When the intermediate pressure in a two-stage system is selected at a very high value or a very low value, the benefits are reduced. In fact, if the intermediate pressure is the same as either the condensing or the evaporating pressure, the system reverts to single stage. We are led to the conclusion, then, that there must be some optimum intermediate pressure that results in minimum total power requirements. In the two-stage compression of air with ideal compression in both compressors, the optimum intermediate pressure is the geometric mean of the suction and discharge pressure,
The optimum intermediate pressure in a two-stage refrigeration system is quite close, but not equal, to that shown in Eq. 3.6. The reason for the deviation is that the cooling process in air compression is without cost, but in the refrigeration system there is a power cost associated. with compressing the refrigerant vapor that performs the cooling. Figure 3.18 shows a graph of the total power in a two-stage R-22 system operating with an evaporating temperature of -30°C (-22°F) and a condensing temperature of 35°C (95°F). The optimum intermediate pressure in two-stage refrigeration systems is slightly higher than that indicated by Eq. 3.6, because of the bias toward a higher intermediate pressure to reduce the flow rate of refrigerant performing the desuperheating.
A conclusion that can be drawn from Fig. 3.18 is that the curve showing the power is quite flat, so a few degrees difference in intermediate temperature has little practical influence on power required by the plant. The relative insensitivity of the power to the intermediate temperature is particularly apparent when comparing the values shown in Fig. 3.18 to the power required in single-stage compression, which is 36.1 kW (48.4 hp), for these evaporating and condensing temperatures. The noncritical nature of the intermediate temperature is fortunate, because in those systems with evaporators at the intermediate temperature, (see Sec. 3.12), the temperature requirements of these evaporators dictate the intermediate saturation temperature.