(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%.
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Chapter 18 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
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