Dulong-Petit 3R
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Dulong-Petit 3R Calculator applies the empirical Dulong-Petit law to estimate the molar heat capacity (Cv) of crystalline solids. According to this law, for many solids at room temperature, Cv approaches 3R, where R is the ideal gas constant (approximately 8.314 J/mol·K). The tool automatically calculates the value of 3R, providing a quick reference for comparison with experimental data.
The operation is simple: the user inputs the temperature (in Kelvin) and the measured molar heat capacity (in J/mol·K). The calculator then displays the Dulong-Petit predicted value (3R) and calculates the percentage deviation between the measured and predicted values. This helps to verify whether the material follows the law or if quantum contributions (e.g., at low temperatures) reduce Cv.
This calculator is useful in solid-state physics and thermodynamics classes, allowing students to quickly compare experimental data with the classical prediction. It also serves researchers who need a preliminary check on whether a new solid material behaves classically. The law is mainly valid for temperatures above the Debye temperature of the material.
Cautions: the Dulong-Petit law fails for solids at low temperatures (where Cv decreases) and for materials with complex crystal structures or strong covalent bonds. Additionally, the measured heat capacity must be at constant volume (Cv), not constant pressure (Cp). The calculator assumes the entered value is Cv; ensure you use correct data.
Frequently asked questions
What does Cv ≈ 3R mean?
Cv is the molar heat capacity at constant volume. Dulong-Petit law states that for many solids, Cv is approximately 3 times the ideal gas constant R, i.e., about 24.94 J/mol·K.
Does Dulong-Petit law apply to all solids?
No. It applies to simple crystalline solids at temperatures above the Debye temperature. At low temperatures or for materials with strong bonds, Cv is lower.
What is the difference between Cv and Cp?
Cv is heat capacity at constant volume, while Cp is at constant pressure. For solids, the difference is small, but Dulong-Petit law applies to Cv, not Cp.
How do I use the calculator to check my experimental data?
Enter the temperature and measured Cv value. The calculator shows the percentage deviation. A small deviation indicates the material follows the law; a large deviation suggests non-classical behavior.
Why is the predicted value always 3R regardless of temperature?
Dulong-Petit law is a classical approximation that ignores quantum effects. It predicts Cv is constant at 3R for sufficiently high temperatures. In reality, Cv varies with temperature.