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Unformatted text preview: Assignment #5 PHYSICS 8.284 due 11:04 am Friday 2006 March 17th Reading: Hansen and Kawaler (Hayden reserve only): 3.1-3.5 (eqn 3.67) on quan- tum statistics, distribution functions and equations of state and 7.1-7.2 (eqn 7.45) on polytropes. 1. Solve the Lane-Emden equation for an n=3/2 polytrope using Runge-Kutta integra- tion from = to the point where the density first reaches zero. Plot n (which is proportional to density) and 4 2 d (which is proportional to the mass interior to d ) as a function of . 2. In class we derived an expression for the gravitational binding energy, , of a poly- trope of index n. Use the virial theorem to derive and expression for the total in- ternal energy, U , of such a polytrope. Define the average temperature, T , such that U = M 3 kT . Compute the ratio of the central temperature T c to this average tem- m p 2 perature....
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- Spring '06