I am reading the book "Science a History 1543 - 2001" by John Gribbin. There was a mathemation who lived from 1768 to 1830 and his name was Fouier and he developed equations that dealt with time varying phenmena, which means he developed heat equations, how much time if takes for things to cool off. So googled Fouiers and found his equations and then did the math for if the earth was 10,000, let me tell you; NO I will show you.

1. I will use present day values (so I will not here any crap about things were different back then, which means that God can not create a consistant system, or he is playing games for the Baptist) of heat production from radioactive decay in the earth produce by ²³⁸U, ²³⁵U, ²³²Th, and ⁴⁰K and has a value of 6.18 x 10^-12W/kg (Turcotte and Schubert, 1982)

2. If you only take inaccount for agument sake heat flow from the mantle and crust

(6.18 x 10^-12W/kg) x (4.0 x 10²⁴kg) = 2.47 x 10¹³W

Fourier's Law of Heat Conduction

Q = K dt/dz

k = thermnal conductivity of rocks W/m ^oC
dt/ds = geo thermal gradiant or "rate of change"
Q = W/m²

total surface of the earth = 5.1 x 10¹⁴m²

2.47 x 10¹³W
----------------------- = .048 W/m² surface heat flow
5.1 x 10¹⁴m²

3.00 W/m ^o is a average thermal conductivity of rocks

dt/dz = .048 W/m²


500 years will be used as 1/2 life for the radactive elements listed above

Now figure out the decay rate constant labda (ʎ) so we can caclculate the heat producdion of the past

t = ^1/2 ln 2/ʎ or

ʎ = ln 2 / t^1/2

using 500 years for t^1/2 ʎ = 1.38 x 10^-3

H^past = H^present x e^ʎ(t-10)

H^present = 6.18 x 10^-12W/kg

t - t₀ = 10,000 years & ʎ

(6.18 x 10^-12) x (e^{1.38 x 10-3 - 10,000})
= 6.08 x 10^-6 W/kg

H_past x (mass of mantle and crust) = total heat production

H_past = (6.08 x 10^-6W/kg) x (4.0 x 10²⁴kg)
= 2.43 x 10¹⁹W

2.43 x 10¹⁹W
Q = --------------------- = 47724.58 W/m²
5.1 x 10¹⁴m²


47724.58 W/m²
------------------------ = 15,908^oC/km
3.00 W/m

Which means if the earth was 10,000 years old the surface of the earth would be as hot as Hell (15,908 degrees Celsius).