Consider the unary phase diagram for carbon below. Natural diamond is formed fai

Question

Consider the unary phase diagram for carbon below. Natural diamond is formed fairly deep in the earth where high temperatures and pressures exist -120-200 km below the surface. We know the center of the earth is quite hot and cools going outwards. 1f we assume that the average density of the earth is 5500 kgim1 and we can estimate pressure below the earth as pressure = pgh Where p is the density. g is gravity, and h is depth. calculate the earth?s geothermal temperature gradient (rate of increase in temperature with depth)

Explanation / Answer

Let us calculate the pressure first,

pressure (P) = pgh

where,

p = density = 5500 kg/m^3

g = 9.81 m/s^2

h = 120-200 km = we take an average 150 km below the surface

So, feeding the values,

P = 5500 kg/m^3 x 9.81 m/s^2 x 150000 m^3 = 8.09 x 10^9 kg.m/s^2 (N/m.s^2) = 8.09 GPa

Let the surface temperature be 25 oC (298 K) (or any value you are provided with)

Temperature at 8.09 GPa = approximately for diamond = 2000 K [from graph above]

So dT = 2000-298 = 1702 K

dx = 150 km

So we simply find the ratio of the two values,

temperature gradient obtained would be = dT/dx = 1702/150 = 11.347 K/km

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