(a)
The entropy rise of the entire system.
(a)
Answer to Problem 56P
The entropy rise of the entire system is
Explanation of Solution
Given info: The mass of the athlete and the water is
Write the expression to calculate the change in entropy of the system.
Here,
Write the expression to calculate the change in entropy of water.
Here,
Write the expression to convert the temperature from Fahrenheit to Kelvin.
Substitute
Thus, the temperature of body in Kelvin is
Substitute
Thus, the temperature of water in Kelvin is
Substitute
Integrate the above expression from the limit of
Write the expression to calculate the change in entropy of water.
Here,
Substitute
Substitute
Thus, the entropy rise of the entire system is
Conclusion:
Therefore, the entropy rise of the entire system is
(b)
The athlete’s temperature after she drinks the cold water.
(b)
Answer to Problem 56P
The final temperature of the body is
Explanation of Solution
Given info: The mass of the athlete and the water is
Write the expression of heat balance equation.
Here,
Substitute
Conclusion:
Therefore, the final temperature of the body is
(c)
The entropy rise of the entire system.
(c)
Answer to Problem 56P
The entropy rise of the entire system is
Explanation of Solution
Given info: The mass of the athlete and the water is
Write the expression to calculate the change in entropy of the system.
Write the expression to calculate the change in entropy of water.
Integrate the above expression from the limit of
Substitute
Write the expression to calculate the change in entropy of body.
Here,
Integrate the above expression from the limit of
Substitute
Substitute
`
Thus, the entropy rise of the entire system is
Conclusion:
Therefore, the entropy rise of the entire system is
(d)
The result by comparing the part (a) and (c).
(d)
Answer to Problem 56P
The change in entropy in part (c) is less than that of part (a) by less than 1%.
Explanation of Solution
Given info: The mass of the athlete and the water is
The percentage change in entropy is,
Thus the change in entropy in part (c) is less than that of part (a) by less than 1%.
Conclusion:
Therefore, the change in entropy in part (c) is less than that of part (a) by less than 1%.
Want to see more full solutions like this?
Chapter 18 Solutions
Principles of Physics: A Calculus-Based Text
- Assume a sample of an ideal gas is at room temperature. What action will necessarily make the entropy of the sample increase? (a) Transfer energy into it by heat. (b) Transfer energy into it irreversibly by heat. (c) Do work on it. (d) Increase either its temperature or its volume, without letting the other variable decrease. (e) None of those choices is correct.arrow_forwardIs it possible for a system to have an entropy change if it neither absorbs nor emits heat during a reversible? transition? What happens it the process is irreversible?arrow_forwardAn athlete whose mass is 70.0 kg drinks 16.0 ounces (454 g) of refrigerated water. The water is at a temperature of 35.0F. (a) Ignoring the temperature change of the body that results from the water intake (so that the body is regarded as a reservoir always at 98.6F), find the entropy increase of the entire system. (b) What If? Assume the entire body is cooled by the drink and the average specific heat of a person is equal to the specific heat of liquid water. Ignoring any other energy transfers by heat and any metabolic energy release, find the athletes temperature after she drinks the cold water given an initial body temperature of 98.6F. (c) Under these assumptions, what is the entropy increase of the entire system? (d) State how this result compares with the one you obtained in part (a).arrow_forward
- An ideal gas is taken from an initial temperature Ti to a higher final temperature Tf along two different reversible paths. Path A is at constant pressure, and path B is at constant volume. What is the relation between the entropy changes of the gas for these paths? (a) SA SB (b) SA = SB (c) SA SBarrow_forwardWhich of the following is true for the entropy change of a system that undergoes a reversible, adiabatic process? (a) S 0 (b) S = 0 (c) S 0arrow_forwardDoes the entropy increase for a Carnot engine for each cycle?arrow_forward
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning