The temperature within the Earth\'s crust increases about 1.0 C for each 30 m of

Question

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/Cm.

1-Determine the heat transferred from the interior to the surface for the entire Earth in 9.0 h .

Qinterior = (J)

2-Compare this heat to the amount of energy incident on the Earth in 9.0 h due to radiation from the Sun.   

Qinterior = (J)

2-Compare this heat to the amount of energy incident on the Earth in 9.0 h due to radiation from the Sun.   

Explanation / Answer

1) the equation for thermal conduction:
dQ/dt = k*A*(dT/dx)   dT/dx is temperature gradient.

= 0.8*(4pi*6.38*6.38*10^12)*(1/30)

dQ/dt = 1.364*10^13 J/s

dQ = 1.364*10^13*9*3600 = 4.42*10^17 J

b) dQ due to sun = 1.1*10^22 J/day at 1.0 kW/m^2

in 9.0 hr, dQ = 4.125*10^21 J

So this is about 10000 times greater than that of earth.

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