Chapter 14, Problem 43P

To determine

The temperature at the point of joining

Answer to Problem 43P

Solution:

$\text{134}°\text{C}$

Explanation of Solution

Given Info:

Copper and aluminum rods have same length and cross sectional area. Copper end is at 205°C and aluminum end is at 0°C

Formula used:

Rate of heat flow can be calculated by

$\frac{Q}{t}=kA\frac{T_1-T_2}{l}$

Calculation:

Rate of heat flow is equal for both so on equating

$k_{Cu}A\frac{\Delta T}{l}=k_{Al}A\frac{\Delta T}{l}$

Let the temperature of junction be T_m

$\begin{array}{l}{k}_{Cu}A(T_h-T_m)=k_{Al}A(T_m-T_c)\\ T_m=\frac{T_h{k}_{Cu}+k_{Al}{T}_c}{k_{Cu}+k_{Al}}\\ T_m=\frac{205(380)+200(0)}{380+200}\\ T_m=134\end{array}$