A main sequence star gradually expands into a red giant, increasing its radius by a factor of 100, while its surface temperature decreases slightly. Based on the Stefan-Boltzmann Law, what happens to its luminosity?

The Stefan-Boltzmann Law gives luminosity as L = 4πR²σT⁴. Increasing the radius by a factor of 100 multiplies the radius-squared part by 10,000; a slight decrease in surface temperature reduces luminosity, but not enough to offset that large increase. Therefore, the luminosity increases dramatically.

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