## Problem 4.8 - A Home Heat Pump for Space Heating

We wish to do a preliminary thermodynamic evaluation of a 1kW input power home heat pump system for space heating using refrigerant R134a. Consider the following system flow diagram

Thus the heat pump system absorbs heat from the evaporator placed outside in order to pump heat into the air flowing through the insulated duct over the condenser section. The fan provides an air flow of 8 m3/minute, which is enough to cool the refrigerant in the condenser to 30°C, In this analysis we will neglect the power provided to the fan. We also assume that the duct is adiabatic, and that all the heat rejected by the condenser is absorbed by the air flowing in the duct.

Plot the four processes on the P-h diagram provided below and use the R134a refrigerant property tables in order to determine the following:

• Determine the mass flow rate of the refrigerant R134a [0.0185kg/s]
• Determine the mass flow rate of the air flowing in the insulated duct [0.161kg/s].
• Determine the heat rejected by the condenser [-3.7kW]. Assuming that all this heat is absorbed by the air, determine the exit temperature of the air at station (6) [37.9°C]. Is this value reasonable? Why? (Note: This problem involves heat being transferred from the refrigerant in the condenser to the air flowing through the condenser, and is solved as shown below)

• Determine the heat absorbed by the evaporator [2.7kW].
• Determine the Coefficient of Performance of the heat pump (COPHP) (defined as the heat rejected by the condenser divided by the work done on the compressor) [3.7].

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