An igneous intrusion has heated a 2.5 km^3 underground bed of fractured quartzit

Question

An igneous intrusion has heated a 2.5 km^3 underground bed of fractured quartzite (rho = 2650 kg/m^3, C = 800 J/(kg K)). The average temperature of the rock is 600 K and that of the surroundings is 300 K. How much useful energy is stored in the rock? Calculate how long you could produce 1000 MW of electricity by extracting thermal energy from the rock if you do this most efficiently. Note that this production rate is the same as that of a large power plant. If you can sell electricity to the local power company at 6 cents per kWh, how much is this energy worth?

Explanation / Answer

a.Equation to calculate the heat stored in the rock

c=q/m*delta T

c=specific heat capacity=800J/kg/k

delta T= difference in temperature=600-300=300K

m=??

First we need to calculate the mass

mass=density*volume

density=2650kg/m3

volume=2.5km3=2.5*10^9m3

mass=2650*2.5*10^9

=6625*10^9kg

Now q=cm/delta T

=800*6625*10^9/3000

=53*10^5*10^9/3000

=0.017*10^14

=1.7*10^12 J

Since we know that 1 MW=10^6 joule

We have 1.7*10^6 J=17,000,00 MW

b.cost of energy=17,000,00 MW* 6

=10,200,000cents

Since 1 dollar=0.01 cents

=10,2000 dollar

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