(a)
The expression for the final length of the rod.
(a)
Answer to Problem 19.77CP
The expression for the final length of the rod is
Explanation of Solution
Given Info: The length of the rod is
The relation of the coefficient of the linear expansion with the changing length with temperature is,
Here,
To get the expression for the final length at high temperature, integrate the above expression.
Here,
Conclusion:
Therefore, the expression for the final length of the rod is
(b)
The error caused by the approximation.
(b)
Answer to Problem 19.77CP
The error caused by the approximation is
Explanation of Solution
Given Info: The length of the rod is
Formula to calculate the new length of the rod at higher temperature is,
Substitute
Thus, the length of the rod at higher temperature is
The formula used in part (a) to calculate the new length of the rod at higher temperature is,
Substitute
Formula to calculate the percentage difference of the new length is,
Substitute
Conclusion:
Therefore, error caused by the approximation is
(c)
The error caused by the approximation.
(c)
Answer to Problem 19.77CP
The error caused by the approximation is
Explanation of Solution
Given Info: The length of the rod is
Formula to calculate the new length of the rod at higher temperature is,
Substitute
Thus, the new length of the rod at higher temperature is
The formula used in part (a) to calculate the new length of the rod at higher temperature is,
Substitute
Formula to calculate the percentage difference of the new length is,
Substitute
Conclusion:
Therefore, the error caused by the approximation is
(d)
The receding level of the turpentine.
(d)
Answer to Problem 19.77CP
The receding level of the turpentine is
Explanation of Solution
Given info: The length of the rod is
The formula used in part (a) to calculate the new length of the rod at higher temperature is,
The volume varies correspondingly as the above expression.
Here,
The change in the temperature is,
Substitute
Thus, the change in temperature is
Substitute
Thus, the final volume of the turpentine is
Substitute
Write the expression to calculate the volume of the turpentine that overflows.
Substitute
To calculate the volume of the turpentine remaining is,
Thus, the volume of the turpentine remaining is
Receding level of turpentine is,
Conclusion:
Therefore, receding level of the turpentine is
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Chapter 19 Solutions
PHYSICS:F/SCI.+ENG.,TECH.UPD.-WEBASSIGN
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