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Unformatted text preview: Print your name clearly: Signature: I agree to neither give nor receive aid during this exam. Midterm Exam for Physics/ECE 176 Professor Greenside Thursday, March 3, 2011 This exam is closed book and no electronic devices are allowed. The test will last the entire class period. Please note the following: 1. All questions except true-false should be answered on the extra blank pages. Please use plenty of space and paper so that I can read and understand what you wrote with a reasonable effort. 2. Please write your name and the problem number at the top of each extra page. 3. Unless otherwise stated, you need to justify your answers, at least briefly. Problems That Require Writing 1. Black holes are simple pure objects in that, no matter what kind of matter collapsed to form the black hole, only three numbers are needed to define its macrostate: the black holes mass M , its electrical charge Q , and its angular momentum L . For an electrically-neutral non-rotating black hole ( Q = 0, L = ), the black holes entropy S depends only on M and is given by S = 8 2 kG hc M 2 (1) where k is Boltzmanns constant, G is the gravitational constant, h is Plancks constant, and c is the speed of light. (a) (5 points) Given that the energy of a black hole is its relativistic rest mass U = Mc 2 , derive a formula for the temperature T of a black hole in terms of its mass M . Does decreasing the mass of a black hole make it hotter or colder? (b) (5 points) Estimate to the nearest power of ten the temperature 1 T of a black hole whose mass is one solar mass, M 10 30 kg. (c) (5 points) Qualitatively sketch how the heat capacity C ( T ) of the black hole varies with the black holes temperature T for T 0, and discuss whether C ( T ) is compatible with the third law of thermodynamics. 1 Since black holes are effectively in thermal contact with the cosmological photon gas that fills the universe, the really interesting question is whether a particular black hole is hotter or colder than the temperature of this photon gas, T 3 K. 1 2. A kilogram of ice ( T 1 = 0 C) and a kilogram of boiling water ( T 2 = 100 C) at atmospheric pressure are mixed together in a thermally isolated container and allowed to come to thermodynamic equilibrium. (a) (5 points) To one significant digit, calculate the final temperature T f in Celsius inside the container and describe what you will find in the container if you open it up....
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This note was uploaded on 10/20/2011 for the course PHYSICS 176 taught by Professor Behringer during the Spring '08 term at Duke.
- Spring '08