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Standard VII

Physics

Conduction

Three rods of...

Question

Three rods of material x and three of material y are connected as shown in figure. All the rods are identical in length and cross sectional area. If the end A is maintained at $60^{o} C$ and the junction E at $10^{o} C$ , calculate the temperature of the junction B. The thermal conductivity of x is $800 W m^{- 1_{0}} C^{- 1}$ and that of y is $400 W m^{- 1_{o}} C^{- 1}$

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Solution

$\Rightarrow \frac{(60 - T) K_{1} A}{L} = \frac{(T - 10)}{(\frac{l}{K_{1} A} + \frac{l}{K_{2} A})} \times 2$
$\Rightarrow T = 40^{\circ} C$
$∴$ Temperature at B is $40^{\circ} C$

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⇒(60−T)K1AL=(T−10)(lK1A+lK2A)×2⇒T=40∘C∴ Temperature at B is 40∘C

$\Rightarrow \frac{(60 - T) K_{1} A}{L} = \frac{(T - 10)}{(\frac{l}{K_{1} A} + \frac{l}{K_{2} A})} \times 2$
$\Rightarrow T = 40^{\circ} C$
$∴$ Temperature at B is $40^{\circ} C$