Question

A metal plate $4mm$ thick has a temperature difference of $32^{\circ }C$ between its faces. It transmits $200kcal/h$ through an area of $5c{m}^2$. Thermal conductivity of the material is

• A. $58.33W/m-{}^{\circ }C$
• B. $33.58W/m-{}^{\circ }C$
• C. $5\times 10^{-4}W/m-{}^{\circ }C$
• D. None of these

Answer 1

Answer: (A)

Here, $\Delta x=4mm=4\times 10^{-3}m$
$\Delta T=32^{\circ }C$
Transmit heat per hours
$\frac{\Delta Q}{\Delta T}=200kcal/h$
$=\frac{200\times 1000\times 4.2}{60\times 60}J/s$
$=233.33J/s$
$A=5c{m}^2=5\times 10^{-4}{m}^2$
We know that
$\frac{\Delta Q}{\Delta T}=KA\left(\frac{\Delta T}{\Delta x}\right)$
$\therefore$ Thermal conductivity of material
$K=\frac{\Delta Q/\Delta T}{A(\Delta T/\Delta x)}$
or $K=\frac{233.33\times 4\times 10^{-3}}{5\times 10^{-4}\times 32}$
$=58.33W/m-{}^{\circ }C$