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Q.

Three rods made of the 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^oC and $90^{o}$ respectively. The temperature of the junction of the three rods will be

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a

$45^{o} C$

b

$20^{o} C$

c

$30^{o} C$

d

$60^{o} C$

answer is B.

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Detailed Solution

Let the temperature at the point of contact of three rod is T, as we know that total incoming of heat is equal to total outgoing heat. We know that heat flow is given as Q $= \frac{K A (Δ T)}{L}$
So, $\frac{K A (0 - T)}{L} = \frac{K A (T - 90)}{L} + \frac{K A (T - 90)}{L}$
Therefore, $3 T = 180^{0} C$
$T = 60^{0} C$

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Three rods made of the 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 0oC and 90o respectively. The temperature of the junction of the three rods will be