Final answer:
The best coefficient of performance for a heat pump with a hot reservoir temperature of 50.0ºC and a cold reservoir temperature of -20.0ºC is 7.00. Option c is the correct answer.
Step-by-step explanation:
The coefficient of performance (COP) is a measure of the efficiency of a heat pump. The best coefficient of performance for a heat pump can be determined using the Carnot efficiency formula.
For a heat pump with a hot reservoir temperature of 50.0ºC and a cold reservoir temperature of -20.0ºC, we can calculate the Carnot efficiency as follows:
Carnot efficiency (Effc) = 1 - (cold temperature / hot temperature)
Substituting the given values:
Effc = 1 - (-20.0 / 50.0) = 1 - (-0.4) = 1.4
The coefficient of performance is the reciprocal of the Carnot efficiency, so the best coefficient of performance for this heat pump is:
COP = 1 / Effc = 1 / 1.4 = 0.714
Therefore, the correct option is c) 7.00