What heat is
Take equal amounts of water at room temperature in two identical beakers, each with a thermometer, over two Bunsen burners. Light only one burner.
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The observation
The temperature of the water in (a) stays the same; the water in (b) slowly gets hotter. Something has passed from the flame into the water and raised its temperature: heat.
Heat
Heat is the energy that flows from one object to another because of the difference in temperature between them. Its flow from one object to another is heat transfer.
Heat is energy
The American-born Benjamin Thompson (Count Rumford, 1753–1814) was the first to show that heat is a form of energy, experimentally, in 1798. James Joule repeated the experiments in 1840.