HW5

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School

University of Illinois, Urbana Champaign *

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Course

436

Subject

Mechanical Engineering

Date

Dec 6, 2023

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pdf

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2

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ABE 436 HW5 1. (10 pts)In the Imperial Valley, CA, a commercial lease of 6 km 2 is expected to support genera�ng capacity of some 55 MW e , (which will require at least 350 MW th ). Assuming an average heat flow of 250 mW/m 2 : a. What is the thermal recharge rate? b. What is the r a�o of extrac�on to thermal recharge rate? 2. (10 pts)A dry steam plant uses 210ºC saturated steam from a geothermal source in an ideal Rankine cycle (without the pump). The water leaves the condenser at 90ºC as saturated liquid. If the plant mass flow r ate of steam is 800 kg/s, what is the power output of the turbine? 3. (10 pts)A geothermal dry steam plant uses 200 ºC saturated vapor in an ideal Rankine cycle (without the pump). The water leaves the condenser at 85ºC as saturated liquid. If the power output of the turbine is 500 MW , what is the mass flow rate of steam? 4. (10 pts)Assuming the heat pump works in Carnot Cycle, if the outside temperature is 32 ° F and you wish to keep the inside temperature at 72 ° F using a heat pump (air source) system. Find the COP h and display all work. In the summer, the same heat pump is used to cool the house (75 ° F) when it is 98 ° F outside, please find the EER value. 5. (10 pts) As you learned in the class, ground source heat pumps are more efficient than other HVAC equipment, including other heat pumps. Assuming the same outdoor and indoor temperatures as in the previous problem, if the ground temperature is approximately 50 ° F at a depth of 10 feet, what is the COP h in the winter and what is the EER value for the summer? (hint: A reasonable assumption for the Tc and Te is needed and the water temperature in a refrigerant -to-water heat exchanger is not equal to 50 ° F. It is higher than 50 ° F in summer and it is less than 50 ° F in winter.) 6. (10 pts)Assuming a heat pump has an EER of 1 4, how many heat (Btu) is added to the house for every 100 kW-h put into the compressor of the system. Assume a desired indoor temperature of 70 ° F. 7. (10 pts) What is the Enhanced Geothermal System (EGS)? Please explain the benefits and limita�on s of EGS. 8. (15 pts)A house located in Champaign IL demands 22 0 million Btu heat over one hea�ng season. What are the opera�ng (fuel) costs if a. if a 95 % efficiency furnace is used with natural gas? (Natural gas @ $9.00/1000 � 3 . Hea�ng value: 1.03 million Btu/1000 � 3 ). b. if a 95 % efficiency furnace is used with propane? (Propane @ $2.36 per gallon, hea�ng value: 92,500 Btu/gal). c. if a ground source heat pump with an average COP of 4.0 is proposed (electricity @$0.1 2/kWh). d. How much heat (Btu) is removed from the ground source over one hea�ng season if a
ground source heat pump with an average COP of 4.0 is used? 9. (15 pts) Geothermal energy can be used for space hea�ng. a) If the plant mass flow rate of hot water ( 1 m ) is 1,200 kg/s, what is the thermal energy output of the plant? C p = 4,186 J/Kg °C b) If the COP h of the heat pump is 4, what is the water mass flow rate 2 m ? m 1 =1,20 0 kg/s m 2 =?
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