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 550.0 °C the pressure on the line is 2.761×109Pa. At 2660.0 °C the pressure on the line is 9.091×109Pa. What is the minimum depth at which diamonds can form if the local temperature is 1309.6 °C and the subsurface rocks have density 4.0 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

At temperature, T1 = 550 oC = 823 K

Pressure, P1 = 2.761x109 Pa

At, T2 = 2660 oC = 2933 K

Pressure, P2 = 9.091x109 Pa

At T = 1309.6 oC = 1582.6 K

Pressure, P = P1 * T / T1

= 2.761×109 Pa * 1582.6 K / 823 K

Pressure, P = 5.31x109 Pa

= 5.31x109 N/m2

Density = 4.0 g/cm3 = 4000 kg/m3

Using,

P = mgh

5.31x109 N/m2 = 4000 kg/m3 * 9.81 m/s2 * h

h = 1.35x105 m

H = 135 km

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