(D) In the steady state,the rate of heat flow through cube $A$ must be equal to the rate of heat flow through cube $B$.Let $T$ be the temperature of t

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(D) In the steady state,the rate of heat flow through cube $A$ must be equal to the rate of heat flow through cube $B$.Let $T$ be the temperature of the interface.The rate of heat flow $H$ is given by $H = \frac{KA(T_1 - T_2)}{L}$.Since the cubes have the same size,their cross-sectional area $A$ and length $L$ are equal.For cube $A$: $H_A = \frac{K_A A (100 - T)}{L}$For cube $B$: $H_B = \frac{K_B A (T - 0)}{L}$Equating $H_A = H_B$:$\frac{K_A A (100 - T)}{L} = \frac{K_B A (T - 0)}{L}$$K_A (100 - T) = K_B T$$300(100 - T) = 200T$$3(100 - T) = 2T$$300 - 3T = 2T$$5T = 300$$T = 60^{\circ}C$Thus,the temperature of the interface is $60^{\circ}C$.

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

Medium

Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300 \; W/m^{\circ}C$ and $200 \; W/m^{\circ}C$,respectively. After steady state is reached,the temperature of the interface will be ...... $^{\circ}C$.

IIT 1996 All IIT

A
$45$
B
$90$
C
$30$
D
$60$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

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The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2 \text{ CGS units}$) are at $100^{\circ}C$ and $0^{\circ}C$ in ice. If the area of a surface is $4 \text{ cm}^2$,then the mass of ice melted in $10 \text{ minutes}$ will be ...... $\text{gm}$.

Medium

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The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$. If the temperature difference between their ends is equal,the rate of flow of heat in them will be in the ratio: (in $:1$)

Medium

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Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$,respectively,are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $\theta_2$ and $\theta_1$ respectively $(\theta_2 > \theta_1)$. The temperature at the interface is

MediumJEE MAIN 2019

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Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same, and if the rate of flow of heat becomes $H_2$, then $H_2 =$

DifficultMHT CET 2026

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Two ends of rods of length $L$ and radius $r$ of the same material are kept at the same temperature difference. Which of the following rods conducts the most heat?

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The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2 \text{ CGS units}$) are at $100^{\circ}C$ and $0^{\circ}C$ in ice. If the area of a surface is $4 \text{ cm}^2$,then the mass of ice melted in $10 \text{ minutes}$ will be ...... $\text{gm}$.

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