Define coefficient of thermal conductivity. Derive its expression.

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The coefficient of thermal conductivity $k$ (§7.9.1.2) measures how readily a material conducts heat: a high $k$ means a good conductor, a low $k$ means a poor one (an insulator). To derive its expression, consider steady-state conduction through a slab of cross-sectional area $A$ and thickness $x$ , with its two faces held at temperatures $T_1$ and $T_2$ ( $T_1>T_2$ ). Experiments show the heat $Q$ conducted through in time $t$ is: directly proportional to the area, $Q\propto A$ ; directly proportional to the temperature difference, $Q\propto(T_1-T_2)$ ; directly proportional to time, $Q\propto t$ ; and inversely proportional to the thickness, $Q\propto 1/x$ . Combining these four proportionalities with a single constant of proportionality $k$ gives $Q = \dfrac{kA(T_1-T_2)t}{x}$ (Eq. 7.34), and rearranging, $k = \dfrac{Qx}{A(T_1-T_2)t}$ (Eq. 7.35). Setting $A=1\text{ m}^2$ , $(T_1-T_2)=1 …

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CBSE 2025Set ANNUAL3 marks
$Q. Explain various modes of heat transfer.$
›Reveal solutionSolution
Heat travels by conduction (molecule-to-molecule, no bulk motion), convection (bulk fluid motion), or radiation (electromagnetic waves, no medium needed) -- each mechanism operates differently and dominates in different situations.

Conduction: Heat is transferred through a material by direct collisions between vibrating/energetic molecules (or free electrons in metals) passing kinetic energy to their neighbours, without the material itself moving from place to place. It is the dominant mode of heat transfer in solids, especially metals (good conductors). Example: one end of an iron rod placed in a fire becomes hot at the other end after some time.

Convection: Heat is transferred by the actual bulk movement of a fluid (liquid or gas) -- the heated fluid becomes less dense, rises, and is replaced by cooler fluid, setting up convection currents that carry thermal energy along with the moving fluid itself. This requires a fluid medium and cannot occur in solids or vacuum. Example: water boiling in a pot, air circulation in a heated room, sea breezes.

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CBSE 2021Set sz3 marks
$Q. Discuss various modes of transfer of heat.$
›Reveal solutionSolution
Heat transfer occurs by three modes: conduction (through a stationary medium via molecular collisions), convection (via bulk fluid motion), and radiation (via electromagnetic waves, no medium needed).

Conduction: In this mode, heat is transferred from the hotter to the colder part of a body (typically a solid) through the vibration and collision of neighbouring molecules/free electrons, without any actual bulk movement of the material itself. Metals are good conductors due to free electrons; heat conducted through a rod is a classic example.

Convection: Here heat is carried by the physical, bulk movement of a fluid (liquid or gas). The heated fluid, becoming less dense, rises and is replaced by cooler fluid, setting up convection currents that transport heat from one region to another. Examples include boiling water in a vessel, land and sea breezes, and heating of a room by a radiator.

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Q.Define coefficient of thermal conductivity. Derive its expression.

Concept understanding — Heat Transfer

Q.Define coefficient of thermal conductivity. Derive its expression.

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