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  4. A rod CD of thermal resistance 10.0 KW -1 is joined at the middle of an identical rod AB as shown in figure, The end A, B and D are maintained at 200° C , 100° C and 125° C respectively. The heat current in CD is P watt. The value of P is....

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Q. A rod $CD$ of thermal resistance $10.0 \,KW ^{-1}$ is joined at the middle of an identical rod $AB$ as shown in figure, The end $A, B$ and $D$ are maintained at $200^{\circ} C , 100^{\circ} C$ and $125^{\circ} C$ respectively. The heat current in $CD$ is $P$ watt. The value of $P$ is....Physics Question Image

JEE MainJEE Main 2021Thermal Properties of Matter

Solution:

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Rods are identical so
$R _{ AB }= R _{ CD }=10 KW ^{-1}$
$C$ is mid-point of $AB$,
so $R _{ AC }= R _{ CB }=5 KW ^{-1}$
at point $C$
$\frac{200- T }{5}=\frac{ T -125}{10}+\frac{ T -100}{5}$
$2(200- T )= T -125+2( T -100)$
$400-2 T = T -125+2 T -200$
$T =\frac{725}{5}=145^{\circ} C$
$I _{ h }=\frac{145-125}{10} w =\frac{20}{10} w$
$I _{ h }=2 w$