How Does Earth's Core Contribute to Surface Heat Compared to Solar Radiation?

[toothpaste666]

Homework Statement

The temperature within the Earth's crust increases about 1.0 C∘ for each 30 m of depth. The thermal conductivity of the crust is 0.80 W/C∘⋅m.
A)Determine the heat transferred from the interior to the surface for the entire Earth in 9.0h .
B)Compare this heat to the amount of energy incident on the Earth in 9.0h due to radiation from the Sun.

Homework Equations

dQ/dt = kA(dT/l)

The Attempt at a Solution

I have solved the first part.
surface area of Earth = 4pir^2 = 4pi(6.378x10^6 m)^2 = 5.1x10^14 m^2
dQ/dt = kA(dT/l)
dQ/dt = (.80 J/smC)(5.1x 10^14 m^2)(1 C/ 30m)
dQ/dt = 1.36x10^13 J/s

9h is 9h(3600 s/h) = 32400 s

32400s(1.36x10^13 J/s) = 4.4x10^17 J

The second part I am having a hard time understanding. I'm not really sure I even know what they are asking

 

[BvU]

Well, I take it they want you to estimate solar irradiance, right ?
Don't worry about more than one or two decimals of accuracy...
And pay attention to the fact that values such as in the table here are for perpendicular incidence.

 

[conner]

part b of the problem asks you to compare energy into the surface from the core and compare it to the sun,
energy from the sun:
1300 W/m^2 *(4*pi*(6.37*10^6)^2)* .5 (only half the Earth is hit per second) = 3.32*10^17 W sun.
3.32*10^17 W * 32400 s = 1.07*10^22 J
now create a ratio:
Jcore/Jsun = (4.4*10^17)/(1.07*10^22)

the Earth's core only adds .004% of the suns solar intensity to the surface.