Question

One end of an iron rod is placed in a fire where the temperature is ${499}^{\circ }\text{C}$, and the other end is kept at a temperature of ${25}^{\circ }\text{C}$. The rod is $1.2\text{m}$ long and has an area of $5.0\times {10}^{–3}{\text{m}}^2$. Ignoring the heat lost along the length of the rod, find the amount of heat conducted (in $\text{J}$) from one end of the rod to the other in $5.0\text{s}$. Take the coefficient of thermal conductivity of iron as $80\text{J}/\left({\text{s.m.C}}^{\circ }\right)$.

Answer 1

In this task we have to find the amount of heat conducted from one end of the iron rod to other in 5 seconds.
Given :
$T_1={499}^{\circ }\text{C}$
$T_2={25}^{\circ }\text{C}$
$L=1.2\text{m}$
$A=5.0\times {10}^{–3}{\text{m}}^2$
Where $T_1$ and $T_2$ are temperature on the end of an iron rod, $L$ is length of the rod, $A$ is the area of the rod and $t$ is time
In this case we will calculate heat as :
$\frac{Q}{t}=\frac{KA\Delta T}{L}$
Where $K$ is the thermal conductivity constant for material
$Q=\frac{KA\Delta Tt}{L}$
$Q=\frac{80\times (5\times {10}^{-3})\times 474\times 5}{1.2}$
$Q=\frac{800}{12}\times 5\times 5\times 474\times {10}^{-3}$
$Q=790\text{J}$