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Maximum power from geothermal energy

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The maximum amount of electricity that you can extract follows from the fact that the total entropy cannot decrease. Let's first find an expression for the entropy of the rock as a function of its temperature. We can use the formula:

dS = dQ/T

If we put dQ = C_{tot} dT, where C_{tot} is the total heat capacity (this is the mass of the rock times the specific heat capacity), we get:

dS = C_{tot} dT/T

Integrating both sides gives:

S = ...

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