Concept explainers
(a)
To Calculate:The thermal current in each cube.
(a)
Answer to Problem 37P
The thermal current in copper cube is approximately
The thermal current in aluminum cube is approximately
Explanation of Solution
Given:
Thermal
Areaof cross-section of copper,
Temperature difference,
Thermal conductivity of aluminum,
Areaof cross-section of aluminum,
Formula used: The amount of heat
Here, L the thickness of the substance. The cross-section area of the substance,
temperature difference among the ends of the substance and k the thermal conductivity of thesubstance.
The thermal resistance is given by:
Then the equation (1) is written as
Here, the thermal current
Calculation:
The thermal current within each cube, is expressed as follows:
The thermal resistance of each cube is:
By using the equation (2), the thermal current through the copper can be expressed as follows:
By using the equation (2), the thermal current through the Aluminum can be expressed asfollows:
Hence, the thermal current in aluminum cube is approximately
Conclusion: The thermal current in each cube is to be calculated by using temperature difference and thermal conductivity.
(b)
To Calculate: The total thermal current.
(b)
Answer to Problem 37P
The total thermal current is
Explanation of Solution
Given:Current passing through the copper
Current passing through the aluminum
Formula used:
Given that the cubes are in parallel, therefore total thermal current can be expressed as:
Calculation:
Substitute the values and solve:
Conclusion: Hence,the total thermal current is
(c)
To Calculate:The thermal resistance of two cube combination.
(c)
Answer to Problem 37P
The equivalent thermal resistance is
Explanation of Solution
Given:The temperature difference
Formula used:
The equivalent thermal resistance is obtained by:
Where,
Calculation:
Substitute the values and solve:
Hence, the equivalent thermal resistance is
Conclusion:Equivalent thermal resistance can be calculated using temperature difference and thermal current.
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Chapter 20 Solutions
Physics for Scientists and Engineers
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