(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 10-2.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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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

Four identical conducting rods are joined to form a square $ABCD$. The temperatures of junctions $A, B,$ and $C$ are maintained at $100^{\circ}C, 40^{\circ}C,$ and $0^{\circ}C$ respectively. Choose the $\text{INCORRECT}$ statement for this arrangement in a steady state. (The value of $\frac{KA}{L} = 1 \text{ J}/(s \cdot ^{\circ}C)$).

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$A$ brass boiler has a base area of $0.15\; m^{2}$ and thickness $1.0\; cm$. It boils water at the rate of $6.0\; kg/min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $= 109\; J s^{-1} m^{-1} K^{-1}$; Heat of vaporisation of water $= 2256 \times 10^{3}\; J kg^{-1}$.

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Two rods are connected as shown. The rods are of the same length and same cross-sectional area. In the steady state,the temperature $(\theta)$ of the interface will be........ $^oC$

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The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).

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$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

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Two rods are connected as shown. The rods are of the same length and same cross-sectional area. In the steady state,the temperature $(\theta)$ of the interface will be........ $^oC$

The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

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