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$A$ wall is made up of two layers $A$ and $B$ . The thickness of the two layers is the same, but materials are different. The thermal conductivity of $A$ is double than that of $B$ . In thermal equilibrium the temperature difference between the two ends is ${36^o}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^oC$
The rectangular surface of area $8$ cm $ \times $ 4cm of a black body at a temperature of ${127^o}C$ emits energy at the rate of $E$ per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to ${327^o}C$, the rate of emission of energy will become
Two bottles $A$ and $B$ have radii $R_{A}$ and $R_{B}$ and heights $h_{A}$ and $h_{B}$ respectively, with $R_{B}=2 R_{A}$ and $h_{B}=2 h_{A}$. These are filled with hot water at $60^{\circ} C$. Consider that heat loss for the bottles takes place only from side surfaces. If the time, the water takes to cool down to $50^{\circ} C$ is $t_{A}$ and $t_{B}$ for bottles $A$ and $B$, respectively. Then, $t_{A}$ and $t_{B}$ are best related as
A container with $1 kg$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 Wm ^{-2}$ and it is absorbed by the water over an effective area of $0.05 m ^2$. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${ }^{\circ} C$ ) in the temperature of water and the surroundings after a long time will be. . . . . . . . (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 s ^{-1}$, Heat capacity of water $\left.=4200 J kg ^{-1} K ^{-1}\right)$
Six wire each of cross-sectional area $A$ and length $l$ are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is :-