Question

In an experiment to determine the thermal conductivity of a bar of a new metal alloy, one end of the bar is maintained at 0.00 0C and the other end at 100. 0C. The rectangular bar is 2.25 cm x 2.25cm and a length of 0.500 m. If the rate of heat transfer through the bar is 15.0 J/s, what is the thermal conductivity of the bar to 3 sig fig?

Answer 1

Given

The temperatures are;

$\begin{gathered} T_1=0^oC \\ T_2=100^oC \end{gathered}$

The area of the rectangular bar

$A=2.25cm\times2.25cm=5.06\times10^{-4}m$

The length of the rectangular bar is

$l=0.500\text{ m}$

The rate of heat transferr is

$\frac{Q}{t}=15\text{ J/s}$

To find

The thermal conductivity of the bar

Explanation:

The rate of heat transfer is:

$\begin{gathered} \frac{Q}{t}=kA\frac{T_2-T_1}{l} \\ \Rightarrow15=k\times5.06\times10^{-4}\times\frac{100-0}{0.5} \\ \Rightarrow k=148.221W/m^oC \end{gathered}$

Conclusion

The thernal conductivity is

$148.221W/m^oC$