# 21.4: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures

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The Debye function has been experimentally determined to calculate the heat capacity at low temperatures, between 0 K and 15 K, for nonmetallic crystals:

$\bar{C}_P=aT^3 \nonumber$

Constant $$a$$ can be found by ensuring $${\bar{C}}_P$$ is continuous up to lowest $${\bar{C}}_P$$ data point. The Debye function is named after the Dutch chemistry Peter Debye, who theoretically showed this relationship. Metallic crystals have a slightly different equation at low temperature:

$\bar{C}_P=aT+bT^3 \nonumber$

where $$a$$ and $$b$$ are constants.

21.4: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.