When you heat a liquid, the molecules of the liquid gain energy and move more vigorously. These molecules bump into other molecules, transferring energy and making them move around too. When you take away the heat source, the molecules keep transferring energy, but no new energy is coming into the system so the molecules lose energy and the liquid cools down. Insulators help slow this process. Another form of heat loss is radiation, which involves no particles.
A vacuum makes an outstanding insulator. Inside a perfect vacuum there are no molecules to bump into each other and transfer energy, which slows down the rate at which heat energy is lost from a liquid. Heat can no longer be lost through conduction, although it can be lost through radiation. The first practical application of this principle was the Dewar flask, invented in the 1800s by Scottish researcher James Dewar. Modern vacuum flasks use the same principle. In real life, of course, the vacuums used to insulate hot liquids aren't perfect, but partial.
Air can help to insulate hot objects, but if you expose a hot liquid to air, it cools via evaporation. Heat is lost into the air and the liquid cools more rapidly than it would in a sealed container. To get around this fact, you need a way to surround the liquid with air without it being exposed to the air itself. There are various ways of doing this: a double-walled flask is one example, but other methods use materials that trap air next to the container of hot liquid.
Expanded polystyrene (EP) is often used to contain hot foods and beverages. EP foam keeps liquids hot because it consists of millions of tiny bubbles of air, a useful insulator. Because of this property, EP slows down the rate of heat transfer and keeps liquids hot.
Like EP foam, fibre insulation also works by trapping air. Instead of being trapped in bubbles, air is trapped in the gaps between the fibres. An example of fibre insulation being used to keep a liquid hot would be a cardboard cup. The fibres in the cardboard trap a small amount of air, which slows down the rate at which heat can be lost through the cup's walls.
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