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Three rods of lengths $3 l, 2 l a n d 3 l$ with same area of cross section and thermal conductivities $3 K, 2 K a n d K$ respectively are joined in $Y$ shape. The temperatures of the free ends are kept constant at $3 T, 2 T a n d T$ respectively. Then

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Heat flows towards the junction in one rod

The temperature of the Y junction is $\frac{16 T}{7}$

Heat flows towards the junction in two rods

The temperature of the Y junction is $\frac{13 T}{7}$

answer is B, D.

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Detailed Solution

Let $\frac{l}{K A} = R$
The resistances will be $R, R a n d 3 R$
$\frac{3 T - T_{0}}{R} + \frac{2 T - T_{0}}{R} + \frac{T - T_{0}}{3 R} = 0$
$T_{0} = \frac{16 T}{7}$ which is greater then T and 2T.
Heat flows towards the junction in only one rod.

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