Chemistry - Thermodynamics - I Question with Solution | TestHub

Question Explanation: Matching gases to their molar heat capacity at constant volume.

Concept: Degree of Freedom and Equipartition Theorem

Solution:

The molar heat capacity at constant volume is given by $C_{V,m}=\frac{f}{2}R$, where $f$ is the total degrees of freedom. When vibration is active, each vibrational mode contributes R ( 1 for kinetic and 1 for potential energy).

Monoatomic (He): f = 3 (translation), C_V = 1.5R.

Diatomic (O₂ ) : f = 3 (trans) + 2 (rot) + 2 (1 vib mode), C_V = 3.5R.

Non-linear Triatomic (SO₂ ): f = 3 (trans) + 3 (rot) + 6 (3 vib modes), C_V = 6R.

Non-linear Polyatomic (CH₄ ): f = 3 (trans) + 3 (rot) + 18 (9 vib modes), C_V = 12R.

Final Answer: (A)