In actual air-conditioning applications for R-12 and R-22 refrigerant and operating at a condenser temperature of 40°C and an evaporator temperature of 5°C, the heat rejection factor is about:  

Explanation:

Vapour Compression Refrigeration Cycle:

Process 1-2: Isentropic Work Done by Compressor

Process 2-3: Constant Pressure Heat Removal by Condenser

Process 3-4: Isentropic Expansion by Throttling Valve

Process 4-1: Constant Pressure Heat Addition by Evaporator

From the Heat Balance Equation:

Energy transferred from Condenser = Energy Transferred to Evaporator + Work Input to the compressor 

Heat rejection ratio is given by:

\({\rm{HRR}} = 1 + \frac{1}{{{\rm{COP}}}} = 1 + \frac{W_{input}}{{{\rm{RE}}}} =\frac{{{{\rm{Q}}_{{\rm{COND}}}}}}{{{\rm{RE}}}}\)

Or

\({\rm{HRR}} = {\rm{Heat\;rejection\;ratio}} = \frac{{{{\rm{Q}}_{\rm{COND}}}}}{{{{\rm{RE}}}}}\)

Where,

QCOND is heat rejected in the condenser,

RE  is the Refrigeration effect and Winput  is the work input to the Refrigeration System

Calculation:

Given:
T_C = 40°C  and T_E = 5°C 
Heat rejection factor = \(\frac{{{Q_{Rejected}}}}{{RE}}\)

\({\left( {COP} \right)_{Ref}} = \frac{{{T_L}}}{{{T_H} - {T_L}}} =\frac{{5+273}}{{40 - 5}}= \frac{{278}}{{40 - 5}} = 7.9428\)

\({\rm{HRR}} = 1 + \frac{1}{{{\rm{COP}}}} = 1 + \frac{1}{{7.9428}} \) = 1.125