Which thermodynamic quantity represents the energy required to increase the temperature of a system?

The energy required to increase the temperature of a system is best represented by enthalpy. Enthalpy is a thermodynamic quantity that accounts for the heat content of a system at constant pressure. It combines internal energy, pressure, and volume, making it particularly useful for processes that occur at constant pressure, such as many chemical reactions.

When heat is added to a system, particularly at constant pressure, the change in enthalpy reflects the amount of heat absorbed or released by the system, which is directly related to temperature changes. While internal energy also relates to the total energy of a system, it does not account for the work done by or on the system due to pressure. The Helmholtz and Gibbs free energies are measures of system stability and spontaneity, but they do not directly represent the energy required to raise the temperature of a system. Thus, enthalpy is the appropriate quantity to describe the energy needed for temperature change in various thermodynamic processes.