Find the radius of the star Rigel, the bright blue star in the constellation Ori

Question

Find the radius of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7*10^32 W and has a surface temperature of 11,000 K . Assume that the star is spherical.
Use 5.67*10^-8 w/m^2*K for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
R rigel = ______________ m

Find the radius of the star Procyon B, which radiates energy at a rate of 2.1*10^32 and has a surface temperature of 10,000 K . Assume that the star is spherical.
Use 5.67*10^-8 w/m^2*K for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
R procyon b = ________________________m

Explanation / Answer

Given : . Energy radiated (Q) = 2.7 * 1032 W . Temp (T) = 11000 K ; . Stefan-Boltzmann law states that the energy flux by radiationis proportional to the forth power of the temperature: . q = e ·s · T4 . The total energy flux at a spherical surface of Radius R is : . Q =q·p·R² =e·s·T4 * p R² Hence the radius is : . R = v( Q /(e·s·T^4·p) ) . = v(2.7 * 1032 W / (1 * 5.67 *10-8 W/m²K4 *(1100K)4 · p) ) . = 3.22 *1013 m . Similarly calculate for (b) . Hope this helps u1

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