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Standard XII

Physics

Thermal Resistance

Six identical...

Question

Six identical conducting rods having uniform cross-section area are fixed to make a regular hexagon as shown. The ends A and C are maintained at constant temperature $2 T_{0}$ and $6 T_{0}$ . After the steady state is reached, pick up the correct relation between temperatures $T_{B}, T_{D}, T_{E}$ and $T_{F}$ of ends B, D, E and F respectively :
(Neglect convection and radiation losses)

T_{D} > T_{E} = T_{B} > T_{F}

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T_{D} = T_{B} > T_{E} > T_{F}

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T_{D} > T_{E} > T_{F} = T_{B}

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T_{B} > T_{F} = T_{E} > T_{D}

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Solution

The correct option is B $T_{D} > T_{E} = T_{B} > T_{F}$
The thermal resistance of above and lower portions will be $2 R$
and $4 R$ respectively where $R$ is thermal resistance of any one rod.

Hence,

In the above portion, $T_{B}$ will be average of $T_{A}$ and $T_{C}$ . Thus $T_{B} = 4 T_{0}$

In the lower portion,

$4 T_{0} = Q^{'} (4 R)$

$Q^{'} = \frac{T_{0}}{R}$

Hence, fall across one rod will be $Q^{'} R = T_{0}$

Thus, $T_{F} = 2 T_{0} + T_{0} = 3 T_{0}$

$T_{E} = 3 T_{0} + T_{0} = 4 T_{0}$

$T_{D} = 4 T_{0} + T_{0} = 5 T_{0}$

Answer is option A.

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