Molar heat capacity
The heat to raise one mole of a substance by one degree — the per-atom measure that reveals the Dulong–Petit regularity.
Definition
The molar heat capacity is the heat required to raise one mole of a substance — a fixed number of particles — by one degree of temperature, in J/(mol·K). Measuring per mole rather than per gram exposes regularities hidden by mass-based specific heat, because it counts atoms directly rather than weighing them.
For simple solids the molar heat capacity clusters near 3R ≈ 24.9 J/(mol·K) at ordinary temperatures, the Dulong–Petit law, reflecting that each atom holds energy in three vibrational degrees of freedom (kinetic and potential), as predicted by equipartition. For ideal gases the molar capacity comes in two forms, C_v and C_p, differing by R; their ratio γ governs adiabatic processes and the speed of sound.
At low temperatures the classical values fail and heat capacities fall toward zero, a quantum effect (the Einstein and Debye theories of solids) and one of the early clues that classical physics was incomplete.