Concept explainers
(a)
The amount of turpentine overflows when the turpentine and aluminum cylinder are warmed slowly.
(a)
Answer to Problem 19P
The amount of turpentine overflows when the turpentine and aluminum cylinder are warmed slowly is
Explanation of Solution
Write the expression for change in volume when the temperature rises by
Here,
From the equation (I), write the expression for changing volume of the cylinder and the turpentine.
Here,
Substitute,
Conclusion:
Substitute,
Therefore, the amount of turpentine overflows when the turpentine and aluminum cylinder are warmed slowly is
(b)
The volume of the turpentine remaining in the cylinder.
(b)
Answer to Problem 19P
The volume of the turpentine remaining in the cylinder is
Explanation of Solution
The volume of the aluminum cylinder at
Here,
Substitute,
Conclusion:
Substitute,
Therefore, the volume of the turpentine remaining in the cylinder is
(c)
The empty height of the cylinder above the turpentine if the combination with turpentine cooled back to
(c)
Answer to Problem 19P
The empty height of the cylinder above the turpentine if the combination with turpentine cooled back to
Explanation of Solution
Write the expression for volume of the turpentine in the cylinder after it cools back.
Simplify the equation (IV).
Conclusion:
Substitute,
The percentage of cylinder that is empty at
Then the empty height of the cylinder above the turpentine can calculated as follows,
Therefore, the empty height of the cylinder above the turpentine if the combination with turpentine cooled back to
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Chapter 16 Solutions
Principles of Physics: A Calculus-Based Text
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