At absolute zero temperature (T=0), the Fermi energy in metals is equal to the chemical potential, which is a key concept in the free electron model. This relationship holds true specifically for metals with free electrons, distinguishing it from behaviors at temperatures above absolute zero. The discussion emphasizes the importance of understanding this limit correctly, as misconceptions can arise regarding the behavior of Fermi energy and chemical potential at varying temperatures. Clarification is provided that the equality only applies at T=0, not at higher temperatures. Understanding this principle is crucial for studying electronic properties in solid-state physics.