An American city of 1 million people uses energy at the rate of about 10GW (104W per person times 106 people). Assume the city occupies a circular area 15km in diameter. Make the approximation that the top kilometre of Earth’s crust consists of granite (density 2,700 kg/m3and specific heat 840J/kg/K, and thermal conductivity 3.37 W/m*K) and that the average temperature in this layer is 60°C higher than the surface temperature
a)Estimate the total energy that could be extracted in cooling the 1km thick layer of crust beneath the city to the temperature of the surface
b)If the efficiency in converting this low-quality thermal energy to useful energy is 5%, how long would the 1km geothermal resource below the city last

The actual efficiency of a geothermal power plant using a 200°C geothermal resource is only about 7%. Take this value as typical of California’s Geysers geothermal field, which produces 850 MW of electric power
a)Find the actual rate of geothermal heat extraction at the Geysers
b)It’s estimated that 35 EJ of energy could be extracted from The Geysers before the temperature dropped from 250°C to the 150°C minimum for a vapour dominated geothermal plant. Given your answer in (a), how long will the Geysers geothermal resource last before the temperature reaches 150°C

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