Q.Explain the three modes of heat transfer with illustrations. Also state and explain Stefan's law.

Heat transfers by conduction (through matter), convection (bulk fluid movement), and radiation (electromagnetic waves); Stefan's law gives the radiated power of a black body as sigma T^4.

1. Conduction: Heat transfer through a material medium (typically solids) WITHOUT any actual bulk movement of the particles of the medium — heat passes from molecule to molecule via molecular vibrations/collisions transferring kinetic energy from hotter to colder regions. Example: if one end of a metal rod is heated, the other end gradually becomes hot as heat conducts along the rod; the handle of a metal spoon left in hot tea gets warm.

2. Convection: Heat transfer through the actual bulk movement of the heated particles of a fluid (liquid or gas) from one place to another, carrying thermal energy with them. It can be natural (driven by density differences, e.g. hot fluid rising, cold fluid sinking) or forced (driven by a fan/pump). Example: water in a pot being heated from below — hot water rises, cooler water sinks to take its place, forming convection currents; land and sea breezes; atmospheric weather circulation.

3. Radiation: Heat transfer via electromagnetic waves (mostly infrared), which requires NO material medium and can even travel through a vacuum. Every body above absolute zero radiates thermal energy this way. Example: heat from the sun reaching the earth through empty space; the warmth felt on skin near a fire without touching it directly.

Stefan's law (Stefan-Boltzmann law): The total energy radiated per unit time per unit surface area (the emissive power) of a perfect black body is directly proportional to the fourth power of its absolute temperature:

E = sigma T^4

where sigma is the Stefan-Boltzmann constant, sigma = 5.67 x 10^-8 W/(m^2 K^4), and T is the absolute temperature in kelvin. For a real (non-black) body with emissivity epsilon (0 < epsilon less than or equal to 1), the law generalises to E = epsilon sigma T^4. This shows that radiated power increases very steeply (as the fourth power) with temperature.

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