The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.9 × 1015 m (around 6 light years) with a total mass 4000 times the mass of the Sun. If the gas is all diatomic hydrogen and the pressure in the nebula is Pn = 6.8 × 10-9 Pa, what is the average temperature (in K) of the nebula? Assume the mass of the sun is Ms = 1.989 × 1030 kg and the mass of a hydrogen atom is mH = 1.67 × 10-27 kg.