(C) In a steady state,the rate of heat flow through both bars must be equal.Let the interface temperature be $\varphi$.The rate of heat flow $H$ is gi

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(C) In a steady state,the rate of heat flow through both bars must be equal.Let the interface temperature be $\varphi$.The rate of heat flow $H$ is given by $H = \frac{KA(\Delta T)}{L}$.For the first bar: $H_1 = \frac{K \cdot A \cdot (\varphi - 0)}{1}$.For the second bar: $H_2 = \frac{3K \cdot A \cdot (100 - \varphi)}{2}$.Since $H_1 = H_2$,we have:$K \cdot A \cdot \varphi = \frac{3K \cdot A \cdot (100 - \varphi)}{2}$.Canceling $K$ and $A$ from both sides:$\varphi = \frac{3(100 - \varphi)}{2}$.$2\varphi = 300 - 3\varphi$.$5\varphi = 300$.$\varphi = 60\,^{\circ}C$.

Class 11 Physics 2 Thermal Properties of Matter: Heat Transfer Heat Conduction and Thermal Conductivity

Medium

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\, cm$ and $2\, cm$ respectively have equal cross-sectional area. They are joined length-wise as shown in the figure. If the temperatures at the ends of this composite bar are $0\,^{\circ}C$ and $100\,^{\circ}C$ respectively,then the temperature $\varphi$ of the interface is......... $^oC$.

A
$50$
B
$\frac{100}{3}$
C
$60$
D
$\frac{200}{3}$

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2 Thermal Properties of Matter: Heat Transfer

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Heat Conduction and Thermal Conductivity

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These days,people use steel utensils with copper bottoms. This is considered good for uniform heating of food. Explain this effect using the fact that copper is a better conductor of heat.

The thermal conductivity of a wire is $1.7 \ W \ m^{-1} \ K^{-1}$ and that of cement is $2.9 \ W \ m^{-1} \ K^{-1}$. The thickness of the cement insulation is $..... \ cm$. Here,the thickness of the wire is $20 \ cm$.

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