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

r = 1.61 x 10^{11} m

Step-by-step 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{(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