Under the kinetic theory, the internal energy of a substance is generated from the motion of individual atoms or molecules. Heat energy is the form of energy which transfers this energy from one body or system to another. This heat transfer can take place in a number of ways:
Conduction is when heat flows through a heated solid.
Convection is when heated particles transfer heat to another substance, such as cooking something in boiling water.
Radiation is when heat is transferred through electromagnetic waves, such as from the sun. Radiation can transfer heat through empty space, while the other two methods require some form of matter-on-matter contact for the transfer.
In order for two substances to affect each other they must be in thermal contact with each other. If you leave your oven open while turned on and stand several feet in front of it, you are in thermal contact with the oven and can feel the heat it transfers to you (by convection through the air).
Normally, of course, you do not feel the heat from the oven when you're several feet away and that is because the oven has thermal insulation to keep the heat inside of it, thus preventing thermal contact with the outside of the oven. This is of course not perfect, so if you stand nearby you do feel some heat from the oven.
Thermal equilibrium is when two items that are in thermal contact no longer transfer heat between them. Note that this does not necessarily mean the two are at the same exact temperature.
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