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Chapter 9: Problem 30

On average, the temperature beneath the Earth's crust increases at a rate of \(20^{\circ} \mathrm{C}\) per kilometer. At what depth would water boil? (Assume the surface temperature is \(20^{\circ} \mathrm{C}\) and ignore the effect of the pressure of overlying rock on the boiling point of water.)

Short Answer

Expert verified
The water will boil at a depth of 4 kilometers below the surface.

Step by step solution

01

Note the Temperature at which Water Boils

It is a common scientific fact that water boils at a temperature of 100 degrees Celsius under normal atmospheric pressure.
02

Calculate the Required Temperature Increase

We need to find out how much the temperature needs to increase for water to reach its boiling point. Our starting temperature is 20 degrees Celsius (surface temperature) and we want it to increase to 100 degrees Celsius (boiling point). The required temperature increase is therefore \(100^{\circ} \mathrm{C} - 20^{\circ} \mathrm{C} = 80^{\circ} \mathrm{C}\)
03

Determine the Depth

Now that we know water needs to heat up by 80 degrees Celsius in order to boil, we find how deep beneath the Earth's crust this would occur. Given the temperature increases by 20 degrees Celsius per kilometer, the depth is \(80^{\circ} \mathrm{C} / 20^{\circ} \mathrm{C}\)/km = 4 km.

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