Question

In a very mild winter climate, a heat pump has heat transfer from an environment at 5.00ºC to one at 35.0ºC. What is the best possible coefficient of performance for these temperatures?

a) 5.83
b) 6.25
c) 6.50
d) 7.00

Answer 1

The best possible coefficient of performance for a heat pump transferring heat from an environment at 5.00°C to one at 35.0°C is 6.50.

Step-by-step explanation:

When calculating the coefficient of performance (COP) of a heat pump, we can use the formula:

COP = Qh / W

where Qh is the amount of heat transferred to the hot reservoir and W is the amount of work done to achieve that heat transfer. In this case, the goal is to find the best possible COP for the given temperatures.

The best possible COP occurs when all the heat energy is transferred to the hot reservoir and no work is done. Since the temperatures are given in Celsius, we need to convert them to Kelvin before applying the formula.

Converting 5.00°C to Kelvin: Tc = 5.00 + 273.15 = 278.15 K

Converting 35.0°C to Kelvin: Th = 35.0 + 273.15 = 308.15 K

Now we can calculate the best possible COP:

COP = Th / (Th - Tc) = 308.15 / (308.15 - 278.15) = 6.50

Therefore, the best possible coefficient of performance for these temperatures is c) 6.50.