schroeder introduction to thermal physics solutions 2.42

b) In the spirit of below Problem, 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. Calculate the approximate radius of a one-solar-mass black hole ( M = 2 × 1030 kg). a) Use dimensional analysis to show that a black hole of mass M should have a radius of order GM/c 2, where G is Newton’s gravitational constant and c is the speed of light. Knowing this, it’s not hard to estimate the entropy of a black hole. 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. The problems and worked examples explore applications not just within physics but also to engineering, chemistry, biology, geology, atmospheric science, astrophysics, cosmology, and everyday life.Problem 42P A black hole is a region of space where gravity is so strong that nothing, not even light, can escape.

You will also learn to use basic quantum physics and powerful statistical methods to predict in detail how temperature affects molecular speeds, vibrations of solids, electrical and magnetic behaviors, emission of light, and exotic low-temperature phenomena. You will learn to apply the general laws of energy and entropy to engines, refrigerators, chemical reactions, phase transformations, and mixtures. This book will give you a working understanding of thermal physics, assuming that you have already studied introductory physics and calculus. Alternatively, we can measure the bulk properties of a material, and from these infer something about the particles it is made of. So in thermal physics we assume that these motions are random, and we use the laws of probability to predict how the material as a whole ought to behave. We can't possibly follow every detail of the motions of so many particles. Examples include the air in a balloon, the water in a lake, the electrons in a chunk of metal, and the photons given off by the sun. Thermal physics deals with collections of large numbers of particles - typically 10 to the 23rd power or so.

Oxford Research Encyclopedias: Global Public Health.

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Oxford Commentaries on International Law.

Schroeder introduction to thermal physics solutions 2.42