### Problem 4.12 - Home Air Conditioner and Hot
Water System with an Internal Heat Exchanger

We wish to do a preliminary thermodynamic evaluation
of the following proposed heat pump system designed for summertime
hot water heating and space cooling.

Notice that this system uses a heat exchanger to subcool the refrigerant
at the outlet of the hot water heater while heating the refrigerant
at the outlet of the evaporator. This is intended to serve the
dual purpose of increasing the both the hot water heating and
air cooling capacity of the system

.Using the conditions shown on the diagram

- a) Neatly sketch the complete air conditioning
cycle above on the
*P-h* diagram provided, showing clearly
all six processes (1) - (2) - (3) - (4) - (5) - (6) - (1).

- b) Using the R134a property tables determine
the enthalpies at all six stations and verify and indicate their
values on the
*P-h* diagram. Note that in order to determine
the enthalpy at stations (4) and (5) you will need to consider
the heat transferred in the heat exchanger as well as the energy
equation applied to an adiabatic throttle. [h_{5} = h_{4} = 107.3 kJ/kg]

- c) Determine the mass flow rate of the refrigerant
R134a. [0.023 kg/s]

- d) Determine the power absorbed by the hot
water heater [4.41 kW] and the Coefficient of Performance of the hot water
heater [COP
_{HW}
= 4.41] (defined as the heat absorbed
by the hot water divided by the work done on the compressor).
Determine the time taken for 120 liters of water at 30°C
to reach the required temperature of 50°C. [38 minutes]

- e) Determine the heat transferred from the
air blowing through the insulated cooling duct to the evaporator
[3.41 kW], and the Coefficient of Performance [COP
_{AC} = 3.41] of the air conditioning system.

- f) Consider the air passing through the insulated
duct of the evaporator section. Notice that the temperature of
the air passing through the duct is decreased by 10°C. Neglecting
the work done by the fan determine the mass flow rate of the
air through the duct [20.4
kg/min].

- g) Discuss the advantages of the above heat
pump system over other means of space cooling and water heating.