(C) The heat required to melt the ice is given by $Q = m L_f$.The heat conducted through the slab is given by $Q = \frac{K A (T_1 - T_2) t}{L}$.Equati

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(C) The heat required to melt the ice is given by $Q = m L_f$.The heat conducted through the slab is given by $Q = \frac{K A (T_1 - T_2) t}{L}$.Equating the two, we get $\frac{K A (T_1 - T_2) t}{L} = m L_f$.Rearranging for thermal conductivity $K$, we have $K = \frac{m L_f L}{A (T_1 - T_2) t}$.Given values: $m = 4.8\, kg$, $L_f = 3.36 \times 10^5\, J/kg$, $L = 0.1\, m$, $A = 0.36\, m^2$, $(T_1 - T_2) = 100^{\circ} C$, and $t = 1\, hour = 3600\, s$.Substituting the values: $K = \frac{4.8 \times 3.36 \times 10^5 \times 0.1}{0.36 \times 100 \times 3600}$.$K = \frac{4.8 \times 3.36 \times 10^4}{0.36 \times 3.6 \times 10^5} = \frac{16.128}{129.6} \times 10 = 1.24\, J/m/s/^{\circ} C$.

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

Medium

$A$ slab of stone of area $0.36\, m^2$ and thickness $0.1\, m$ is exposed on the lower surface to steam at $100^{\circ} C$. $A$ block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour $4.8\, kg$ of ice is melted. The thermal conductivity of the slab is .......... $J/m/s/^{\circ} C$ (Given latent heat of fusion of ice $= 3.36 \times 10^5\, J/kg$)

AIPMT 2012 All AIPMT

A
$1.02$
B
$1.29$
C
$1.24$
D
$2.05$

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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 metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........

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Two concentric spheres of radii $r_1$ and $r_2$ are maintained at temperatures $T_1$ and $T_2$ respectively. The rate of radial heat flow between the two concentric spheres is proportional to:

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$A$ copper rod and a steel rod of equal cross-sections and lengths $L$ are joined side by side and connected between two heat baths as shown in the figure. If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and thermal conductivities of the metals are $K_{Cu}$ and $K_{Steel}$ $(K_{Cu} > K_{Steel})$,then the temperature varies as (convection and radiation are negligible):

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Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If the thermal conductivities of rods $A$ and $B$ are $3K$ and $K$ respectively,and $T_A$ and $T_B$ are the temperature drops across rods $A$ and $B$,then:

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Two metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........

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