(Heat transfer) The formula developed in Exercise can be used to determine the cooling tim...

(Heat transfer) The formula developed in Exercise 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 for a definition of each symbol):

A = surface area of a sphere = 4 π r2

The volume of a single atom is approximately 1 × 10-29m3. 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.

Exercise:

(Heat transfer) The time it takes for a spherical object to cool from an initial temperature of Tinit to a final temperature of Tfin, caused entirely by radiation, is provided by Kelvin’s cooling equation:

t is the cooling time in years.

N is the number of atoms.

k is Boltzmann’s constant (1.38 × 10-23 m2kg/s2K; note that 1 Joule = 1 m2kg/s2).

e is emissivity of the object.

σ is Stefan-Boltzmann’s constant (5.6703 × 10-8 watts/m2K4).

A is the surface area.

Tfin is the final temperature.

Tinit is the initial temperature. 

Assuming an infinitely hot initial temperature, this formula reduces to

Using this second formula, write a C++ program to determine the time it took Earth to cool to its current surface temperature of 300°K from its initial infinitely hot state, assuming the cooling is caused only by radiation. Use the information that the area of the Earth’s surface is 5.15 × 1014m2, its emissivity is 1, the number of atoms contained in the Earth is 1.1 × 1050, and the radius of the Earth is 6.4 × 106 meters. Additionally, use the relationship that a sphere’s

surface area is given by this formula:

Surface area of a sphere = 4πr2