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A shell of gas surrounds a supernova remnant. The shell has thickness t, inner radius R (such that t / R <<1) and constant temperature T. Let P_{0} and rho_{0} be the gas pressure and density, the base of the shell (not under the shell, which is empty!). Assume a density profile dot rho(r) = rho_{0} * (r/8) ^ - 1 . Assuming that the shell is supported against gravitational collapse by its internal energy and pressure, use the Virial Theorem to find the equilibrium mass M of the shell in terms of its pressure, density, and radius.