Question

According to the experiment of Ingen Hauz’s the relation between the thermal conductivity of a metal rod is K and the length of the rod whenever the wax melts
A. \[\dfrac{K}{l} = \text{constant}\]
B. \[\dfrac{{{K^2}}}{l} = \text{constant}\]
C. \[\dfrac{K}{{{l^2}}} = \text{constant}\]
D. \[Kl = \text{constant}\]

Answer 1

Hint: According to Ingen Hauz’s experiment if a number of identical rods made up of different metals are coated with wax and one of the ends is put in boiled water then a square of the length over which the wax melts is directly proportional to the thermal conductivity of the rod.

Complete step by step solution:
Consider the experiment of Ingen Hausz. Here when the wax starts melting, we need to find the relation between the thermal conductivity of a metal rod K, and the length of the rod. As we know, according to Ingen Hauz’s experiment, the relation between the thermal conductivity of a metal rod is K and the length of the rod is given by,
\[K \propto {l^2}\]

That means, the thermal conductivity of the rod is directly proportional to the square of the length of the given rod. This can also be written in the form of,
\[\dfrac{K}{{{l^2}}} = cons\tan t\]
Therefore, the relation between the thermal conductivity of a metal rod is K and the length of the rod is \[\dfrac{K}{{{l^2}}} = \text{constant}\].

Hence, option C is the correct answer.

Note:Here in the given problem it is important to remember the relation between the thermal conductivity of a metal rod is K and the length of the rod. In this experiment, several rods of different metals and of the equal area of cross section and polish to ensure equal emissivity are coated with wax. One end of each of the rods is placed in an oil bath and heat is transferred from the end introduced into the bath towards the other end exposed outside causing the melting of wax on the surface. The thermal conductivities of different materials are compared and determined if that of any one material is known.