(C) In a steady state,the rate of heat flow through both rods must be equal.Let the junction temperature be $\phi$.The rate of heat flow is given by $

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(C) In a steady state,the rate of heat flow through both rods must be equal.Let the junction temperature be $\phi$.The rate of heat flow is given by $H = \frac{KA(\Delta T)}{L}$.For the first rod: $H_1 = \frac{K A (\phi - 0)}{1}$.For the second rod: $H_2 = \frac{(3K) A (100 - \phi)}{2}$.Since $H_1 = H_2$:$\frac{KA\phi}{1} = \frac{3KA(100 - \phi)}{2}$$\phi = \frac{3}{2}(100 - \phi)$$2\phi = 300 - 3\phi$$5\phi = 300$$\phi = 60^{\circ}C$.

Class 11 Physics 10-2.Heat Transfer Heat Conduction and Thermal Conductivity

Difficult

Two rods have thermal conductivities $K$ and $3K$ and lengths $1 \ cm$ and $2 \ cm$ respectively. Their cross-sectional areas are equal. They are joined in series as shown in the figure. If the temperatures of the outer ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ respectively,find the junction temperature $\phi$ in $^{\circ}C$.

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

Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,then the ratio of the amounts of heat conducted through per unit time will be

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Define thermal conductivity. Also,provide its $SI$ unit and dimensional formula.

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The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$. The rate of heat transfer,$\frac{dQ}{dt}$ through the rod in a steady state is given by:

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The area of the glass of a window of a room is $10\;m^2$ and thickness is $2\;mm$. The outer and inner temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity of glass in the $MKS$ system is $0.2\;W/(m\cdot K)$. The heat flowing into the room per second will be:

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Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown with their ends at $100^{\circ}C, 50^{\circ}C$ and $0^{\circ}C$. The temperature of the junction is

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Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,then the ratio of the amounts of heat conducted through per unit time will be

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