Two stars have the same mass and luminosity, but the surface of one of them is twice as hot as the surface of the other. Which star has a higher average density? How many times?
According to the Stefan-Boltzmann law, the luminosity of a star is proportional to R ^ 2T ^ 4, where R and T are its radius and temperature. Equality of luminosities at temperatures other than two times means that a cooler star has a radius 4 times larger than that of a hot star. And if the masses are equal, this means that the density of a cooler star is 64 times less than that of a hot star.
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