Three conducting rods of same material and cross section are shown in figure- Temperature of A- D and C are maintained at 20 - C- 90 - C and 0 - C respectively- If there is no heat flow in AB then the ratio of length BD and BC is x2- Find x -

If there is no heat flow in AB, then, T_A and T_B are equal. ∴ T_B=T_A=20 ∴( dQdt)_DB = ( dQdt)_BC ∴ KA90 20l_DB = KA20 0l_BC ∴l_ ...

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Standard XII

Physics

Dimensional Analysis

Three conduct...

Question

Three conducting rods of same material and cross section are shown in figure. Temperature of $A, D a n d C$ are maintained at $20^{\circ} C$ , $90^{\circ} C$ and $0^{\circ} C$ respectively. If there is no heat flow in $A B$ then the ratio of length $B D$ and $B C$ is $\frac{x}{2}$ . Find $x$ :

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Solution

If there is no heat flow in AB, then, $T_{A}$ and $T_{B}$ are equal.
$∴ T_{B} = T_{A} = 20$
$∴ (\frac{d Q}{d t})_{D B} = (\frac{d Q}{d t})_{B C}$
$∴ K A \frac{90 - 20}{l_{D B}} = K A \frac{20 - 0}{l_{B C}}$
$∴ \frac{l_{D B}}{l_{B C}} = \frac{7}{2}$

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Three conducting rods of same material and cross section are shown in figure. Temperature of A,DandC are maintained at 20∘C, 90∘C and 0∘C respectively. If there is no heat flow in AB then the ratio of length BD and BC is x2. Find x :

If there is no heat flow in AB, then, TA and TB are equal.∴TB=TA=20∴(dQdt)DB=(dQdt)BC∴KA90−20lDB=KA20−0lBC∴lDBlBC=72

Three conducting rods of same material and cross section are shown in figure. Temperature of $A, D a n d C$ are maintained at $20^{\circ} C$ , $90^{\circ} C$ and $0^{\circ} C$ respectively. If there is no heat flow in $A B$ then the ratio of length $B D$ and $B C$ is $\frac{x}{2}$ . Find $x$ :

If there is no heat flow in AB, then, $T_{A}$ and $T_{B}$ are equal.
$∴ T_{B} = T_{A} = 20$
$∴ (\frac{d Q}{d t})_{D B} = (\frac{d Q}{d t})_{B C}$
$∴ K A \frac{90 - 20}{l_{D B}} = K A \frac{20 - 0}{l_{B C}}$
$∴ \frac{l_{D B}}{l_{B C}} = \frac{7}{2}$