The phase diagram of carbon is a graph of pressure ( y-axis or dependent variabl

Question

The phase diagram of carbon is a graph of pressure ( y-axis or dependent variable ) versus temperature ( x-axis or independent variable ) on which a straight line separates the diamond phase on the high pressure side of the line from the graphite phase on the low pressure side. At 590.0 °C the pressure on the line is 2.881×10^9 Pa. At 2970.0 °C the pressure on the line is 1.002×10^10 Pa. What is the minimum depth at which diamonds can form if the local temperature is 1827.6 °C and the subsurface rocks have density 4.5 g/cm3? Assume that, just as in a fluid, the pressure at some depth is due to the weight of material lying above.

Explanation / Answer

In this problem we must make several assumptions.

Pressure seek graphite-diamond transition. Suppose that the variation is linear, so we can build an equation of the line

P-P0 = m T-T0

m = (P2-P1)/(T2-T1)

m = (1.002 1010 -2.881 109) / (2970-590) = 7.139 109 / 2380

m = 2.9996 106= 3 106Pa/°C

(P – 2.881 109 ) = 3 106 ( T – 590)

We give us the local temperature, pressure calculated transformation

P = 3 106( 1827.6 – 590) + 2.881 109= 3.712 109+ 2.881 109

P = 6.593 109 Pa

We calculate the depth we have this pressure,

Assuming a density and gravitational acceleration is constant

Data

Patm = 1.013 105 Pa

= 4.5 g/cm3 (1Kg/1000g) (100 cm/1 m)3 = 4.5 103 Kg/m³

P = Patm + g Y

g Y = P – Patm

Y = (P – Patm)/ g

Y = (6.593 109Pa – 1.013 105) / (4.5 1039.8)

Y = 65929 105 / 44.1 103

Y = 1498.99 102m

This is the minimum depth training

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