Final answer:
The coefficient of performance for an ideal heat pump moving heat from a cold temperature of -25.0°C to a hot temperature of 40.0°C is approximately 3.82. However, given the options, the closest is 3.50 (option d). This suggests there may be a discrepancy or a need for approximation.
Step-by-step explanation:
Calculating the Coefficient of Performance for a Heat Pump
The coefficient of performance (COP) of a heat pump is a measure of its efficiency, calculated as the ratio of heat transfer to the work input. For an ideal heat pump, we can use the temperatures of the cold and hot reservoirs to calculate the COP. The formula for an ideal heat pump's COP is COP = QH / W = 1 / ((TH/TC) - 1) where TH and TC are the absolute temperatures of the hot and cold reservoirs, respectively, and W is the work input. Here, TH = 40.0°C = 313.15 K and TC = -25.0°C = 248.15 K.
Thus, COP = 1 / ((313.15 / 248.15) - 1) = 1 / ((1.262) - 1) = 1 / (0.262) ≈ 3.82. However, since this value is not among the choices given, it's important to verify if the options or the question itself contains a mistake.
By using the correct formula and calculations, we determine that the ideal COP for a heat pump operating between these temperatures is not exactly the same as any of the options provided. It is important to ensure that the temperature values and the COP formula are being used correctly. If no rounding or slight differences in temperature scales are considered, the given answer may be an approximate value. In such scenarios, the closest value to the calculated COP would be option (d) 3.50.