To calculate the efficiency of a heat engine, we can use the formula for thermal efficiency \(\eta\):
\[ \eta = \frac{W}{Q_{in}} \]
Where:
- \(W\) is the work output (in this case, the amount of electric power produced),
- \(Q_{in}\) is the heat energy input.
In your case:
- The electric power produced (work output, \(W\)) is 3 MW.
- The thermal energy input (\(Q_{in}\)) is also given as 3 MW.
However, to correctly evaluate the efficiency, we need to consider the amount of energy rejected to the sink. The heat rejected to the sink (\(Q_{out}\)) is given as 1 MW. Thus, we first need to determine the net work output:
- The work done by the system can be calculated by the difference between the heat input and the heat rejected:
\[ W = Q_{in} - Q_{out} = 3 \text{ MW} - 1 \text{ MW} = 2 \text{ MW} \]
- Then we can calculate the efficiency using the heat input:
\[ \eta = \frac{W}{Q_{in}} = \frac{2 \text{ MW}}{3 \text{ MW}} = \frac{2}{3} \approx 0.6667 \]
- To express this as a percentage, multiply by 100:
\[ \eta \approx 66.67% \]
So the thermal efficiency of the geothermal power plant, based on the provided data, is approximately 66.67%.
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