Question

A cylindrical metal bar conducts heat at a rate R from a hot object to a cold object.
If both its length and diameter are doubled, it will conduct heat at a rate
(a) R
(b) 2R
(c) 4R
(d) 8R

Answer 1

is it b

Answer 2

@cormacpayne

Answer 3

How did you get B?

Answer 4

since the length and the diameter is doubled!

Answer 5

@surjithayer

Answer 6

B is the right answer, I was just seeing how you got it. If the length and diameter are both doubled, how is the heat transfer doubled as well?

Answer 7

I really don't know I was more like a guess to be honest with you

Answer 8

Okay, so heat transfer is proportional to the area of the circle of the cylinder, and inversely related to the length of the cylinder. So it would look like
\[R = \frac{ kA }{ L }\]
where R is the heat transfer, A is the area, L is the length, and k is some constant (don't worry about that)

Answer 9

So if the diameter is doubled, then the radius is doubled, meaning the area is quadrupled, or 4A, and if the length is doubled, that means we have 2L in the denominator. Then we just have to do the division and we get 2.

Answer 10

now I understand it thank you

Answer 11

No problem!