Question

Energy of 10 non rigid diatomic molecules at temperature T is :

• A. $\frac{7}{2} \, RT$
• B. $70 \, K_B T$
• C. $35 \, RT$
• D. $35 \, K_B T$

Answer 1

The Correct Option is D

The degrees of freedom \( f \) for a non-rigid diatomic molecule are calculated as follows:
\[f = 5 + 2(3N - 5)\]
For diatomic molecules, \( N = 2 \). Substituting this value yields:
\[f = 5 + 2(3 \times 2 - 5) = 7\]
The energy of a single molecule is expressed as:
\[\text{Energy} = \frac{f}{2} k_B T = \frac{7}{2} k_B T\]
The total energy for 10 molecules is therefore:
\[10 \times \frac{7}{2} k_B T = 35 k_B T\]