Question

metamorphic environments in a geothermal environment where the geothermal gradient is 75*c per km, how deep does a rock have to be buried in order to reach high grade metamorphism (700*c) as a result of temperature? report your answer in kilometers and as one significant figure.

Answer 1

A rock must be buried approximately 9 kilometers deep to reach a high-grade metamorphic temperature of 700°C in a geothermal environment with a geothermal gradient of 75°C per km.

Step-by-step explanation:

To calculate the depth at which a rock must be buried to reach high-grade metamorphism at a temperature of 700°C in a geothermal environment with a geothermal gradient of 75°C per km, we use the following steps:

1. Determine the temperature difference that must be achieved for metamorphism. This is done by subtracting the surface temperature from the desired metamorphic temperature. Assuming a surface temperature of approximately 0°C, the difference needed is 700°C.
2. Use the geothermal gradient to calculate at what depth this temperature difference will be achieved. The formula to use is: Depth = Temperature Difference ÷ Geothermal Gradient.
3. Now, plug the numbers into the formula: Depth = 700°C ÷ 75°C/km = 9.33 km.

To provide an answer with one significant figure, the depth is rounded to 9 km.

Therefore, a rock needs to be buried roughly 9 kilometers deep to reach the high-grade metamorphic temperature of 700°C in a geothermal environment with a geothermal gradient of 75°C per km.