NEET Class neet Answered
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Asked by nssharma001969 | 03 Jun, 2020, 01:54: AM
Given:
Degree of freedom = 75%
For triatomic gas,
N = 3
Degree of freedom = 3N
= 3×3 =9
= transnational DoF + rotational DoF + Vibrational DoF
= 3+2+4 = 9
energy =
![equals space 3 over 2 kT space plus space 2 over 2 kT space plus space open parentheses 4 kT close parentheses open parentheses 75 over 100 close parentheses
equals space 3 over 2 kT space plus kT space plus space 3 kT
equals 11 over 2 kT](https://images.topperlearning.com/topper/tinymce/cache/1428ae7b26c740a865cb826356f0969d.png)
We know,
Cv = ![dU over dT](https://images.topperlearning.com/topper/tinymce/cache/5d2742ff6ac8398e78472830a10c9417.png)
![dU over dT](https://images.topperlearning.com/topper/tinymce/cache/5d2742ff6ac8398e78472830a10c9417.png)
Cv = ![11 over 2 straight k](https://images.topperlearning.com/topper/tinymce/cache/98ea42bf577ce54f40abee7d735fbe43.png)
![11 over 2 straight k](https://images.topperlearning.com/topper/tinymce/cache/98ea42bf577ce54f40abee7d735fbe43.png)
Cv = ![11 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/dca5ba32c380a0f3a67f8a81e33cd575.png)
![11 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/dca5ba32c380a0f3a67f8a81e33cd575.png)
Now, we know,
Cp - Cv = R
Cp = R + Cv
= R + ![11 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/dca5ba32c380a0f3a67f8a81e33cd575.png)
![11 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/dca5ba32c380a0f3a67f8a81e33cd575.png)
Cp = ![13 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/cc7dcb5bb7b4047dfb6eefe9f345c7b8.png)
![13 over 2 straight R](https://images.topperlearning.com/topper/tinymce/cache/cc7dcb5bb7b4047dfb6eefe9f345c7b8.png)
γ =![straight C subscript straight p over straight C subscript straight v space equals space fraction numerator begin display style bevelled 11 over 2 end style straight R over denominator begin display style bevelled 13 over 2 end style straight R end fraction](https://images.topperlearning.com/topper/tinymce/cache/883473e55ad213f4ea183123c03bf468.png)
![straight C subscript straight p over straight C subscript straight v space equals space fraction numerator begin display style bevelled 11 over 2 end style straight R over denominator begin display style bevelled 13 over 2 end style straight R end fraction](https://images.topperlearning.com/topper/tinymce/cache/883473e55ad213f4ea183123c03bf468.png)
γ = ![13 over 11](https://images.topperlearning.com/topper/tinymce/cache/5a469ac16125d0e238cc51fa0e9699d5.png)
![13 over 11](https://images.topperlearning.com/topper/tinymce/cache/5a469ac16125d0e238cc51fa0e9699d5.png)
γ =![straight C subscript straight p over straight C subscript straight v space equals 1.18](https://images.topperlearning.com/topper/tinymce/cache/fdeab3b55a4e452b9d0241373471d9a8.png)
![straight C subscript straight p over straight C subscript straight v space equals 1.18](https://images.topperlearning.com/topper/tinymce/cache/fdeab3b55a4e452b9d0241373471d9a8.png)
Answered by Varsha | 03 Jun, 2020, 13:14: PM
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