Question

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

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

Answer 1

Answer: (A)

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