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!