An athlete whose mass is 70.0 kg drinks 16.0 ounces (454 g) of refrigerated water. The water is at a temperature of 35.0°F. (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 98.6°F), 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
(a)
The entropy rise of the entire system.
Answer to Problem 22.78AP
The entropy rise of the entire system is
Explanation of Solution
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
Here,
Substitute
Here,
Substitute
Integrate the above expression from the limit of
Write the expression to calculate the change in entropy of water.
Substitute
Conclusion:
Substitute
Thus, the entropy rise of the entire system is
(b)
The athlete’s temperature after she drinks the cold water.
Answer to Problem 22.78AP
The final temperature of the body is
Explanation of Solution
Write the expression of heat balance equation.
Here,
Conclusion:
Substitute
Therefore, the final temperature of the body is
(c)
The entropy rise of the entire system.
Answer to Problem 22.78AP
The entropy rise of the entire system is
Explanation of Solution
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
Conclusion:
Substitute
`
Thus, the entropy rise of the entire system is
(d)
The result by comparing the part (a) and (c).
Answer to Problem 22.78AP
The the change in entropy in part (c) is less than that of part (a) by a factor of
Explanation of Solution
Write the expression for the ratio of entropy in part (c) and (a)
Here,
Conclusion:
Thus the change in entropy in part (c) is less than that of part (a) by a factor of
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Chapter 22 Solutions
Physics for Scientists and Engineers, Volume 1
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