Question

A clyinderical metallic rod in thermal contact with two resevoirs of heat at it's two ends and conduct an amount of heat q in time t. The metallic rod is melted and the material is formed into a new rod having radius 1/2 of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the same two resevoirs in time t .

Answer 1

Let the thermal conductivity be K

Heat =Q

Time equal to t

Length equal to L

Radius equal to r

Let ∆T be the difference of temperature of the two reservoir.

Q =Kπr² (∆T)*t)/L

Now the rod is melted radius is made half times the original radius.

Let the new length of the rod = L'

Volume of the rod= V

V=πr² =π(r/2)²L'

So, L'=4L

Now heat conducted by the new conductor is

Q'=Kπ(r/2)²(∆T)t/(4L)

=Kπr²(∆T)t/16L

= Q/16

[Therefore Q'=Q/16]