Explanation:
Expression to calculate thermal resistance for iron (
) is as follows.
where,
= length of the iron bar
= thermal conductivity of iron
= Area of cross-section for the iron bar
Thermal resistance for copper (
) = \frac{L_{c}}{k_{c} \times A_{c}}[/tex]
where,
= length of copper bar
= thermal conductivity of copper
= Area of cross-section for the copper bar
Now, expression for the transfer of heat per unit cell is as follows.
Q = ![\frac{(100^{o} - 0^{o}}{\frac{L_{I}}{k_{I}.A_{I}} + \frac{L_{c}}{k_{c}.A_{c}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%28100%5E%7Bo%7D%20-%200%5E%7Bo%7D%7D%7B%5Cfrac%7BL_%7BI%7D%7D%7Bk_%7BI%7D.A_%7BI%7D%7D%20%2B%20%5Cfrac%7BL_%7Bc%7D%7D%7Bk_%7Bc%7D.A_%7Bc%7D%7D%7D)
Putting the given values into the above formula as follows.
Q = ![\frac{(100^{o} - 0^{o})}{\frac{L_{I}}{k_{I}.A_{I}} + \frac{L_{c}}{k_{c}.A_{c}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%28100%5E%7Bo%7D%20-%200%5E%7Bo%7D%29%7D%7B%5Cfrac%7BL_%7BI%7D%7D%7Bk_%7BI%7D.A_%7BI%7D%7D%20%2B%20%5Cfrac%7BL_%7Bc%7D%7D%7Bk_%7Bc%7D.A_%7Bc%7D%7D%7D)
= ![\frac{(100^{o} - 0^{o})}{21 \times 10^{-2} m[\frac{1}{73 \times 10^{-4}m^{2}} + \frac{1}{386 \times 10^{-4}m^{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%28100%5E%7Bo%7D%20-%200%5E%7Bo%7D%29%7D%7B21%20%5Ctimes%2010%5E%7B-2%7D%20m%5B%5Cfrac%7B1%7D%7B73%20%5Ctimes%2010%5E%7B-4%7Dm%5E%7B2%7D%7D%20%2B%20%5Cfrac%7B1%7D%7B386%20%5Ctimes%2010%5E%7B-4%7Dm%5E%7B2%7D%7D%7D)
= 2.92 Joule
It is known that heat transfer per unit time is equal to the power conducted through the rod. Hence,
P = ![\frac{Q}{T}](https://tex.z-dn.net/?f=%5Cfrac%7BQ%7D%7BT%7D)
Here, T is 1 second so, power conducted is equal to heat transferred.
So, P = 2.92 watt
Thus, we can conclude that 2.92 watt power will be conducted through the rod when it reaches steady state.