Space Is Full Of Hot Gas

A hot, spherically symmetric cloud of an ideal gas (H2H_2 for example) is in intergalactic space. The gas is in equilibrium and the density ρ(r)\rho(r) of the gas is given by ρ(r)=ρ0r2\rho(r)=\rho_0r^{-2}. What is the ratio of the temperature at a distance r0r_0 to the temperature at a distance 2r02r_0?

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