The hot glowing surfaces of stars emit energy in the form of electromagnetic rad

Question

The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume that the emissivity e is equal to 1 for these surfaces. Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×10^31W and has a surface temperature of 11,000 K. Assume that the star is spherical. Use =5.67×10^8W/m2K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures. Find the radius RProcyonB of the star Procyon B, which radiates energy at a rate of 2.1×10^23W and has a surface temperature of 10,000 K. Assume that the star is spherical. Use =5.67×10^8W/m2K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.

Explanation / Answer

(Stefan-Boltzmann law)
L = 4pi*R^2*sigma*T^4

Solving for R we get:
=> R = (1/(2T^2)) * sqrt(L/(pi*sigma))

a) Plugging in your values you should get:
=> R = (1/(2(11,000K)^2)) *sqrt((2.7*10^31W)/(pi * (5.67*10^-8 W/m^2K^4)))
R = 1.609 * 10^10 m

b)R = (1/(2(10,000K)^2)) *sqrt((2.1*10^23W)/(pi * (5.67*10^-8 W/m^2K^4)))

R = 1.286 * 10^8 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.