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  4. The temperature gradient in the earth's crust is 32 ° C km- 1 and the mean conductivity of earth is 0.008 cal s- 1 cm- 1 ° C- 1 . Considering the earth to be a sphere of radius 6000 km , the loss of heat by the earth every day is about

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Q. The temperature gradient in the earth's crust is $32 \, ^\circ C \, km^{- 1}$ and the mean conductivity of earth is $0.008 \, cal \, s^{- 1} \, cm^{- 1} \, ^\circ C^{- 1}$ . Considering the earth to be a sphere of radius $6000 \, km$ , the loss of heat by the earth every day is about

NTA AbhyasNTA Abhyas 2022

Solution:

$\Delta Q=KA\left(\frac{\Delta T}{\Delta x}\right)\Delta t$
$=\frac{\text{0.008}}{\left(10\right)^{2}}\times 4 \, \times \frac{22}{7}\left(6 \times \left(10\right)^{8}\right)^{2}\times \left(\frac{32}{\left(10\right)^{3}}\right)\times 86400$
$\approx10^{18}cal$