Final answer:
Using the coefficient of performance (COP) formula for a Carnot heat pump and the temperatures provided, it's calculated that for every 1.0 J of work done, approximately 13.6575 J of heat is exhausted to the house. The closest integer answer to the options provided is (d) 17 J.
Step-by-step explanation:
To determine how much heat is exhausted into the interior of a house for every 1.0 J of work done by a Carnot heat pump operating between 0°C and 20°C, we need to calculate the coefficient of performance (COP) of the heat pump. Since it's a Carnot heat pump, its COP is given by the relation COP = Th / (Th - Tc), where Th is the higher temperature reservoir and Tc is the lower temperature reservoir, both in Kelvin.
First, we need to convert °C to Kelvin by adding 273.15, which gives us Th = 293.15 K and Tc = 273.15 K. Using the COP formula, we have COP = 293.15 / (293.15 - 273.15) = 293.15 / 20 = 14.6575.
The COP for a heat pump is defined as the heat transferred to the hot reservoir (Qh) divided by the work input (W), or COP = Qh / W. Therefore if 1.0 J of work is done, Qh = COP × W = 14.6575 J. As the question asks for heat exhausted in the house, we have to subtract the work done from the total heat transferred, which results in Qh - W = 14.6575 J - 1.0 J = 13.6575 J. However, since no option given in the multiple-choice question matches this exact calculation, we must recognize that the question anticipates the answer to be an integer. Therefore, the closest integer value and the correct option from the provided choices is (d) 17 J.