Explanation To convert water at 10.0 ° C to ice at − 20.0 ° C , it undergoes three stages of energy change. First energy is liberated from water at 10.0 ° C to water at 0 ° C . Second stage is the conversion of water into ice at freezing point. In third stage ice at 0 ° C changes to ice at − 20.0 ° C . Write the expression for the thermal energy removed from water to reach freezing point. | Q c 1 | = m water c water ( T w f − T w i ) (I) Here, | Q c 1 | is the thermal energy removed from water to become ice, m water is the mass of water, c water is the specific heat capacity of water, T w f is the final temperature of water and T w i is the initial temperature of water. Write the expression for the thermal energy removed at freezing point of water to become ice at same temperature. | Q c 2 | = m water L fusion (II) Here, | Q c 2 | is the thermal energy removed at freezing point of water, L fusion is the latent heat of fusion of water. Write the expression for the thermal energy removed from ice to reduce temperature. | Q c 3 | = m ice c ice ( T i f − T i i ) (III) Here, | Q c 3 | is the thermal energy removed from ice to reduce temperature, m ice is the mass of the ice, T i f is the final temperature of ice and T i i is the initial temperature of ice. Write the expression for the total heat removed. | Q c | = | Q c 1 | + | Q c 2 | + | Q c 3 | (IV) Q c is the total heat removed. Write the expression for the coefficient of performance of refrigerator. COP c = | Q c | W (V) Here, COP c is coefficient of performance of refrigerator, | Q c | is the energy by heat liberated at cold reservoir and W is the work done. Write the expression for the coefficient of performance of refrigerator. COP c = T c T h − T c (VI) Here, T c is the temperature of cold reservoir and T h is the temperature of heat reservoir. Equate equation (V) and (VI) to get expression for W . | Q c | W = T c T h − T c W = | Q c | ( T h − T c ) T c (VII) Write the expression to convert temperature in degree Celsius into Kelvin scale. T ( K ) = T ( ° C ) + 273 (VIII) Here, T ( K ) is the temperature in Kelvin scale and T ( ° C ) is the temperature in degree Celsius

Physics for Scientists and Engineers with Modern Physics, Technology Update

9th Edition

ISBN: 9781305401969

Author: SERWAY, Raymond A.; Jewett, John W.

Publisher: Cengage Learning

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Chapter 22, Problem 57AP

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The work required to change 0.500 kg of tap water at 10.0 °C into ice at −20.0 °C using an ideal Carnot refrigerator.

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Chapter 22, Problem 56AP

Chapter 22, Problem 58AP

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Chapter 22 Solutions

Physics for Scientists and Engineers with Modern Physics, Technology Update

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The work required to change 0.500 kg of tap water at 10.0 °C into ice at −20.0 °C using an ideal Carnot refrigerator.

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Chapter 22 Solutions