Efficient Heating with Heat Pump: Calculating Energy Requirements
What is the minimum rate of energy that must be supplied to a heat pump in order to maintain an interior temperature of 22°C and offset heat losses in the house?
Answer:
The heat pump needs to receive energy at a minimum rate of 23 kW in order to maintain an interior temperature of 22°C and offset heat losses in the house while operating with an outside temperature of -10°C.
Understanding Heat Pumps:
A heat pump works by extracting heat from a colder region and transferring it to a warmer region. In the scenario provided, the heat pump acts as a refrigerator to heat the house. The outside temperature is -10°C, while the interior temperature is kept at 22°C. To offset normal heat losses in the house, the rate of heat delivery to the interior must be 16 kW.
The key factor in determining the energy requirements of a heat pump is the coefficient of performance (COP). The COP is the ratio of the desired heat output to the required work input. In this case, with a desired heat output of 16 kW, we need to calculate the work input, which represents the energy that must be supplied to the heat pump.
Calculating Energy Requirements:
The COP of a heat pump is influenced by the temperature difference between the regions it operates in. A greater temperature difference results in a lower COP. In this scenario, the temperature difference is 32°C (22°C - (-10°C)).
Using the COP formula COP = Q / W, where Q is the heat output and W is the work input, we can determine the work input needed. Given a hypothetical COP of 2 for a temperature difference of 32°C, the work input required would be 8 kW (16 kW / 2).
However, to supply energy at a rate higher than the work input to account for system losses, we calculate the total energy rate required as 8 kW + 16 kW = 24 kW. Considering real systems have losses, the actual minimum rate would be slightly higher, leading to an approximate value of 23 kW.
In conclusion, a minimum energy rate of 23 kW must be supplied to the heat pump to maintain the desired interior temperature of 22°C and offset heat losses effectively.