5 A heat pump operating with R134a is used to maintain an in

5. A heat pump operating with R-134a is used to maintain an indoor temperature of 21°C using heat from the bottom of a lake that stays at 2°C. Assume an 80% efficient compressor. If the heat pump supplies 100 kW of energy to the building, calculate the required mass flow rate and COP for the heat pump. Calculate a few data points to plot the effect of a 10°C temperature range at the cold side on required mass flow rate and COP. Repeat this for any two different refrigerants. Note that the indoor and water temperatures realistically do not match the condenser and evaporator temperatures. Explain your choices for condenser and evaporator temperatures used in the calculations.

Solution

The COP definition for a heat pump is different from the definition for the refrigerator. Here we are interested in the amount of heat added to the house which is the high temperature heat rejection from the refrigeration cycle. The COP for a heat pump is defined as follows: . We can solve this equation for the power input and plug in the given data to compute the power required. Here we note that the heat supplied by the heat pump to keep the room temperature constant is just the difference between the heat loss and the heat generation. Thus, Q_H = 60,000 kJ/h – 4000 kJ/h = 56,000 kJ/h. The power consumption is then found to be

= 6.22 kW