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A geothermal plant uses geothermal water (yes a liquid) extracted from beneath the Earth using drilling apparatus. The geothermal water (a condensed liquid) comes up at a temperature of 200 C at a rate of 200 kg/s. It is used to drive a turbine that extracts 6000 kw of power. The water leaves the turbine at 80 C and enters a lake at 25 C. What is the actual thermal efficiency of the turbine in percent to three significant digits

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MechEngineer

Answer:

4.1%

Explanation:

Given that water specific heat c = 4186 J/kgC. If water is flowing with mass rate of 200kg/s and temperature is dropping from 200C to 25C. Then the thermal energy rate from the water should be

[tex]P_i = mc\Delta t = 200*4186*(200 - 25) = 146510000 J/s[/tex] or 146510kW

Since the turbine is only able to extract 6000kW of power, then the thermal efficiency is:

[tex]Eff = \frac{P_o}{P_i} = \frac{6000}{146510} = 0.041[/tex] or 4.1%

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