Textbook Question
CALC You make tea with 0.250 kg of 85.0°C water and let it cool to room temperature 120.0°C2. (a) Calculate the entropy change of the water while it cools.
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Ch 20: The Second Law of Thermodynamics
Chapter 20, Problem 20
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 (EER). If a room air conditioner has K = 3.0, what is its EER?
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Identify the given values: Coefficient of performance (K) = 3.0.
Understand the relationship between K and EER. K is the ratio of the heat removed per unit energy input (H/P) when both are measured in the same units. EER is used when H is in Btu/h and P is in watts.
Convert the coefficient of performance (K) to EER using the conversion factor between watts and Btu/h. Note that 1 watt = 0.000947817 Btu/h.
Calculate EER by multiplying K by the conversion factor from watts to Btu/h.
The result from the previous step gives the EER when H is in Btu/h and P is in watts.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coefficient of Performance (K)
The Coefficient of Performance (K) is a measure of the efficiency of a heating or cooling system, defined as the ratio of useful heating or cooling provided (H) to the work input (P). It is a dimensionless quantity, meaning it has no units, and its value remains consistent regardless of the measurement units used for H and P, as long as they are the same.
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Energy Efficiency Ratio (EER)
The Energy Efficiency Ratio (EER) is a specific measure of the efficiency of air conditioning systems, calculated as the ratio of the cooling output in British thermal units per hour (Btu/h) to the electrical input in watts. When using mixed units, such as Btu/h for H and watts for P, the EER provides a standardized way to compare the performance of different air conditioning units.
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Unit Conversion
Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In the context of the question, converting the Coefficient of Performance from a dimensionless ratio to the Energy Efficiency Ratio requires careful attention to the units of measurement for heating (H) and power (P). Understanding how to perform these conversions is essential for accurately interpreting and comparing efficiency metrics.
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