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23. The Second Law of Thermodynamics

Refrigerators

Physics

23. The Second Law of Thermodynamics

Refrigerators

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3:04 minutes

Problem 8

Textbook Question

The coefficient of performance $K = H / P$ is a dimensionless quantity. Its value is independent of the units used for $H$ and $P$ , as long as the same units, such as watts, are used for both quantities. However, it is common practice to express $H$ in Btu/h and $P$ in watts. When these mixed units are used, the ratio $H / P$ is called the energy efficiency ratio ( $E E R$ ). If a room air conditioner has $K equals 3.0$ , what is its $E E R$ ?

Verified step by step guidance

Understand that the coefficient of performance (K) is defined as the ratio of heat output (H) to power input (P), both measured in the same units, typically watts. Here, K = 3.0.

Recognize that the energy efficiency ratio (EER) is a similar concept to K, but it uses mixed units: H is measured in Btu/h and P in watts.

To convert the coefficient of performance (K) to the energy efficiency ratio (EER), you need to account for the unit conversion between Btu/h and watts. The conversion factor is 1 watt = 3.412 Btu/h.

Express the relationship between K and EER using the conversion factor: EER = K * 3.412.

Substitute the given value of K (3.0) into the equation to find the EER: EER = 3.0 * 3.412. This will give you the EER in Btu/h per watt.

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Key Concepts

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

Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure of the efficiency of a heat pump or air conditioning system, defined as the ratio of useful heating or cooling provided (H) to the work or energy input (P). It is dimensionless and indicates how effectively a system converts energy input into heating or cooling output.

Energy Efficiency Ratio (EER)

The Energy Efficiency Ratio (EER) is a metric used to evaluate the efficiency of cooling devices, calculated as the ratio of cooling capacity (H) in British thermal units per hour (Btu/h) to the electrical power input (P) in watts. EER provides a standardized way to compare the energy efficiency of air conditioners using mixed units.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set, ensuring consistency in calculations. In the context of EER, converting between Btu/h and watts is crucial for accurate efficiency assessment, as it involves understanding the relationship between different energy units and maintaining dimensional consistency.

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What is the maximum possible coefficient of performance for a refrigerator operating between 2.0°C (a typical refrigerator temperature) and 20°C (a typical kitchen temperature)?

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A certain brand of freezer is advertised to use $730$ kWh of energy per year. What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at $20.0$ °C?

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Textbook Question

A certain brand of freezer is advertised to use $730$ kWh of energy per year. Assuming the freezer operates for $5$ hours each day, how much power does it require while operating?

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Textbook Question

A refrigerator has a coefficient of performance of $2.25$ , runs on an input of $135$ W of electrical power, and keeps its inside compartment at $5$ °C. If you put a dozen $1.0$ -L plastic bottles of water at $31$ °C into this refrigerator, how long will it take for them to be cooled down to $5$ °C? (Ignore any heat that leaves the plastic.)

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Textbook Question

Home air conditioners in the United States have their power specified in the truly obscure units of tons, where 1 ton is the power needed to melt 1 ton (2000 lb or 910 kg) of ice in 24 hours. A modest-size house typically has a 4.0 ton air conditioner. If a 4.0 ton air conditioner has a coefficient of performance of 2.5, a typical value, at what rate in kW is heat energy removed from the house?

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Textbook Question

100 mL of water at 15℃ is placed in the freezer compartment of a refrigerator with a coefficient of performance of 4.0. How much heat energy is exhausted into the room as the water is changed to ice at -15℃?

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Textbook Question

An air conditioner removes 5.0 x 10⁵ J/min of heat from a house and exhausts 8.0 x 10⁵ J/min to the hot outdoors. What is the air conditioner's coefficient of performance?

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Textbook Question

What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in FIGURE EX21.21?

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