Question

The two rods shown in figure (28-E6) have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.
Figure

Answer 1

The temperature of the junction if the rods are interchanged is $T=30^{\circ} \mathrm{C}$

Explanation:

Step 1:

Let the two rods are P and Q

These rods are in series so rate of heat flow is equal $q_{p}=q_{Q}$

Given, the temperature of heat baths = 100°C and 0°C

Temperature of the junction = 70°C

Step 2:

Both the rods have identical dimension that is equal length and area

$\frac{K_{P} A(100-70)}{l}=\frac{K_{Q} A(70-0)}{l}$

$3 K_{P}=7 K_{Q}$

$\frac{K Q}{K_{P}}=\frac{3}{7}$

Step 3:

If the rods are interchanged again the rate of heat flow is equal $q_{Q=}$$q_{p}$

Let the temperature at junction is T $\frac{K_{Q} A(100-T)}{l}=\frac{K_{P} A(T-0)}{l}$

By solving above equation $100 K_{Q}=\mathrm{T}\left(K_{Q}+7 K_{Q} / 3\right)$

$T=30^{\circ} \mathrm{C}$