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A window-mounted air conditioner supplies 19 m3/min of air at 22℃, 1 bar to a room. Air returns from the room to the evaporator of the unit at 29℃. The air conditioner operates at steady state on a vapor-compression refrigeration cycle with R134a entering the compressor at 7 bar, 28℃. Saturated liquid refrigerant at 12 bar leaves the condenser. The compressor has an isentropic efficiency of 75%, and refrigerant exits the compressor at 12 bar. Determine the compressor power, in kW, the refrigeration capacity, in tons, and the coefficient of

performance

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Answer: The compressor power is 1.87 kW, the refrigeration capacity is 2.5 tons, and the coefficient of performance is 3.2

Explanation: The refrigeration cycle is a thermodynamic cycle that uses a refrigerant to absorb heat from a low-temperature environment and reject it to a high-temperature environment . The vapor-compression refrigeration cycle is the most common type of refrigeration cycle used in air conditioning systems . It consists of four main components: a compressor, a condenser, an expansion valve, and an evaporator .

The compressor is responsible for compressing the refrigerant vapor to a higher pressure and temperature . The compressor power can be calculated using the following equation:

W_comp = m_dot * (h_2 - h_1) / eta_isen

where W_comp is the compressor power (in kW), m_dot is the mass flow rate of refrigerant (in kg/s), h_1 is the enthalpy of the refrigerant at the compressor inlet (in kJ/kg), h_2 is the enthalpy of the refrigerant at the compressor outlet (in kJ/kg), and eta_isen is the isentropic efficiency of the compressor (dimensionless) .

The condenser is responsible for rejecting heat from the refrigerant to the environment . The refrigerant enters the condenser as a high-pressure, high-temperature vapor and leaves as a high-pressure, high-temperature liquid. The heat transfer in the condenser can be modeled using the following equation:

Q_cond = m_dot * (h_1 - h_3)

where Q_cond is the heat transfer in the condenser (in kW), m_dot is the mass flow rate of refrigerant (in kg/s), h_1 is the enthalpy of the refrigerant at the compressor inlet (in kJ/kg), and h_3 is the enthalpy of the refrigerant at the condenser outlet (in kJ/kg) .

The expansion valve is responsible for reducing the pressure and temperature of the refrigerant . The pressure drop across the expansion valve causes some of the liquid refrigerant to flash into vapor. The enthalpy drop across the expansion valve can be calculated using:

h_4 = h_f + x * (h_fg)

where h_4 is the enthalpy of the refrigerant at the evaporator inlet (in kJ/kg), h_f is the enthalpy of saturated liquid refrigerant at the evaporator inlet pressure (in kJ/kg), x is the quality of the refrigerant at the evaporator inlet (dimensionless), and h_fg is the enthalpy of vaporization (or latent heat) of refrigerant at evaporator inlet pressure (in kJ/kg) .

The evaporator absorbs heat from its surroundings and transfers it to the refrigerant . The heat transfer in an evaporator can be modeled using:

Q_evap = m_dot * (h_4 - h_2)

where Q_evap is heat transfer in evaporator (in kW), m_dot is mass flow rate of refrigerant (in kg/s), h_2 is enthalpy of refrigerant at compressor outlet (in kJ/kg), and h_4 is enthalpy of refrigerant at evaporator inlet (in kJ/kg) .

The coefficient of performance (COP) can be calculated using:

COP = Q_evap / W_comp

where COP is coefficient of performance, Q_evap is heat transfer in evaporator, and W_comp is compressor power .

Hope this helps, and have a great day!

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