In Fig. 16-2 for a siaglsspeed heat pump, assume that each on and off peria is 10 min long, that is, there are three cycles per hour. When the compressor is turned on, its output increases exponentially, reaching 99% of its maximum capacity at the end of the 10-min on interval. Once the compressor is turned off, the heating (or cooling) decays with a much smaller time constant and can be assumed to be instantaneous.
(a) If the rated electrical power is drawn throughout the on interval, calculate the loss in efficiency due to the exponential rise in the compressor output.
(b) A load-proportional capacity-modulated heat pump is used to eliminate the above on-off cycling. The efficiency of the solid-state controller is 96% and the motor efficiency is lower by I percentage point because of reduced speed, reduced load operation, and inverter harmonics. Assume that the compressor efficiency remains unchanged. Compare the system efficiency with the single-speed compressor system of part a if the motor efficiency in part a can be assumed to be 85%
