Question

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. Tire metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod. when placed in thermal contact with the two reservoirs in time t ?

(a) Q/4

(b) Q/16

(c) 2Q

(d) Q/2

Answer 1

Correct option (b) Q/16

Explanation:

The amount of heat flows in time t through a cylindrical metallic rod of length L and uniform area of cross-section A(=πR²) with its ends maintained at temperatures T₁ and T₂ (T₁ >T₂) is  given by

where K is the thermal conductivity of the material of the rod.

Area of cross-section of new rod

Now. the amount of heat flows in same time t in the new rod with its ends maintained at the same temperatures T₁ and T₂ is given by

Substituting the values of A' and L' from equations (ii) and (iii) in the above equation, we get