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. 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 σ=5.67×10−8W/m2⋅K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures. RRigel = 5.1×1010 m SubmitHintsMy AnswersGive UpReview Part Correct This is over 50 times the size of our own sun and about a third of the orbital radius of the earth around the sun. Rigel is an example of a supergiant star. 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 σ=5.67×10−8W/m2⋅K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures. RProcyonB = 1.61•1011 m

Answer 1

Answer:

A) 5.1*10^10m B) 5.4*10^6m

Explanation:

Using the surface radiation formula of P (energy per second in Watt) = emissivity constant * surface area * Stefan-boltzmann constant*Temperature in kelvin^4*

2.7*10^31 = 1* 5.67*10^-8*A*11000^4

Making A subject of the formula = 2.7*10^31/ (5.67*10^-8*1.46*10^16) = 0.3261*10^23m^2

Since the shape is a sphere, the surface area = 4πR^2(radius of the Rigel)

R = √ (0.3261*10^23/ 4*π) = 5.1 * 10^ 10m

B) repeating the same step

2.1 *10^23 = 1*A*5.67*10^-8*10000^4 where A is the surface area of the Procyon

Make A subject of the formula

A = 2.1*10^23/(5.67*10^-8*10^16)

A = 0.37*10^15

The star assumed to be a sphere;

A = 4πR^2 where R is the radius of Procyon

R = √(0.37*10^15/4π) = 5.4*10^6m