Internal energy is the bookkeeping total of all the molecular energies. Treating it as a function of state, and knowing it depends only on temperature for an ideal gas, makes the first law that follows much simpler.
Internal energy is the sum of the random kinetic and potential energies of a system's molecules. It is a function of state, and for an ideal gas it depends only on the temperature.
Internal energy is not the heat in a body or its temperature; it is the grand total of the random kinetic and potential energies of every molecule. The simulation shows the molecular energy, and the internal energy with it, climbing as the gas is warmed.
Internal energy depends only on the present state of the system, not on how it got there, so any change ΔU between two states is the same by any route. For an ideal gas there are no intermolecular forces, so the internal energy is entirely kinetic and is fixed by the temperature alone: same temperature, same internal energy, whatever the pressure or volume.
Four quick checks on what internal energy is and what it depends on. Each correct answer earns XP and lights this skill on your star map.
The internal energy of a system is:
For an ideal gas the internal energy is entirely kinetic because:
Raising the temperature of a fixed mass of ideal gas:
Two equal masses of the same ideal gas are at the same temperature but different pressures. Their internal energies are:
Internal energy is not heat and not temperature; it is the total molecular energy. Because it is a function of state, ΔU depends only on the start and end states, not the path. For an ideal gas U depends only on T, so an isothermal change has ΔU = 0 even though p and V both change.
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