Question

# A cylindrical rod has a hot end at 70∘C and cold end at 30∘C. 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.9 W81 W18 W27 W

Solution

## The correct option is D 27 WLength 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 or 313 K Given, Rate of heat flow (Q1)=9 W If the dimension 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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