(A) In steady state,the rate of heat flow through both rods is equal.Let $T$ be the temperature at the junction.$\left(\frac{kA(T_1 - T)}{l}\right)_{\

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(A) In steady state,the rate of heat flow through both rods is equal.Let $T$ be the temperature at the junction.$\left(\frac{kA(T_1 - T)}{l}\right)_{\text{steel}} = \left(\frac{kA(T - T_2)}{l}\right)_{\text{copper}}$Since the area $A$ is the same for both rods,it cancels out:$\frac{50(100 - T)}{0.1} = \frac{400(T - 0)}{0.2}$$500(100 - T) = 2000(T)$$100 - T = 4T$$5T = 100$$T = 20^{\circ}C$

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

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$A$ cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm^{-1}K^{-1}$ is welded end to end to a copper rod of thermal conductivity $400 \,Wm^{-1}K^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ}C$ and that of the copper rod at $0^{\circ}C$. Assuming that the rods are perfectly insulated from the surroundings,the temperature at the junction of the two rods is ................... $^{\circ}C$.

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A
$20$
B
$30$
C
$40$
D
$50$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

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How is thermal conduction represented for a given temperature difference for any material by the rate of heat conduction?

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There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals is:

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Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same,the rate of flow of heat becomes $H_2$. Then:

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$A$ large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac{L}{2})$ each. The rods are completely insulated from the surroundings. If the free end of the copper rod is maintained at $100\,^oC$ and that of the steel rod at $0\,^oC$,then the temperature of the junction is........$^oC$ (Thermal conductivity of copper is $9$ times that of steel).

MediumAIEEE 2012

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An ice box is used to keep food cool,having a surface area of $1 \, m^2$ and a thickness of $5.0 \, cm$. The thermal conductivity of the ice box material is $K = 0.01 \, J/(m \cdot s \cdot ^\circ C)$. The inside temperature is maintained at $0 \, ^\circ C$ and the outside temperature is $30 \, ^\circ C$. If the latent heat of fusion of ice is $334 \times 10^3 \, J/kg$,calculate the mass of ice that melts in one day.

Medium

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How is thermal conduction represented for a given temperature difference for any material by the rate of heat conduction?

There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals is:

Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same,the rate of flow of heat becomes $H_2$. Then:

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