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Step 1:: To find the temperature at the bottom of the mine that extends to a depth of 2 km, we use the geothermal gradient of $25^{\circ} extrm{C}$ per km.
= 50^{\circ} extrm{C}
We multiply the geothermal gradient by the depth of the mine. Temperature at 2 km depth = Geothermal gradient * Depth
Final Answer
Step 2: To find the range of temperatures at a depth of 8 km, we use the minimum and maximum geothermal gradients given: $15^{\circ} extrm{C}$ /km and $50^{\circ} extrm{C}$ /km. We multiply each gradient by the depth of 8 km to find the corresponding temperatures. Temperature range at 8 km depth: Minimum temperature = Minimum geothermal gradient * Depth = 15^{\circ} extrm{C/km} imes 8 km = 120^{\circ} extrm{C} Maximum temperature = Maximum geothermal gradient * Depth = 50^{\circ} extrm{C/km} imes 8 km = 400^{\circ} extrm{C}
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