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Explain why a radiator quickly warms all the air in a room even though air is poor thermal conductor

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A radiator works on the principle of Convection. When the radiator is switched on, it heats the air immediately surrounding it. Since hot air is less dense than surrounding cooler air, it tends to rise up. This gap is immediately filled by the surrounding cooler air, which gets heated up because of the radiator. As this process repeats, a convection current is set up in the room until all the air in the room reaches one particular temperature, at which point the convection stops.

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