Question

According to the law of equipartition of energy, the molar specific heat of solids at low temperatures is equal to (R = universal gas constant):

• A. \(3R\)
• B. \(R\)
• C. \(R/2\)
• D. \(R/3\)

Hint:

Dulong-Petit law gives \(C_V = 3R\) for solids in classical approximation.

Answer 1

The Correct Option is A

Step 1: Equipartition theorem.
Each quadratic degree of freedom contributes ½ RT per mole to internal energy.

Step 2: Degrees of freedom in a solid.
Atoms have 3 kinetic and 3 potential vibrational modes, totaling 6 quadratic terms → U = 3RT.

Step 3: Specific heat derivation.
C_V = dU/dT = 3R.

Step 4: Classical context.
This aligns with the Dulong-Petit law at moderate to high temperatures.

Step 5: Conclusion.
The molar specific heat is 3R.