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14 days ago

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The ends of a cylindrical steel rod are maintained at two different temperatures. The rod conducts heat from one end to the othe

r at a rate of 10 cal/s. At what rate would a steel rod twice as long and twice the diameter conduct heat between the same two temperatures?

1 answer:

serg [3.5K]14 days ago

7 0

Answer:20 cal/s

Explanation:

Given

Heat transfer rate is $\dot{Q}=10 cal/s$

Also heat rate is given by

$\dot{Q}=kA\frac{dT}{dx}$

where $k=thermal\ conductivity$

$A=area\ of\ cross-section$

$dT=change\ in\ temperature$

$dx=change\ in\ length$

$10=k\frac{\pi }{4}d^2\frac{dT}{L}----1$ For $d'=2d, Length L'=2L$

$\dot{Q}=k\frac{\pi }{4}(2d)^2\frac{dT}{2L}---2$

dividing 1 and 2 we get

$\frac{10}{\dot{Q}}=\frac{2d^2}{4d^2}$

$\dot{Q}=20 cal/s$

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<pconsequently the="" car="" was="" driving="" at:="">

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