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Through a comparison of solar luminosity and temperature seen with the H-R diagram. On this diagram, stars sharing the same temperature but different luminosities show measurable differences in radius as well as mass. So if two stars both have the same visible surface temperature but one is more luminous, it has to be larger. This is further explained by Stefan Boltzmann's law,
L=(4πR^2 x sigma(constant) x T^4)
A Star with the the same surface temperature with larger surface area results in more Luminosity.

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