An R-12 refrigerating machine works on the vapour-compression cycle. The evaporator temperature is −20 °C; the vapour is dry saturated when it enters the compressor and leaves it superheated. The condenser temperature is 30 °C. Taking c_{p} of superheated R-12 vapour as 1.884 kJ/kg·K, determine (1) the temperature of the vapour at entry to the condenser (°C), (2) the dryness fraction at entry to the evaporator and (3) the theoretical COP. Properties of R-12: at −20 °C, h_{f} = 17.82, h_{g} = 178.73 kJ/kg, s_{f} = 0.0731, s_{g} = 0.7087 kJ/kg·K; at 30 °C, h_{f} = 64.59, h_{g} = 199.62 kJ/kg, s_{f} = 0.2400, s_{g} = 0.6853 kJ/kg·K.