According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-
- $\frac{3}{2} R$
- $\frac{7}{2} R$
- $\frac{9}{2} R$
- $\frac{5}{2} R$
The Correct Option is B
Solution and Explanation
The molecule adds two more degrees of freedom that correspond to one vibrational mode as it is known that it has one vibrational mode.
Thus, The total degrees of freedom are as follows: \[ f = 3 (\text{translational}) + 2 (\text{rotational}) + 2 (\text{vibrational}) = 7. \] Applying the formula for molar specific heat at constant volume: \[ C_v = \frac{f}{2}R = \frac{7}{2}R. \] Final Answer: \[ \boxed{\frac{7}{2}R} \]
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
