A cylindrical rod has a hot end at 70∘C and cold end at 30∘C. The rate of heat flow is 9W. 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
9W
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B
81W
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C
18W
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D
27W
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Solution
The correct option is D27W 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: (T1−T2)=40∘C
Given, Rate of heat flow: (Q1)=9W
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=27W