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Initially, a main sequence star has a surface temperature of 25000 K and a radius 10 times that of the sun. Its temperature drop to 5000 K as it becomes a supergiant. What is its radius in term of solar radii?

a) 25

b) 50

c) 100

d) 250

e) 500

Well, I tried to do it using luminosity , L=4πR²σT⁴. Since the luminosity is not given, i use the Morgan-Keenan spectral classification to get the luminosity of the star at each phase, thats is at temperature of 25000 K has luminosity of 20,000 and for 5000 K has luminosity of 0.4. I got my final answer as 1.18 solar radius, which mean my answer is wrong. How should i approach the problem? and is that the spectral classification is only for main star sequence? and my friend use the relationship of temperature^4 is inversely proportional to 1/(radius)^2 and he got the answer for 250. BUt doesnt that mean that the luminosity is the same, is this true?

Thanks!

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# Relationship of temperature and radius.

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