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Assertion: At ordinary temperatures. the...

Assertion: At ordinary temperatures. the Vibrational degrees of freedom do not contribute to the specific heat of gases
Reason:The average charge corresponding to a degree of vibration is not kT and hence the molecular vibrations are not excited.

A

both Assertion and Reason are both are both wrong

B

Assertion is right, Reason is wrong

C

both Assertion and Reason are correct and Reason explains Assertion

D

both Assertion and Reason are correct, but Reason does not explain Assertion

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given assertion and reason, we will break down the concepts step by step. ### Step 1: Understanding the Assertion The assertion states that at ordinary temperatures, the vibrational degrees of freedom do not contribute to the specific heat of gases. **Explanation:** - In thermodynamics, specific heat refers to the amount of heat required to change the temperature of a substance. For gases, the specific heat is influenced by the degrees of freedom available to the molecules. - At ordinary temperatures, the thermal energy (kT, where k is the Boltzmann constant and T is the temperature) is not sufficient to excite vibrational modes in gas molecules. Hence, these vibrational degrees of freedom do not contribute to the specific heat. ### Step 2: Understanding the Reason The reason provided states that the average energy corresponding to a degree of vibration is not kT, and thus the molecular vibrations are not excited. **Explanation:** - The energy levels for vibrational modes are quantized, meaning that molecules can only vibrate at specific energy levels. - The lowest energy state for vibration is given by E = hν (where h is Planck's constant and ν is the frequency of vibration). - At ordinary temperatures, the energy available (kT) is insufficient to reach these vibrational energy levels, leading to the conclusion that vibrational modes remain unexcited. ### Step 3: Conclusion Both the assertion and the reason are correct. The reason accurately explains why the vibrational degrees of freedom do not contribute to the specific heat of gases at ordinary temperatures. ### Final Answer Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the correct option is C. ---
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