Question

A heat pump extracts 7.0 × 10⁶ J of heat per hour from a well at 280 K and delivers its output heat into a house at 320 K. If the heat pump uses an ideal Carnot cycle in its operation, what is the minimum work that must be supplied to the heat pump per hour?

Answer 1

The minimum work required by an ideal Carnot heat pump that extracts 7.0 × 10⁶ J of heat per hour from a well at 280 K and delivers it into a house at 320 K is 875,000 J per hour.

Step-by-step explanation:

To calculate the minimum work required by an ideal Carnot heat pump, we use the performance coefficient equation for a heat pump, which is Kp = Qh/W, where Qh is the heat delivered to the hot reservoir (house), W is the work supplied, and Th and Tc are the temperatures of the hot and cold reservoirs, respectively. For this question, Qh is given as 7.0 × 10⁶ J per hour, Th is 320 K, and Tc is 280 K. Thus, the performance coefficient of the heat pump is Kp = 320 / (320 - 280) = 8. Using this value, we can find the minimum work, W, that must be supplied:

W = Qh/Kp

W = (7.0 × 10⁶ J) / 8

W = 8.75 × 10⁵ J (or 875,000 J)

Therefore, the minimum work required by this heat pump per hour is 875,000 J.