Physics

Problem

A Carnot refrigerator operates between a cold reservoir at

270\,\text{K}

and a hot reservoir at

300\,\text{K}

. When the same device is used as a heat pump between these two reservoirs, its coefficient of performance is a)

9

10

8

12

Intuitive explanation

A Carnot refrigerator and heat pump are the same device run in opposite directions—the key is recognizing that their performance coefficients are related by the reservoir temperatures. For a heat pump, you're interested in how much heat is delivered to the hot side per unit work input, which depends on the temperature ratio between the reservoirs. Use the Carnot efficiency relationships to connect the refrigerator's coefficient of performance to the heat pump's, or derive the heat pump COP directly from $Q_h = W + Q_c$ and the reversible condition.

Intuitive explanation

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