Question

According to the Dulong and Petit's law, the atomic heat of an element at constant volume:

• A. increases with increase of temperature
• B. decreases with increase of temperature
• C. becomes zero at absolute zerop
• D. is constant

Hint:

Dulong-Petit is a classical high-temperature limit. It fails at low temperatures where quantum effects become important. Einstein's and Debye's models were developed to explain this low-temperature deviation.

Answer 1

The Correct Option is D

The Law of Dulong and Petit is a classical thermodynamic law that describes the molar specific heat capacity of a solid element. It is based on the classical equipartition theorem. The law states that, at sufficiently high temperatures, the molar specific heat at constant volume (\(C_V\)) for all solid elements is approximately constant and equal to \(3R\), where \(R\) is the universal gas constant. \[ C_V \approx 3R \approx 3 \times 8.314 \, \text{J/(mol}\cdot\text{K)} \approx 25 \, \text{J/(mol}\cdot\text{K)} \] "Atomic heat" is another term for molar specific heat. The law predicts this value to be constant, independent of the substance and temperature (at high temperatures). While modern quantum theories (like the Debye model) show that the specific heat does decrease and approach zero at absolute zero, the classical law of Dulong and Petit itself predicts a constant value. The question asks what the law states, not what is observed experimentally at low temperatures.