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Why is it desirable to have cooking vessels blackened at their bottom and with shining sides?

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Answer
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Hint For a cooking vessel, heat needs to be kept in for foods to be cooked faster. Black bodies are good absorbers of heat while shiny bodies are good reflectors. Using this property we can explain why we prefer cooking vessels with blackened bottoms.

Complete step by step answer
Usually, for the same given material, the blackened one is a good absorber (and also a good radiator) of heat compared to other colours of the same substance. For example, light rays incident on a black object is almost completely absorbed and hence converted to heat within the materials of the object. This is the exact reason they are black. Coloured objects reflect the wavelength of light corresponding to the colour it is seen to have. For example, a blue object reflects the range of wavelengths corresponding to the colour blue. White colours reflect all colours.
On the other hand, silvery or shiny objects are good reflectors of heat. For example, polished silver reflects about ninety eight per cent of radiation incident on it and polished copper about 97 per cent.
Hence, we can conclude that the bottoms are blackened to absorb heat into the food, and the sides shiny to keep the heat in the vessel.

Note
Although they are called black bodies, they are not only the bodies that are actually black and are good absorbers of heat. Some materials even if they are white or other colours can be very good absorbers of heat. For example white paper absorbs about ninety four percent of heat or other radiation that is incident on it.