Cold, interstellar, molecular clouds have been seen to contain the cynogen molecule, CN, whose first rotational excited states have an energy of 4.7*10^-4 eV above the ground state. There are actually 3 such excited states, all with the same energy. In 1941, studies of these molecular clouds, using the absorption of starlight passing through them, showed that for every ten CN molecules that are in the ground state, a total of approximately three others are in the three excited states (this means that, on average, one is in each of these 3 excited states). To account for this data, astronomers postulated that the molecules were in thermal equilibrium with some reservoir at a well defined temperature.
What is that T?
In thermal equilibrium with temperature T, which is the temperature of the thermal reservoir we are requested to find, the ratio of populations of energy levels E_a and E_b is
n_b/n_a = (g_b/g_a) exp( - (E_b-E_a) / kT ), ...