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Ch 20: The Second Law of Thermodynamics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Capitolo 20, Problema 19c

A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320320 K and 270270 K. What is the coefficient of performance of the refrigerator?

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Understand the concept: The coefficient of performance (COP) for a refrigerator is a measure of its efficiency and is defined as the ratio of the heat removed from the cold reservoir (Qc) to the work input (W) required to remove that heat.
Recall the formula for the COP of a Carnot refrigerator: \( \text{COP} = \frac{T_c}{T_h - T_c} \), where \( T_c \) is the temperature of the cold reservoir and \( T_h \) is the temperature of the hot reservoir. Both temperatures should be in Kelvin.
Identify the given temperatures: The cold reservoir temperature \( T_c = 270 \text{ K} \) and the hot reservoir temperature \( T_h = 320 \text{ K} \).
Substitute the given temperatures into the COP formula: \( \text{COP} = \frac{270}{320 - 270} \).
Simplify the expression to find the COP: Calculate the difference in the denominator and then divide the cold reservoir temperature by this difference to find the COP.

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Carnot Refrigerator

A Carnot refrigerator is an idealized thermodynamic cycle that operates between two heat reservoirs. It is the most efficient refrigeration cycle possible, as it is reversible and operates without any entropy production. The performance of a Carnot refrigerator is determined by the temperatures of the hot and cold reservoirs.
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Coefficient of Performance (COP)

The Coefficient of Performance (COP) of a refrigerator is a measure of its efficiency, defined as the ratio of the heat removed from the cold reservoir to the work input required to remove that heat. For a Carnot refrigerator, the COP is given by the formula COP = T_c / (T_h - T_c), where T_c and T_h are the absolute temperatures of the cold and hot reservoirs, respectively.
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Absolute Temperature

Absolute temperature is measured in Kelvin (K) and is a fundamental concept in thermodynamics. It starts from absolute zero, the point at which all molecular motion ceases. In the context of the Carnot cycle, using absolute temperatures ensures that calculations of efficiency and performance are accurate, as these depend on the temperature difference between the reservoirs.
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Percorso guidato
04:54
Introduction To Temperature Scales
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