Dulong & Petit's Law for Specific Heat
The expression \(C_V = 3R\) relates to the molar specific heat capacity at constant volume (\(C_V\)) for certain materials. Here, \(R\) is the universal gas constant.
Dulong & Petit's Law, established in the early 19th century, states that the molar heat capacity of many solid elements at room temperature is approximately constant and equal to \(3R\). This law arises from the classical equipartition theorem, where each atom in the solid lattice is assumed to have 3 vibrational degrees of freedom, each contributing \(kT\) energy.
The expression \(C_V = 3R\) is a direct consequence of this law. It provides a good approximation for simple solid elements at sufficiently high temperatures (relative to their characteristic vibrational frequencies).
Comparing with Other Laws
Other options represent different physical phenomena:
- Debye's Law provides a more sophisticated quantum mechanical model for specific heat, especially accurate at low temperatures, but does not simplify to \(C_V = 3R\) generally.
- Planck's Law describes the spectral density of electromagnetic radiation emitted by a black body, related to quantum theory.
- Wien's Law relates the peak wavelength of black-body radiation to its temperature.
Therefore, the expression \(C_V = 3R\) specifically represents Dulong & Petit's Law.
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