Vibrational Energy and Degrees of Freedom – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

Assertion (A): Vibrational energy of molecule at temperature \(T\) is \(kT\). Reason (R): For every molecule, vibrational degree of freedom is 2.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true as each vibrational mode contributes \(kT\) to the internal energy. Reason (R) is false; vibrational degrees of freedom vary by molecular structure (e.g., diatomic molecules have 1). Thus, (A) is true and (R) is false.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. 110 J of heat is added to a gaseous system whose internal energy is increased by 40 J then amount of external work done is
2. Assertion (A): In adiabatic expansion of monoatomic ideal gas, if volume increases by 12%, then pressure decreases by 20%. Reason (R): In adiabatic process \(PV^{5/3} = \text{constant}\).  
3. A gas of volume changes $2\text{ litre}$ to $10\text{ litre}$ at constant temperature $300\text{ K}$, then the change in internal energy will be: (1998)
4. Assertion (A): According to kinetic theory of gases the internal energy of a given sample of an ideal gas is only kinetic. Reason (R): The ideal gas molecules exert force on each other only when they collide.  
5. Assertion (A): When hot water is suddenly poured in cold beaker of thick glass, the beaker cracks. Reason (R): Glass is bad conductor of heat and outer surface of the beaker does not expand.