Coefficient of performance (COP) of a heat pump process...

Question

BlackTom AI · Accepted Answer

The question concerns the coefficient of performance (COP) of a heat pump process and which statements about it are true.
Option a: 'is increasing with decreasing difference between the minimum and maximum temperatures of the process' The COP of a heat pump is influenced by the temperature lift, which is the difference between the hot and cold reservoir temperatures. For an ideal reversible (Carnot) heat pump, COP_HP = T_hot/(T_hot - T_cold). As the temperature difference (lift) decreases, the denominator shrinks, causing COP_HP to rise. Therefore, this statement is conceptually correct: a smaller temperature lift generally yields a higher COP.
Option d: 'increases with increasing isentropic efficiency of the compressor' The isentropic efficiency of the compressor reflects how close the actual compression process is to the ideal, lower-than-ideal work. Higher isentropic efficiency means less work input for the same heat transfer, or equivalently more useful heat delivered per unit of work. Since COP_HP = Q_h / W, increasing compressor efficiency reduces W for the same Q_h, leading to a higher COP. Thus, this statement is also correct.
Note on the missing options: The provided data lists only options a and d as part of answer choices, with no explicit text for options b and c. Without their content, we cannot analyze them, but the two given statements (a and d) align with standard thermodynamics of heat pumps: COP improves when the temperature lift is reduced, and improves when compressor is more efficient. 
In practical terms, both relationships hold under typical operating conditions, though real systems may exhibit additional factors (heat exchanger effectiveness, part-load operation, refrigerant properties, etc.) that can influence COP beyond the simplified ideal relationships.

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