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10.2 , transmission of heat — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics10.2 , transmission of heat1 Mark
MCQ
A rod $C D$ 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 ... .
  • ✓
    $2$
  • B
    $3$
  • C
    $1$
  • D
    $4$
✓

Answer

Correct option: A.
$2$
a
Rods are identical so

${R}_{{AB}}={R}_{{CD}}=10 {Kw}^{-1}$

${C}$ is mid-point of ${AB}$, so

${R}_{{AC}}={R}_{{CB}}=5 {K} {w}^{-1}$

at point ${C}$

$\frac{200-{T}}{5}=\frac{{T}-125}{10}+\frac{{T}-100}{5}$

$2(200-{T})={T}-125+2({T}-100)$

$400-2 {T}={T}-125+2 {T}-200$

${T}=\frac{725}{5}=145^{\circ} {C}$ ${I}_{{b}}=\frac{145-125}{10} {w}=\frac{20}{10} {w}$

${I}_{{h}}=2 {w}$

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