Q.A metal rod of length $2\ \text{m}$ and uniform cross-sectional area $5\ \text{cm}^2$ has its two ends maintained at steady temperatures of $100\,^\circ\text{C}$ and $0\,^\circ\text{C}$. If the thermal conductivity of the metal is $k = 200\ \text{W m}^{-1}\text{K}^{-1}$ and the sides of the rod are perfectly lagged (insulated), find the rate at which heat is conducted through the rod in the steady state.

Given: $k = 200\ \text{W m}^{-1}\text{K}^{-1}$, $A = 5\ \text{cm}^2 = 5\times10^{-4}\ \text{m}^2$, $\Delta T = 100 - 0 = 100\,^\circ\text{C}$, $L = 2\ \text{m}$.

Using the steady-state conduction law:

$\frac{Q}{t} = \frac{kA\,\Delta T}{L} = \frac{200 \times 5\times10^{-4} \times 100}{2}$ …

Convert the cross-sectional area to $\text{m}^2$, identify $\Delta T$ and $L$, and substitu …

• Forgetting to convert the area from $\text{cm}^2$ to $\text{m}^2$ (a factor-of-$10^4$ error). …