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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
Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown, with their ends at $100\,^oC, 50\,^oC$ and $0\,^oC$. The temperature of their junction is
  • A
    $75\,^oC$
  • ✓
    $\frac{{200}}{3}\,^oC$
  • C
    $40\,^oC$
  • D
    $\frac{{100}}{3}\,^oC$
✓

Answer

Correct option: B.
$\frac{{200}}{3}\,^oC$
b
$\frac{3 \mathrm{K}(100-\theta)}{\mathrm{L}}=\frac{2 \mathrm{K}(\theta-50)}{\mathrm{L}}+\frac{\mathrm{K}(\theta-0)}{\mathrm{L}}$

$300-3 \theta=2 \theta-100+\theta$

$400=6 \theta$

$\theta=\frac{200}{3}^{\circ} \mathrm{C}$

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