Power Radiation of a Planet

jeudi 31 octobre 2013

1. The problem statement, all variables and given/known data

Venus and Earth may be regarded as behaving as black bodies. The mean temperature at the surface of Venus is about 600K and at the surface of Earth is about 300K. Which of the following is the best estimate for the ratio

[tex]\frac{power.radiated.per.unit.area.on.Earth}{power.radiated.per.unit.ar ea.on.Venus}[/tex]

(A) 1/2

(B) 1/4

(C) 1/8

(D) 1/16

I had to put dots in between words.. It won't let me space them

2. Relevant equations

[tex]σAT^4[/tex]

3. The attempt at a solution

Venus: [tex]σAT^4 = σA(600)^4[/tex]

Earth: [tex]σAT^4 = σA(300)^4[/tex]

The actual answer is (D)

and I got this by

[tex]\frac{σA(300)^4}{σA(600)^4}= 1/16[/tex]

If the above working is right, I want to know where 'A' or 'Area' disappeared to. I thought Area of Earth and Venus are different so they can't cancel out? Or is power radiated always referring to the unit surface area, or 1m^2 ?

p.s. is if fine if I post a lot consecutively?