Space Is Full Of Hot Gas

Classical Mechanics Level 5

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 $2r_0$ ?