Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be [2001]

Question

Smart Achievers · Accepted Answer

(2)

Let $θ ° C$ be the temperature of junction at $B$ . Let $Q$ is the heat flowing per second from $A$ at $90 ° C$ to $B$ at $θ ° C$ on account of temperature difference.

$∴$ $Q = \frac{K A (90 - θ)}{l}$ ...(i)

And same for $C$ to $B$ .

$Q = \frac{K A (90 - θ)}{l}$

$∴$ The heat flowing per second from B to D

$2 Q = \frac{K A (θ - 0)}{l}$ ...(ii)

Dividing eq. (ii) by (i)

$2 = \frac{θ}{90 - θ} \Rightarrow θ = 60 °$

Hence temperature of the junction $θ = 60 ° C$

Solution

Q.
Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be [2001]

1 45°C

2 60°C

3 30°C

4 20°C

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