How Does Changing Area, Temperature, and Emissivity Affect Energy Radiation?

[thecol6172]

Homework Statement

A sphere radiates 4.3 Joules of energy per second. How much energy per second would it radiate if its area was to be doubled, its absolute temperature was to halved and its emissivity was to be tripled?
A.)1.3J/s
B.)2.7J/s
C.)1.6J/s
D.)3.8J/s
E.)4.2J/s

Homework Equations

P=σAeT^4
P=power
σ=Stefan-Boltzmann constant=5.6696x10^-8
A=surface area
T=temp in Kelvin

The Attempt at a Solution

I really don't even know where to begin. I Believe that this is more of a theory question? If someone could just point me in the right direction to start that would be plenty of help.

 

[gash789]

Firstly you need to realize what information the question has given you, namely that the sphere radiates 4.3 J/s^2. Recognize that this is a power (Power=Energy per unit time) and you have an expression which relates some variables with the Power it will emit.

Since it does not give you explicitly any information on the parameters in P=σAeT^4
but it wants to know what happens if you area doubles, you will need to use some algebra.

So if the right hand side of that equation doubles, then so also does the left hand side. You need to work out what happens when the given values change.

Really what you are getting at here is how things scale, so for instance given the equation velocity=distance/time I know that if I double the distance I have to drive, then to do it in the same time I will need to go twice as fast! This is a linear relationship, or directly proportional between the distance and velocity (if we constrain ourselves to making the journey in the same time)

A more complex example is the area of a square say, where A=x^2 . Then if I double x, the area will increase by 2^2=4 so this relation is nonlinear.

Hope that helps

 

[thecol6172]

yes thank you very much! I have a test on this on Tue. and last week when I asked my professor for help, he told me he didn't have time.