consider two spheres of ionized hydrogen plasma, which emits bremsstrahlung radi- ation. both have a mass m and a uniform temperature t. the first sphere has radius r1 and is optically thin. the second sphere has radius r2 and is optically thick. the rough physical scenario this represents is the isothermal collapse of a cloud of gas that is cooled by bremsstrahlung. what are the luminosities of the spheres in terms of their masses, radii, and/or temperatures?