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

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 800.0 °C the pressure on the line is 3.511×109Pa. At 2780.0 °C the pressure on the line is 9.451×109Pa. What is the minimum depth at which diamonds can form if the local temperature is 1235.6 °C and the subsurface rocks have density 3.2 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

Let us assume that

P(t) =a T ,

a =(P(T2)-P(T1))/(T2 -T1)=3.0 X106 PaK-1

P(To=1508.6 K)= 3.0 X106X1.5086X103 Pa=4.5258 X 109 Pa

P(To) rho gh=,

then h is given by

h= P(To) /rho g = 4.5258 X 109/ (3.2 X 103 X 9.8)= 1.44 X 105 m=144 Km

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