First slide

Conduction

Question

A rod CD of thermal resistance 5.0 K/W is joined at the middle of an identical rod AB as shown in fig. The ends A, B and D are maintained at 100°C, 0°C and 25°C respectively. The temperature of junction C will be

Moderate

A

30°C
B

45°C
C

60°C
D

80°C

Solution

We know that thermal resistance $R = l / KA$
Let heat currents between AC, CB and CD be i, i₁ and. i₂ respectively as shown in the fig. (3).Then $i = {\dot{I}}_{1} + i_{2}$
So, $\frac{100 - T}{(R / 2)} = \frac{T - 0}{(R / 2)} + \frac{T - 25}{R}$
or $200 - 2 T = 2 T + (T - 25)$
or $225 = 5 T or T = 45^{\circ} C$

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