A hot, spherically symmetric cloud of an ideal gas (\(H_2\) for example) is in intergalactic space. The gas is in equilibrium and the density \(\rho(r)\) of the gas is given by \(\rho(r)=\rho_0r^{-2}\). What is the ratio of the temperature at a distance \(r_0\) to the temperature at a distance \(2r_0\)?

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