Problem 4.9 - A Home Air Conditioner & Hot Water Heater

We wish to do a preliminary thermodynamic evaluation of a 500W input power home air conditioner/hot water heater system using refrigerant R134a. Consider the following system flow diagram

This unique combined air conditioning / hot water heating system is designed to absorb heat from the 32°C air flowing through the insulated duct in order to pump heat into the hot water heating tank. The fan provides enough air flow over the evaporator to cool the air to 15°C at the outlet of the duct, and the hot water is heated to a maximum of 50°C. In this analysis we neglect the power provided to the fan. We also assume that both the duct and the hot water tank are adiabatic.

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 [0.0133 kg/s]
• Determine the heat rejected by the condenser [-2.09 kW]. Assuming that all this heat is absorbed by the water in the hot water tank, determine the time taken for 100 liters of water at 32°C to reach the required temperature of 50°C [1 hour]. (Note: The hot water heater is not a flow system, thus we need to first evaluate the energy required to heat the water [7524 kJ]. This section is solved as shown below)

• Determine the heat absorbed by the evaporator [1.59 kW]. Assuming that all this heat is absorbed from the air in the duct and neglecting the fan power, determine the required mass flow rate of the inlet air at station (5) in order reduce the air temperature from 32°C to 15°C at the outlet of the duct [0.093 kg/s].
• Determine the Coefficient of Performance of the hot water heater (COPHW) (defined as the heat rejected by the condenser divided by the work done on the compressor) [COPHW = 4.17].
• Determine the Coefficient of Performance of the air conditioner (COPAC) (defined as the heat absorbed by the evaporator divided by the work done on the compressor) [COPAC = 3.17].
• Is this a suitable and practical system for hot climates? Discuss.

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