(B) Given: Thickness $\Delta x = 5 \ mm = 5 \times 10^{-3} \ m$, Area $A = 5 \ cm^2 = 5 \times 10^{-4} \ m^2$, Temperature difference $\Delta T = 14^{

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(B) Given: Thickness $\Delta x = 5 \ mm = 5 \times 10^{-3} \ m$, Area $A = 5 \ cm^2 = 5 \times 10^{-4} \ m^2$, Temperature difference $\Delta T = 14^{\circ} C$, Heat flow rate $Q = 42 \ J/s = 42 \ W$.The formula for heat conduction in steady state is $Q = \frac{K A \Delta T}{\Delta x}$.Rearranging for thermal conductivity $K$: $K = \frac{Q \Delta x}{A \Delta T}$.Substituting the values: $K = \frac{42 \times 5 \times 10^{-3}}{5 \times 10^{-4} \times 14}$.Simplifying the expression: $K = \frac{42 \times 10^{-3}}{10^{-4} \times 14} = \frac{3 \times 10^{-3}}{10^{-4}} = 3 \times 10 = 30 \ W \ m^{-1} \ K^{-1}$.

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

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The thickness of a uniform rectangular metal plate is $5 \ mm$ and the area of each surface is $5 \ cm^2$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} C$. If the heat flowing through the plate in one second from one surface to the other surface is $42 \ J$, then the thermal conductivity of the metal is

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A
$90 \ W \ m^{-1} \ K^{-1}$
B
$30 \ W \ m^{-1} \ K^{-1}$
C
$45 \ W \ m^{-1} \ K^{-1}$
D
$60 \ W \ m^{-1} \ K^{-1}$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

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$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

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There is a layer of snow $x \ cm$ thick on water,when the temperature of the air is $-\theta ^\circ C$ (less than the freezing point). If the thickness of the layer increases from $x$ to $y$ in time $t$,then the value of $t$ is given by:

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20 \text{ minutes}$ and $30 \text{ minutes}$ respectively. The ratio of their thermal conductivities will be

Two different rods $A$ and $B$ are kept in series as shown in the figure. The variation of temperature across different cross-sections is plotted in the graph. The ratio of thermal conductivities of $A$ and $B$ is

$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

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