(D) The rate of heat flow through the walls is given by the formula: $\frac{dQ}{dt} = \frac{KA \Delta \theta}{l}$.Given: $K = 0.01\;J/(m\cdot s\cdot ^

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(D) The rate of heat flow through the walls is given by the formula: $\frac{dQ}{dt} = \frac{KA \Delta \theta}{l}$.Given: $K = 0.01\;J/(m\cdot s\cdot ^\circ C)$,$A = 1\;m^2$,$l = 5.0\;cm = 0.05\;m$,and $\Delta \theta = 30^\circ C - 0^\circ C = 30^\circ C$.Substituting the values: $\frac{dQ}{dt} = \frac{0.01 \times 1}{0.05} \times 30 = 6\;J/s$.Total heat transferred in one day $(t = 86400\;s)$: $Q = \frac{dQ}{dt} \times t = 6 \times 86400 = 518400\;J$.The mass of ice melted is given by $Q = mL$,where $L = 334 \times 10^3\;J/kg$.$m = \frac{Q}{L} = \frac{518400}{334 \times 10^3} = 1.552\;kg$.Converting to grams: $m = 1.552 \times 1000 = 1552\;g$.

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

Medium

An ice box used for keeping eatables cold has a total wall area of $1\;m^2$ and a wall thickness of $5.0\;cm$. The thermal conductivity of the ice box material is $K = 0.01\;J/(m\cdot s\cdot ^\circ C)$. It is filled with ice at $0^\circ C$ along with eatables on a day when the temperature is $30^\circ C$. The latent heat of fusion of ice is $334 \times 10^3\;J/kg$. The amount of ice melted in one day is ........ $g$ $(1\;day = 86,400\;s)$.

A
$776$
B
$7760$
C
$11520$
D
$1552$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

Mud houses are cooler in summer and warmer in winter because

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Two spheres of different materials,one with double the radius and one-fourth wall thickness of the other,are filled with ice. If the time taken for complete melting of ice in the large radius sphere is $25 \ minutes$ and that for the smaller one is $16 \ minutes$,the ratio of thermal conductivities of the materials of the larger sphere to the smaller sphere is:

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$A$ $5 \ cm$ thick ice block is present on the surface of water in a lake. The temperature of the air is $-10^{\circ}C$. How much time will it take to double the thickness of the block? (Given: $L = 80 \ cal/g$,$K_{ice} = 0.004 \ cal/s \cdot cm \cdot ^{\circ}C$,$\rho_{ice} = 0.92 \ g/cm^3$)

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Two plates of equal area are placed in contact. Their thicknesses are $2$ and $3$ units respectively. The temperature of the outer surface of the first plate is $-25^{\circ}C$ and the temperature of the outer surface of the second plate is $25^{\circ}C$. Find the temperature of the contact surface if: $(a)$ they are made of the same material,$(b)$ their thermal conductivities are in the ratio $2:3$.

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If the thermal conductivity of copper is $9$ times that of steel,what will be the temperature of the junction in $^oC$?

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Mud houses are cooler in summer and warmer in winter because

$A$ $5 \ cm$ thick ice block is present on the surface of water in a lake. The temperature of the air is $-10^{\circ}C$. How much time will it take to double the thickness of the block? (Given: $L = 80 \ cal/g$,$K_{ice} = 0.004 \ cal/s \cdot cm \cdot ^{\circ}C$,$\rho_{ice} = 0.92 \ g/cm^3$)

If the thermal conductivity of copper is $9$ times that of steel,what will be the temperature of the junction in $^oC$?

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