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Question

A cylindrical rod has a hot end at 70C and cold end at 30C. The rate of heat flow is 9 W. If the dimensions of the cylindrical rod are tripled keeping the temperature difference constant, then find the value of new rate of heat flow.

A
9 W
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B
81 W
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C
18 W
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D
27 W
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Solution

The correct option is D 27 W
Let the length of the cylindrical rod be l1,
Area of cross-section of cylindrical rod be A1,
Temperature difference between the ends of rod:
(T1T2)=40C
Given, Rate of heat flow:
(Q1)=9 W
If the dimensions tripled, then:
l2=3l1;A2=πr22=π(3r1)2=9(πr21)=9A1
Applying the equation of thermal conductivity:
Q1Q2=(A1A2)×(l2l1)=19×3=13
Q2=3Q1=3×9=27 W

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