A crustal rock is at a lithostatic pressure of 3 kbar and a temperature of 275°C. If the lithostatic pressure increases at a uniform rate of 0.3 kbar/km, and the surface temperature is 25°C, the geothermal gradient (in °C/km) is ....... (answer in one decimal place).
Show Hint
Correct Answer: 25
Solution and Explanation
Step 1: Understanding geothermal gradient.
The geothermal gradient is the rate of temperature increase with depth. It is calculated by the formula:
\[
\text{Geothermal Gradient} = \frac{\text{Temperature Difference}}{\text{Depth}}
\]
The temperature difference is \( 275°C - 25°C = 250°C \). The depth is calculated using the lithostatic pressure, with the pressure increasing at 0.3 kbar/km. The depth is:
\[
\text{Depth} = \frac{3 \, \text{kbar}}{0.3 \, \text{kbar/km}} = 10 \, \text{km}
\]
Step 2: Calculation.
Now, calculate the geothermal gradient:
\[
\text{Geothermal Gradient} = \frac{250 \, °C}{10 \, \text{km}} = 25.0 \, °C/\text{km}
\]
Step 3: Conclusion.
The geothermal gradient is 25.0°C/km.
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