The hot glowing surfaces of stars emit energy in the form of electromagnetic rad
ID: 1973847 • Letter: T
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 is equal to 1 for these surfaces.Part A: 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^4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
Part B:Find the radius of the star Procyon B, which radiates energy at a rate of 2.1*10^23 W and has a surface temperature of 10,000 K . Assume that the star is spherical.
Use 5.67*10^-8 W/m^2*K^4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures
Explanation / Answer
Stefan-Boltzmann law states that the energy flux by radiation is proportional to the forth power of the temperature: q = e · s · T^4 The total energy flux at a spherical surface of Radius R is Q = q·p·R² = e·s·T^4·p·R² Hence the radius is R = v( Q / (e·s·T^4·p) ) = v( 2.7x10+32 W / (1 · 5.67x10-8W/m²K^4 · (1100K)^4 · p) ) = 3.22x10+13 m
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