Question

The coefficient of thermal conductivity of a metallic rod does not depend upon:
(The question has multiple correct option)
A) The length of the rod.
B) The cross-sectional area of the rod.
C) Temperature difference between the ends of the rod.
D) The nature of the material.

Answer 1

Hint: Thermal conductivity or coefficient of thermal conductivity is the quantity which tells us the ability of a material to transfer heat through them. Here we will discuss the thermal conductivity in detail and the factor on which it depends. By doing so we will get the factors which are independent of thermal conductivity. As it is multiple correct option type questions one or more than one option can be correct.

Complete step by step answer:
Thermal conductivity is the property of the material which tells us its ability to conduct heat; its value varies from material to material hence we can say that the thermal conductivity depends on the nature of material or the type of material.
To know the other factors on which it depends let us consider a metallic rod of length L and the cross sectional area A, and the temperature at the ends of the rod is \[{{T}_{1}}\text{ and }{{T}_{2}}\]respectively.

Then the heat which will flow through the material will be proportional to the cross sectional area as the larger the area the more heat can flow. Similarly it will be proportional to the temperature difference and inversely proportional to the length of the rod.
If heat flow given as Q, then considering all the proportionality we can write
\[\begin{align}
  & Q\propto \dfrac{A({{T}_{1}}-{{T}_{2}})}{L} \\
 & Q=k\dfrac{A({{T}_{1}}-{{T}_{2}})}{L} \\
\end{align}\]
Where k is the proportionality constant and known as coefficient of thermal conductivity. Hence we can say that thermal conductivity or coefficient of thermal conductivity does not depend on length or cross sectional area or the temperature difference. It just depends on the type of material.
Hence correct options are A,B and C.

Note:
We can also see that as thermal conductivity is the internal property of a material to conduct heat therefore it will depend only on the nature of material. Also thermal conductivity is the same as electrical conductivity only difference is electrical conductivity there is transfer of charges whereas here there is transfer of heat.