A 1660.0 ft2 (154.22 m2) single story home is cooled using a geothermal heat pump. A geothermal heat pump is a closed loop of pipe that runs through a house, then runs underground several feet, where the underground temperature is at a stable lower temperature that is cooler than the outdoor temperature during the summer. When the coolent in the pipe, in this case water, returns to the house, it is cooler than the air in the house, and heat flows from the air in the house to the water in the pipe, the air in the house is chilled. The outdoor temperature is 92.0°F (33.3 °C). The temperature of the water in the heat pump entering the house is 58.00°F (14.44°C), the temperature of the water in the heat pump leaving the house is 65.00°F (18.33°C). The walls of the house are 10.0 ft tall, making the volume of air in the house be 4.70 à 102 m3. Assume that the pressure inside the house is constant at 1 atm, and that the heat capacity for air is constant at 20.8 J/(mol·°C). The house is well-insulated, but heat from outside still enters the house at
Q = 1730(To-T)
where Q is in kJ/hr, T0 is the outside temperature in °C, and T is the temperature inside the house in °C. What is the differential energy balance around the house in terms of M, Cv, m, Cp, T1, T2, T0, and T, where M is the mass or number of moles of the system, Cv is the heat capacity of air, m is the mass or moleflow rate of the water stream, Cp is the heat capacity of water, T1 is the incoming water temperature, T2 is the outgoing water temperature, T0 is the outdoor temperature, and T is the temperature inside the house? You can neglect shaft work.
2.) Write the steady state energy balance to determine m, the molar flowrate of water required to keep the house at 68.0°F (20.0°C).
3.)Integrate the transient balance to calculate the time needed to achieve an indoor temperature of 70.0°F (21.1°C), if the indoor temperature started off at 92.0°F (33.3°C), Use the molar flowrate of water that you calculated above.
