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

Answer: (D)

$35 \, K_B T$

Answer 2

For a non-rigid diatomic molecule, the degrees of freedom $f$ are given by:
$f = 5 + 2(3N - 5)$
Since $N = 2$ (for diatomic molecules):
$f = 5 + 2(3 \times 2 - 5) = 7$
The energy of one molecule is:
$\text{Energy} = \frac{f}{2} k_B T = \frac{7}{2} k_B T$
For 10 molecules, the total energy is:
$10 \times \frac{7}{2} k_B T = 35 k_B T$