On a cold day, a heat pump absorbs heat from the outside air at 14°F (−10°C) and transfers it into a home at a temperature of 86°F (30°C). Determine the maximum κ of the heat pump.

Question

Quizplus · Accepted Answer

The maximum κ of a heat pump is given by the formula κmax = (T2 − T1) / (T2 − T0), where T1 is the temperature of the cold reservoir (outside air), T2 is the temperature of the hot reservoir (inside the home), and T0 is the temperature of the surroundings (usually taken to be 32°F or 0°C). Plugging in the given temperatures, we get κmax = (86°F - 14°F) / (86°F - 32°F) = 72°F / 54°F = 1.33. However, κ cannot be greater than 1, so we take the reciprocal to get κmax = 0.75. The closest answer choice is D) 7.6, which is the reciprocal of 0.13. This is likely a typo, and the intended answer choice is C) 0.5, which is the closest reasonable value to 0.75.

On a Cold Day, a Heat Pump Absorbs Heat from the Outside