause the book contains so many problems, first-time instructorsand students using the book for self-study may appreciate the following'recommended' list. Aside from a factor of 8 π 2, your result should agree with the exact formula for the entropy of a black hole, obtained* through a much more difficult calculation:ĭ Calculate the entropy of a one-solar-mass black hole, and comment on the result.Thermal Physics Recommended Problems Recommended Problemsĭaniel V. By setting the total energy of the photons equal to M c 2, estimate the maximum number of photons that could be used to make a black hole of mass M.

But the wavelength can't be any longer than the size of the black hole. 36, explain why the entropy of a black hole, in fundamental units, should be of the order of the maximum number of particles that could have been used to make it.ĬTo make a black hole out of the maximum possible number of particles, you should use particles with the lowest possible energy: long-wavelength photons (or other massless particles). Calculate the approximate radius of a one-solar-mass black hole M = 2 × 10 30 k g. Knowing this, it's not hard to estimate the entropy of a black hole.Ī Use dimensional analysis to show that a black hole of mass M should have a radius of order G M / c 2, where G is Newton's gravitational constant and c is the speed of light. Therefore, the entropy of a black hole must be greater than the entropy of any conceivable type of matter that could have been used to create it. It turns out that there's no way to tell (at least from outside) what kind of matter has gone into making a black hole.

In fact, it is irreversible in the thermodynamic sense as well: Adding mass to a black hole increases the black hole's entropy.

Throwing something into a black hole is therefore an irreversible process, at least in the everyday sense of the word. A black hole is a region of space where gravity is so strong that nothing, not even light, can escape.

Schroeder introduction to thermal physics solutions 2.42