(D) The rate of heat flow is given by $Q = \frac{kA(T_1 - T_2)t}{l}$,where $Q$ is the heat required to melt the ice,$k$ is thermal conductivity,$A$ is

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(D) The rate of heat flow is given by $Q = \frac{kA(T_1 - T_2)t}{l}$,where $Q$ is the heat required to melt the ice,$k$ is thermal conductivity,$A$ is surface area,$l$ is thickness,and $t$ is time.Since $Q = mL = \rho V L$,and $V = 4\pi r^2 l$,we have $Q \propto r^2 l$.Equating the heat flow: $k \frac{r^2}{l} \Delta T t \propto r^2 l$.Thus,$k \propto \frac{l^2}{t}$.Given $r_l = 2r_s$,$l_l = \frac{l_s}{4}$,$t_l = 25 \ min$,and $t_s = 16 \ min$.Ratio $\frac{k_l}{k_s} = \left( \frac{l_l}{l_s} \right)^2 \times \frac{t_s}{t_l} = \left( \frac{1}{4} \right)^2 \times \frac{16}{25} = \frac{1}{16} \times \frac{16}{25} = \frac{1}{25}$.

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

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Two spheres made of different materials have radii in the ratio $2:1$ and wall thicknesses in the ratio $1:4$. They are completely filled with ice. If the time taken to melt the ice completely in the larger sphere is $25 \ min$ and in the smaller sphere is $16 \ min$,then the ratio of the thermal conductivities of the materials of the larger and smaller spheres is ..........

A
$4 : 5$
B
$5 : 4$
C
$25 : 1$
D
$1 : 25$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

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Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

Medium

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Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is:

Medium

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Four rods of the same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct the most heat?

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$A$ wall is made up of two layers $A$ and $B$. The thickness of the two layers is the same,but materials are different. The thermal conductivity of $A$ is double that of $B$. In thermal equilibrium,the temperature difference between the two ends is $36^{\circ}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^{\circ}C$

DifficultIIT 1980

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The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is:

Four rods of the same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct the most heat?

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