Question

A rod $CD$ of thermal resistance $10.0K{W}^{-1}$ 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....

Answer 1

Answer: 2

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