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# Working with rods of different thermal conductivities

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Which of the following cylindrical rods of the same material with its ends at the same steady difference of temperature will conduct maximum heat ?

1. Lenght 100 cm & radius 1 cm

2. length 200 cm & radius 1 cm

3. length 400 cm & radius 2 cm

4. length 100 cm & radius 2 cm

https://brainmass.com/physics/work/working-rods-different-thermal-conductivities-7680

## SOLUTION This solution is FREE courtesy of BrainMass!

We have, the quantity of heat conducted

Q = K A (t1 - t2)/d

(t1 - t2) is the temperature difference existing between the ends of the rod.

Q is proportinal to A/d where A is the area of cross section.

Or we can write, Q proportional to r^2/d

Now we'll examine each case,

1. For this, r^2/d = 1/100 = 0.001

2. here, r^2/d = 1/200 = 0.002

3. r^2/d = 4/400 = 0.001

4. r^2/d = 4/100 = 0.04

Thus, case 4 corresponds to maximum amount of heat transfer.

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