Question

Find the radius Rrigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×10^31 W and has a surface temperature of 11,000 K. Assume that the star is spherical.

Answer 1

Answer:

r = 1.61 x 10^{11} m

Explanation:

energy radiated (H) = 2.7 x 10^31 W

surface temperature (T)  = 11,000 k

assuming ε = 1 and taking σ = 5.67 x 10^{-8} W/m^{2}.K^{4}

we can find the radius of the star from the equation below

H = A x  ε x σ x T^{4}              

where area (A) = 4 x π x r^{2} (assuming it is a sphere)

therefore  the equation becomes

H = 4 x π x r^{2} x  ε x σ x T^{4}  

2.7 x 10^31  = 4 x π x r^{2} x  1 x 5.67 x 10^{-8}  x (11,000)^{4}

r = $\sqrt{\frac{2.7 x 10^31}{4 x π x 1 x 5.67 x 10^{-8} x (11,000)^{4}} }$

r = 1.61 x 10^{11} m