Answer
(a) The amount of heat transferred in one hour is $4.9\times 10^{16}~J$
(b) The amount of heat that reaches the earth's surface from the sun in one hour is $4.6\times 10^{20}~J$
The amount of heat from the sun is about 10,000 times greater than the heat transferred from the interior of the earth.
Work Step by Step
(a) We can find the rate of heat transfer.
$\frac{Q}{t} = k~A~\frac{T_1-T_2}{L}$
$\frac{Q}{t} = k(4\pi~R^2)~\frac{T_1-T_2}{L}$
$\frac{Q}{t} = (0.80~J/s~C^{\circ}~m)(4\pi)(6.38\times 10^6~m)^2~\frac{1.0~C^{\circ}}{30~m}$
$\frac{Q}{t} = 1.364\times 10^{13}~J/s$
We can find the amount of heat transferred in one hour.
$Q = (1.364\times 10^{13}~J/s)(3600~s)$
$Q = 4.9\times 10^{16}~J$
The amount of heat transferred in one hour is $4.9\times 10^{16}~J$
(b) Note that only one side of the earth's "disk" receives light from the sun at any one time. We can find the amount of heat that reaches the earth's surface from the sun in one hour.
$Q = I~A~t$
$Q = I~(\pi~R^2)~t$
$Q = (1000~W/m^2)(\pi)(6.38\times 10^6~m)^2(3600~s)$
$Q = 4.6\times 10^{20}~J$
The amount of heat that reaches the earth's surface from the sun in one hour is $4.6\times 10^{20}~J$
The amount of heat received from the sun is about 10,000 times greater than the heat transferred from the interior of the earth.