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*2.25cm=5.06*10^(-4)m`

The length of the rectangular bar is

`l=0.500\text{ m}`

The rate of heat transferr is

`(Q)/(t)=15\text{ J/s}`

To find

The thermal conductivity of the bar

Step-by-step explanation:

The rate of heat transfer is:

`\begin{gathered} (Q)/(t)=kA(T_2-T_1)/(l) \\ \Rightarrow15=k*5.06*10^(-4)*(100-0)/(0.5) \\ \Rightarrow k=148.221W/m^oC \end{gathered}`

Conclusion

The thernal conductivity is

`148.221W/m^oC`