
(a)
The rate of heat
(a)

Answer to Problem 93P
The rate of heat conduction along the bar is
Explanation of Solution
Write the Fourier’s law of heat conduction.
Here,
Write the equation for
Here,
Put equation (II) in equation (I).
Conclusion:
Given that the cross sectional area of the bar is
Substitute
Therefore, the rate of heat conduction along the bar is
(b)
The temperature gradient in the bar.
(b)

Answer to Problem 93P
The temperature gradient in the bar is
Explanation of Solution
Write the equation for the temperature gradient.
Put equation (II) in the above equation.
Conclusion:
Substitute
Therefore, the temperature gradient in the bar is
(c)
The rate of heat conduction if two bars are placed in series between the same temperature baths.
(c)

Answer to Problem 93P
The rate of heat conduction if two bars are placed in series between the same temperature baths is
Explanation of Solution
When two similar bars are placed in series, the effective length will be doubled. Equation (III) can be used to find the rate of heat conduction with the value of length doubled.
Conclusion:
The new length is
Substitute
Therefore, the rate of heat conduction if two bars are placed in series between the same temperature baths is
(d)
The rate of heat conduction if two bars are placed in parallel between the same temperature baths.
(d)

Answer to Problem 93P
The rate of heat conduction if two bars are placed in parallel between the same temperature baths is
Explanation of Solution
When the two identical bars are placed parallel, the effective area gets doubled. Equation (III) can be used to find the rate of heat conduction with the value of area doubled.
Conclusion:
The new area is
Substitute
Therefore, the rate of heat conduction if two bars are placed in parallel between the same temperature baths is
(e)
The temperature at the junction, where the bars meet, in series case.
(e)

Answer to Problem 93P
The temperature at the junction, where the bars meet, in series case is
Explanation of Solution
The bars are identical. This implies the temperature at the junction will be midway between the temperatures of the constant-temperature paths.
Write the equation for the temperature at the junction.
Here,
Conclusion:
Substitute
Therefore, the temperature at the junction, where the bars meet, in series case is
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Chapter 14 Solutions
Physics
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