The Stephan-Boltzman Law states that a star’s luminosity, temperature and size a

Question

The Stephan-Boltzman Law states that a star’s luminosity, temperature and size are related as: L=4R2T4

a) If a star has a surface temperature four times higher than that of the Sun and twice the radius, by what factor is the star more luminous than the Sun?

b) In about 7 billion years, the Sun will become a red giant star with a luminosity that is 7,500 times greater than its current luminosity and a temperature that is half (0.5) its current temperature. How much larger will the Sun get? Which planets would be swallowed up by the Sun when it becomes a red giant? The current radius of the Sun is 695,500 km and the distances to each planet are listed in the table at the end of this problem set.

Explanation / Answer

L=4R2T4

Given,

star has a surface temperature four times higher than that of the Sun and twice the radius.

Hence, L becomes, (2)^2*(4)^4 = 1024 times that of SUN

b)

R^2 = L/4T4

SO, R ^2 = 7500/(0.5)^4 = 12*10^4

New Radius os Sun, R = 346.4 times the actual Radius of sun

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