Chapter 3, Problem 6PP

(Heat transfer) The formula developed in Exercise 5 can be used to determine the cooling time, t, caused only by radiation, of each planet in the solar system. For convenience, this formula is repeated here (see Exercise 5 for a definition of each symbol):

$t=\frac{Nk}{2e\sigma A{T}^3{}_{fin}}$

$A=surfaceareaofasphere=4\pi r2$

$N=numberofatoms=\frac{\text{volume of the sphere}}{\text{volume of an atom}}$

Volume of a sphere $sphere=\frac{4}{3}\pi radiu{s}^3$

The volume of a single atom is approximately $1\times 10-29m^3$ . Using this information and the current temperatures and radii listed in the following chart, determine the time it took each planet to cool to its current temperature, caused only by radiation.