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Ch 20: The Second Law of Thermodynamics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 20: The Second Law of ThermodynamicsProblem 17c
Chapter 20, Problem 17c

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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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Related Practice
Textbook Question

A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320320 K and 270270 K. If in each cycle the refrigerator receives 415415 J of heat energy from the reservoir at 270270 K, how many joules of heat energy does it deliver to the reservoir at 320320 K?

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Textbook Question

A sophomore with nothing better to do adds heat to 0.3500.350 kg of ice at 0.00.0°C until it is all melted. What is the change in entropy of the water?

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Textbook Question

A certain brand of freezer is advertised to use 730730 kWh of energy per year. What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at 20.020.0°C?

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Textbook Question

A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320320 K and 270270 K. If the refrigerator completes 165165 cycles each minute, what power input is required to operate it?

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Textbook Question

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 55 minutes of operation, the heat rejected by the engine melts 0.04000.0400 kg of ice. During this time, how much work WW is performed by the engine?

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Textbook Question

A 4.504.50-kg block of ice at 0.000.00°C falls into the ocean and melts. The average temperature of the ocean is 3.503.50°C, including all the deep water. By how much does the change of this ice to water at 3.503.50°C alter the entropy of the world? Does the entropy increase or decrease? (Hint: Do you think that the ocean temperature will change appreciably as the ice melts?)

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