Question

Chapter 14

The Size of Stars

10 of 11

Constants

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.

Part A

Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×1031W and has a surface temperature of 11,000 K. Assume that the star is spherical.

Use ?=5.67×10?8W/m2?K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.

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RRigel =

m

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Part B

Find the radius RProcyonB of the star Procyon B, which radiates energy at a rate of 2.1×1023W and has a surface temperature of 10,000 K. Assume that the star is spherical.

Use ?=5.67×10?8W/m2?K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.

RProcyonB =

m

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Answer 1

this refers to stefans law

according to the stefans law the emissive power of a black body is proportional to the fourth power of its absolute temperature

P = A   T⁴

where A is the surface area given by

A = r²

is stefans constant

P = r²   T⁴

r² = P /   ( T⁴)

= (2.7 x 10³¹) / (3.14)(5.67 x 10^-8)(11000)

= 528772 x 10²³

the radius will be

r = 2299 x 10¹¹ m

in the similar manner you can solve for the next one also