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Byju's Answer

Standard XII

Physics

Poisson's Effect

Eleven identi...

Question

Eleven identical rods are arranged as shown in figure. each rod has length $l$ , cross-sectional area A and thermal conductivity of material K. ends A and F are maintained at temperatures $T_{1}$ and $T_{2} (< T_{1})$ , respectively. if lateral surface of each rod is thermally insulated, the rate of heat transfer $(\frac{d Q}{d t})$ in each rod is

(\frac{d Q}{d t})_{A B} = (\frac{d Q}{d t})_{C D}

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(\frac{d Q}{d t})_{B E} = \frac{2}{7} \frac{(T_{1} - T_{2}) K A}{l}

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(\frac{d Q}{d t})_{C H} \neq (\frac{d Q}{d t})_{D G}

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(\frac{d Q}{d t})_{B C} = (\frac{d Q}{d t})_{D C}

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Solution

The correct options are
B $(\frac{d Q}{d t})_{B E} = \frac{2}{7} \frac{(T_{1} - T_{2}) K A}{l}$
C $(\frac{d Q}{d t})_{C H} \neq (\frac{d Q}{d t})_{D G}$
D $(\frac{d Q}{d t})_{B C} = (\frac{d Q}{d t})_{D C}$

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Similar questions

Q. Eleven identical rods are arranged as shown in figure. Each rod has length

L

, cross-sectional area

A

and thermal conductivity of material

K

. Ends A and F are maintained at temperatures

T_{1}

and

T_{2} (T_{2} < T_{1})

respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer

(\frac{d Q}{d t})

in each rod is

Q. The two ends of a rod of length L and a uniform cross-sectional area A are kept at two temperatures

T_{1}

and

T_{2} (T_{1} > T_{2})

. The rate of heat transfer,

\frac{d Q}{d t}

, through the rod in a steady state is given by :

Q. The dimension of coefficient of thermal conductivity is

(\frac{d Q}{d t} = - K A \frac{d T}{d x})

, where

d Q

is heat transferred,

d t

is time taken,

K

is coefficient of thermal conductivity,

A

is cross-sectional area of conductor,

d T

is change in temperature and

d x

is length of conductor.

Q. The inner and outer surfaces of a hollow spherical shell of inner radius 'a' and outer radius 'b' are maintained at temperature

T_{1}

and

T_{2}

(< T_{1})

. The thermal conductivity of material of the shell is k. If the rate of heat flow inner to outer surface is

\frac{d Q}{d t} = N π k a b (\frac{T_{1} - T_{2}}{b - a})

,then value of

N

is:

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross -sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures $T_{1}, T_{2}$ and $T_{3}$ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

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The correct options are B (dQdt)BE=27(T1−T2)KAl C (dQdt)CH≠(dQdt)DG D (dQdt)BC=(dQdt)DC

The correct options are
B $(\frac{d Q}{d t})_{B E} = \frac{2}{7} \frac{(T_{1} - T_{2}) K A}{l}$
C $(\frac{d Q}{d t})_{C H} \neq (\frac{d Q}{d t})_{D G}$
D $(\frac{d Q}{d t})_{B C} = (\frac{d Q}{d t})_{D C}$