The hot glowing surfaces of stars emit energy in the form of electromagnetic rad
ID: 1980731 • 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 and has a surface temperature of 11,000 . Assume that the star is spherical.
Use for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
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Part B
Find the radius of the star Procyon B, which radiates energy at a rate of and has a surface temperature of 10,000 . Assume that the star is spherical.
Use for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
=
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) . Power ( P )= 2.1*10^23W Temperature ( T ) = 10,000 K emissivity ( e ) = 1 P = e s AT4 A = P / e sT4 But the area of the star ( A ) = 4 pr2 4 p r2 = P / es T4 = v [ P / ( es T4 ) * ( 4p ) ] = -----
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