what determines an object's temperature?

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Every substance is comprised of molecules, atoms, and/or other subatomic particles of that substance. These particles are in constant motion, colliding with each other and perpetually moving. These particles each have their own unique velocity at which they are in motion. Therefore, each of these particles has its own unique kinetic energy of motion. The temperature of a substance is a way of measuring the average kinetic energy of all the particles comprising that substance. 

For example, water is made up of H2O molecules that are in constant motion. Each molecule is constantly moving, with its own velocity and kinetic energy. When this water is heated in a pot on a stove, the heat that is transferred as thermal energy from the stove to the pot and then to the water excites the water molecules in the water, increasing the average speed and therefore kinetic energy of the water molecules in the pot. As these particles increase their rate of collision with each other and the pot, they get even faster and faster. Hence, the temperature of the water increases, as the average kinetic energy of the H2O molecules that make up the water goes up as the molecules speed up.

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