Question

The temperature gradient in the earth's crust is ${32}^{o}C$ per km and the mean conductivity of the rock is $0.008$ CGS units. Considering the radius of the earth as $6000$ Km, the loss of heat by the earth everyday is about (in calories)

• A. ${10}^{16}$
• B. ${10}^{18}$
• C. ${10}^{27}$
• D. ${10}^{37}$

Answer 1

Answer: (B)

${10}^{18}$

The heat dissipated per second is given by equation.
$\frac{dQ}{dt}=kA\frac{dT}{dr}$
$k=0.008$d
$A=4\pi r^2$
$r=6000\times 1000\times 100cm$
$\frac{dT}{dr}=\frac{32}{1000\times 100}$
$dt=86400sec$
$Answer={10}^{18}cal$
Substituting the given values(convert everything to CGS), we get answer.