Question

A window-mounted air conditioner supplies 19 m3/min of air at 15° C, 1 bar to a room. Air returns from the room to the evaporator of the unit at 22 C. The air conditioner operates at steady state on a vapor-compression refrigeration cycle with refrigerant 134a entering the compressor at 4 bar, 10° C. Saturated liquid refrigerant at 9 bar leaves the condenser. The compressor has an isentropic efficiency of 70%. Determine 1. a) mass flow rate of refrigerant, in kg/min b) the compressor power needed, in kW c) the refrigeration capacity, in tons d) the coefficient of performance 10

Answer 1

The mass flow rate of refrigerant is 0.167 kg/min, the compressor power needed is 23.36 kW, the refrigeration capacity is 33.20 kJ/min, and the coefficient of performance is 9.40.

Step-by-step explanation:

To determine the mass flow rate of refrigerant, we can use the equation:

Δm = m1 - m2 = ω(V2 - V1)

where Δm is the mass flow rate, m1 is the mass flow rate of air entering the evaporator, m2 is the mass flow rate of air leaving the evaporator, ω is the density of air, V2 is the volume flow rate of air leaving the evaporator, and V1 is the volume flow rate of air entering the evaporator.

Using the given values, we can calculate the mass flow rate of the refrigerant as follows:

Δm = (19 m3/min)(1.225 kg/m3 - 1.146 kg/m3) = 0.167 kg/min

To determine the compressor power needed, we can use the equation:

Pcomp = η(m1h1 - m2h2s)

where Pcomp is the compressor power, η is the isentropic efficiency, m1 is the mass flow rate of refrigerant, h1 is the enthalpy of refrigerant entering the compressor, m2 is the mass flow rate of refrigerant leaving the compressor, and h2s is the enthalpy of refrigerant leaving the compressor in the hypothetical isentropic process.

Plugging in the given values, we can calculate the compressor power needed as follows:

Pcomp = (0.167 kg/min)(267.95 kJ/kg - 245.12 kJ/kg) / (0.70) = 23.36 kW

To determine the refrigeration capacity, we can use the equation:

R = m1(h2 - h1)

where R is the refrigeration capacity, m1 is the mass flow rate of refrigerant, h2 is the enthalpy of refrigerant leaving the evaporator, and h1 is the enthalpy of refrigerant entering the evaporator.

Plugging in the given values, we can calculate the refrigeration capacity as follows:

R = (0.167 kg/min)(267.95 kJ/kg - 69.94 kJ/kg) = 33.20 kJ/min

To determine the coefficient of performance (COP), we can use the equation:

COP = Δh / Pcomp

where Δh is the enthalpy difference between the cold and hot reservoirs.

Plugging in the given values, we can calculate the COP as follows:

COP = (267.95 kJ/kg - 69.94 kJ/kg) / (23.36 kW)

COP = 9.40