Is the average kinetic energy directly proportional to...

Is the average kinetic energy directly proportional to temperature (K. $\mathrm{E}_{\text {ave }} \propto T$ )? If so, then shouldn't water vapor at $100^{\circ} \mathrm{C}$ and boiling water have about the same amount of kinetic energy?

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Key Concepts

Average Kinetic Energy and Temperature Relationship

In kinetic theory, the average kinetic energy of the particles in a substance is directly proportional to the absolute temperature. This relationship holds especially true for ideal gases, where each degree of freedom contributes equally to the kinetic energy. Temperature in Kelvin quantifies the average energy of the microscopic thermal motion of particles, meaning that higher absolute temperatures correspond to higher average kinetic energies.

Phase Transitions and Latent Heat

During a phase transition, such as boiling, a substance absorbs energy without a change in temperature. This energy, known as latent heat, is used to overcome intermolecular forces and change the phase from liquid to gas rather than to increase the kinetic energy of the molecules. Thus, even though the temperature remains constant, the distribution of energy changes significantly, which is why water vapor and boiling water at the same temperature do not share identical characteristics in terms of energy distribution.

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