What thermodynamic state variable is commonly denoted by U?

The thermodynamic state variable commonly denoted by U is internal energy.

Internal energy is the energy contained in a system’s microscopic degrees of freedom, including molecular motion, intermolecular forces, chemical bonds, and other internal contributions. It is a state function: its value depends on the system’s state, not on the particular path used to reach that state. The first law tracks changes in it, commonly written for a closed system as ΔU = Q − W when W is work done by the system.

U is not the same as temperature, entropy, or enthalpy. Temperature relates to thermal equilibrium and average energy behavior; entropy measures the distribution of accessible microstates; enthalpy is the combination H = U + pV. Absolute internal energy is usually defined relative to a reference because experiments generally determine energy changes. For an ideal gas, a particularly useful result is that internal energy depends only on temperature and the amount of gas, not independently on pressure or volume.