A geothermal reserve has the stored heat of 5×10¹⁹ J. If the overall efficiency of a geothermal power plant based on this reserve is 0.04, how much power can be produced by the plant in 1 year?
~ 63.41 GW
To determine how much power can be produced by the geothermal power plant in one year, we need to follow these steps:
- First, calculate the energy that can be converted into work. This is given by multiplying the total stored heat by the efficiency.
The initial stored heat in the reserve is \(5 \times 10^{19} \, \text{J}\). The efficiency (\(\eta\)) of the geothermal power plant is 0.04. Therefore, the usable energy (\(E\)) is calculated as:
\(E = \text{Stored Heat} \times \text{Efficiency} = 5 \times 10^{19} \text{ J} \times 0.04 = 2 \times 10^{18} \text{ J}\)
- Next, determine the power output over one year.
Power is defined as energy per unit time. We need to convert the energy calculated into power over a period of one year. The number of seconds in one year (365 days) is:
\(365 \times 24 \times 3600 = 31,536,000 \, \text{seconds}\)
Thus, the power (\(P\)) is given by:
\(P = \frac{E}{\text{Time}} = \frac{2 \times 10^{18} \text{ J}}{31,536,000 \, \text{s}} \approx 63.41 \, \text{GW}\)
This calculation shows that the power that can be produced by the plant is approximately 63.41 GW, which matches option ~ 63.41 GW.
Therefore, the correct answer is: ~ 63.41 GW
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