An air source heat pump has a cold side of -25 C and a hot side of 50 C. What is the COP of heating?

Question

BlackTom AI · Accepted Answer

First, recall the formula for the heating COP of a heat pump in terms of temperatures: COP_heating ≈ T_hot / (T_hot − T_cold), where temperatures are in Kelvin.

Option a. 4,3
This value is consistent with the calculation using T_hot = 50°C → 323 K and T_cold = −25°C → 248 K. COP_heating ≈ 323 / (323 − 248) = 323 / 75 ≈ 4.31, which aligns with “4,3” when using European decimal notation.

Option b. 11,3
A COP of about 11.3 is far higher than what the thermodynamic limit for the given temperature difference would allow under the Carnot-like idealization. This would imply an extremely efficient device, which is not feasible given a 75 K temperature lift.

Option c. 14,7
Similarly, 14.7 would require an even larger COP than the Carnot limit permits for a 75 K lift. This suggests a misapplication of the formula or a miscalculation of temperatures.

Option d. 3,3
A COP of 3.3 would correspond to a larger temperature lift or lower hot-side temperature in the ideal formula, but with the actual numbers (323 K hot side, 248 K cold side), the calculated COP is notably higher than 3.3, indicating this value is too low for the given conditions.

In summary, the calculation using T_hot = 323 K and T_cold = 248 K yields a COP near 4.31, which corresponds to approximately 4,3 in the given notation. The other options are inconsistent with the thermodynamic relationship and the specific temperature difference provided.

An air source heat pump has a cold side of -25 C and a hot side of 50 C. What is the COP of heating?单项选择题

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