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The wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer and steady state condition exists. Which of the following graphs predicts correctly the variation of temperature T with distance d inside the cavity?
(A)
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(B)
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(C)
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(D)
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Last updated date: 17th Jun 2024
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Answer
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Hint
We should know that heat energy is defined as the result of the movement of tiny particles which are called atoms, molecules or ions in the solids, liquids and gases. Heat energy can be transferred from one object to another. The transfer or flow due to the difference in temperature between the two objects is called heat. The heat is very important in our daily life in warming the house, cooking, heating the water and drawing the wash clothes. The heat has many uses in the industry as making and processing the food and manufacture of the glass, the paper, the textile, etc.

Complete step by step answer
From the concept of Transmission of heat, we can derive the following equations:
 $ \dfrac{dQ}{dt}=KA\dfrac{d\theta }{dx} $
 $ \dfrac{d\theta }{dx}=\text{ slope of graph }\alpha \dfrac{1}{K} $
Here $Q$ is the heat energy, $K$ is temperature constant.
From the graphs in the options, we can see that each of the individual sections are in steady states which means that the temperature drops linearly with distance. Also, we know that lesser the conductivity, larger is the temperature drop.
Therefore, the correct answer is Option (D).

Note
Heat is transmitted by conduction when it passes from the hotter to the colder parts of the medium part material without any movement of the medium itself and all intermediate parts of the material being wanted in this process. Most metals are good conductors which means they can easily transmit heat energy by conduction. The three basic modes of heat generated at the chip surface dissipates to the ambient environment are conduction, convection and radiation.
In case of solids heat is transferred with the help of conduction, in the liquids and gases it is transferred with the help of convection and electromagnetic waves it is transferred using radiation. Heat is usually transferred in a combination of these three types and seldom occurs on its own.