= Thermal energy
<Thermal energy> is a context-dependent name for the microscopic <energy> associated with a system's thermal state, rather than a separate conserved substance. The characteristic single-particle energy scale is $k_BT$, with <Boltzmann constant> $k_B$ and absolute <temperature> $T$. Comparing this scale with an excitation gap or <energy barrier> helps decide which microscopic processes are thermally accessible.
Under the classical <equipartition theorem>, each independent quadratic term in the <Hamiltonian> contributes $k_BT/2$ on average. Three translational terms therefore give $3k_BT/2$ per particle of a monatomic <ideal gas>. Quantum levels can invalidate that count: a degree of freedom with excitation spacing much larger than $k_BT$ can remain nearly frozen. A measured <heat capacity> tests how the stored <internal energy> changes with <temperature>; it does not simply count a fixed amount of heat stored in the sample.
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