Question

Assume: (i) geothermal gradient = 25°C/km in the crust, (ii) density of the crustal rocks = 3000 kg/m\(^3\), and (iii) acceleration due to gravity = 10 m/s\(^2\). Based on these values, the lithostatic pressure at a point where temperature is 400°C will be ___________MPa.

Hint:

Lithostatic pressure increases with depth and is calculated by multiplying the density of the material, gravitational acceleration, and depth.

Answer 1

Correct Answer: 480

Step 1: Determine the Depth from the Geothermal Gradient.
The geothermal gradient is given as 25°C/km, which means that for every kilometer of depth, the temperature increases by 25°C. To find the depth at which the temperature reaches 400°C, we can use the formula: \[ \text{Depth} = \frac{\text{Temperature} - \text{Surface Temperature}}{\text{Geothermal Gradient}} = \frac{400°C - 25°C}{25°C/km} = 15 \, \text{km}. \] So the depth is 15 km (or 15000 m).
Step 2: Calculate the Lithostatic Pressure.
Lithostatic pressure is calculated using the formula: \[ P = \rho \cdot g \cdot h, \] where \(P\) is the lithostatic pressure, \(\rho\) is the density of the crust, \(g\) is the acceleration due to gravity, and \(h\) is the depth. Substituting the given values: \[ P = 3000 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \times 15000 \, \text{m} = 450 \times 10^{6} \, \text{Pa} = 450 \, \text{MPa}. \] Step 3: Conclusion.
The lithostatic pressure at a depth corresponding to a temperature of 400°C is 450 MPa.