Question

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then find the conductivity of the composite plate.
A. 5
B. 2.4
C. 1.5
D. 1.2

Answer 1

Hint: Before we solve this problem, we need to understand thermal conductivity. The rate at which heat is transferred by conduction through a unit cross-section area of a material is known as thermal conductivity. A composite plate is one that is made up of composite material.

Formula Used:
To find the thermal conductivity of a composite plate the formula is,
\[{K_{eq}} = \dfrac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\]
Where, \[{K_1},{K_2}\] are thermal conductivities of two metal plates.

Complete step by step solution:
Consider two identical plates of different metals that are joined to form a single plate whose thickness is double the thickness of each plate. The coefficients of conductivity of each plate are 2 and 3 respectively, that is \[{K_1} = 2\] and \[{K_2} = 3\], then here we need to find the conductivity of the composite plate.

The thermal conductivity of a composite plate is,
\[{K_{eq}} = \dfrac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}\]
substitute the value of \[{K_1}\] and \[{K_2}\] in the above equation, then,
\[{K_{eq}} = \dfrac{{2 \times 2 \times 3}}{{2 + 3}}\]
\[\Rightarrow {K_{eq}} = \dfrac{{12}}{5}\]
\[\therefore {K_{eq}} = 2.4\]
Therefore, the conductivity of the composite plate is 2.4.

Hence, option B is the correct answer.

Note: High thermal conductivity materials are employed as heat sinks, whilst low thermal conductivity materials are used as thermal insulators. There are numerous ways for measuring the thermal conductivities of materials, which are essentially categorised into two categories of approaches: transient and steady-state procedures.