(A) The rate of heat flow $dQ/dt$ through the walls of the box is given by $dQ/dt = (K \cdot A \cdot \Delta T) / d$. Here, the surface area $A = 6 \ti

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(A) The rate of heat flow $dQ/dt$ through the walls of the box is given by $dQ/dt = (K \cdot A \cdot \Delta T) / d$. Here, the surface area $A = 6 \times (side)^2 = 6 \times (0.2 \, m)^2 = 6 \times 0.04 = 0.24 \, m^2$. The thickness $d = 0.04 \, m$ and temperature difference $\Delta T = 50^{\circ}C - 0^{\circ}C = 50^{\circ}C$. So, $dQ/dt = (0.01 \times 0.24 \times 50) / 0.04 = 0.12 / 0.04 = 3 \, Js^{-1}$. Total time $t = 10 \, hours = 10 \times 3600 = 36000 \, s$. Total heat gained $Q = (dQ/dt) \times t = 3 \times 36000 = 108000 \, J$. Mass of ice melted $m_{melted} = Q / L = 108000 / (335 \times 10^3) \approx 0.322 \, kg$. Mass of ice remaining $= 4 \, kg - 0.322 \, kg = 3.678 \, kg$.

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

Medium

If $4 \, kg$ of ice is inside a closed cubical thermocol box of side length $20 \, cm$ and wall thickness $4 \, cm$, then the mass of the ice remaining after $10 \, hours$ is nearly. (Given: Outside temperature $= 50^{\circ}C$, Thermal conductivity of thermocol $K = 0.01 \, Js^{-1}m^{-1\circ}C^{-1}$, Latent heat of fusion of ice $L = 335 \times 10^3 \, Jkg^{-1}$) (in $ \, kg$)

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A
$3.678$
B
$6.378$
C
$2.87$
D
$1.87$

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2 Thermal Properties of Matter: Heat Transfer

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Heat Conduction and Thermal Conductivity

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Two closed containers of same dimensions made of different materials are completely filled with ice. The ice in the first container takes $20 \ min$ and that in the second container takes $10 \ min$,respectively,for complete melting. The ratio of the thermal conductivities of the materials of the two containers is . . . . . . .

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$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

DifficultJEE MAIN 2019

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Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?

EasyAIPMT 2005

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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

Medium

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Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $(r_{1} < r_{2})$ are placed with their centres coinciding. $A$ material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}$ $(\theta_{1} < \theta_{2})$. The rate at which heat flows radially through the material is:

DifficultJEE MAIN 2021

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$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?

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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