Law of Dulong and Petit

Definition

The Law of Dulong and Petit states that the molar heat capacity of a solid element is approximately equal to 3R, where R is the universal gas constant. It indicates that each mole of atoms in a solid contributes around $25 \text{ J/mol·K}$ to the heat capacity.

5 Must Know Facts For Your Next Test

1. The Law of Dulong and Petit applies primarily to metallic elements at room temperature.
2. It predicts a molar heat capacity value close to $25 \text{ J/mol·K}$ for many solid elements.
3. The law is derived from the classical theory of equipartition of energy, which assigns $\frac{1}{2} k_B T$ per degree of freedom per particle.
4. Exceptions to the law occur at very low temperatures or for elements with very low atomic masses, such as boron and carbon.
5. It provides insight into the vibrational modes (degrees of freedom) in a crystal lattice.

Review Questions

• What is the approximate value for molar heat capacity predicted by the Law of Dulong and Petit?
• Why does the Law of Dulong and Petit fail at very low temperatures?
• How does the classical theory of equipartition relate to the Law of Dulong and Petit?

Related terms

Heat Capacity: The amount of heat required to raise the temperature of a substance by one degree Celsius.

Equipartition Theorem: A principle stating that energy is equally distributed among all available degrees of freedom in thermal equilibrium.

Universal Gas Constant (R): $8.314 \text{ J/mol·K}$, a physical constant used in many fundamental equations in thermodynamics.