Chapter 10, Problem 10.13P

Interpretation Introduction

Interpretation:

The range of the geothermal gradient for the formation of natural diamond is to be determined. Also, the pressure below the earth's surface is to be calculated.

Concept Introduction:

Phase diagrams are the geometrical representation of the conditions such as temperature, pressure, composition, etc. of a system at which different phases present in the system coexist and are in thermodynamic equilibrium.

These phase diagrams contain phase boundaries which are lines that mark the conditions under which multiple phases can coexist at the equilibrium. Along these lines, the transition of phase occurs.

The point where these phase boundaries intersect are the triple points. At these points, three different phases can exist simultaneously.

Geothermal gradient (G) is defined as the rate of increase in the temperature with respect to the increase in the depth in the interior of the earth. Mathematically it is defined as:

  $\text{G}=\frac{\text{rate of increase in temperature}}{\text{depth in the Earth's interior}}$   ...... (1)

The formula to calculate the pressure ( P ) below depth ( h ) is:

  $P=\rho gh$   ...... (2)

Here, $\rho$ is the density of the substance and $g$ is the acceleration due to gravity having the value of $9.81{\text{ m/s}}^2$.