(Heat transfer) The time it takes for a spherical object to cool from an initial temperatu...

(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