internal energy
Internal energy is the total energy a chunk of stuff is carrying around inside itself — the grand sum of all the jiggling, spinning, and pulling going on among its molecules. Imagine a sealed box of warm air: the molecules are flying about, bumping the walls, vibrating and tumbling, and tugging on one another. Add up every scrap of that hidden motion and attraction and you have the internal energy. It ignores the box's overall speed or how high it sits on a shelf; only the energy locked inside, among the particles, counts.
In thermodynamics it is written U, and it is a state function: it depends only on the present condition of the material — its temperature, pressure, amount, and so on — not on the route taken to get there. Because of that, what we can ever measure is the change in internal energy, written ΔU, between two states. There is no zero mark from which to count an absolute internal energy in everyday work; we always speak of how much it went up or down.
This matters because U is the bookkeeper at the heart of the first law of thermodynamics. Energy can pour into a system as heat, or be pushed in as work, and the running total of internal energy keeps faithful track of both. It is the conserved quantity that lets us say, with confidence, that energy is never quietly lost — only moved or transformed.
Heat a cup of water on the stove: as its temperature climbs, its molecules move faster, so its internal energy U rises — even though the cup just sits there, not moving anywhere.
Internal energy tracks the molecules' hidden motion, not the object's outward movement.
Don't confuse internal energy with heat. Heat is energy in transit, crossing a boundary because of a temperature difference; internal energy is the stockpile that already lives inside. A warm object does not "contain heat" — it contains internal energy, some of which can leave as heat.