schroeder introduction to thermal physics solutions 2.42

Urn:lcp:introductiontoth0000schr_k1f1:epub:944d1b85-ff17-4cb2-b023-cf71b02d17b1 Foldoutcount 0 Identifier introductiontoth0000schr_k1f1 Identifier-ark ark:/13960/s2skfk44rvz Invoice 1652 Isbn 0201380277 Lccn 99031696 Ocr tesseract 5.0.0-1-g862e Ocr_detected_lang en Ocr_detected_lang_conf 1.0000 Ocr_detected_script Latin Ocr_detected_script_conf 0.9886 Ocr_module_version 0.0.15 Ocr_parameters -l eng Old_pallet IA-WL-1300127 Openlibrary_edition 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.Access-restricted-item true Addeddate 16:08:40 Bookplateleaf 0003 Boxid IA40364009 Camera Sony Alpha-A6300 (Control) Collection_set printdisabled External-identifier 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