Total Internal Energy of a Gas Mixture – Rankers Physics

Uncategorized: Practice Problem & Solution

A gas mixture consists of $2text{ moles of }text{O}_2text{ and }4text{ moles of He}$ at temperature $T$. Neglecting all vibrational modes, total internal energy of the system is
$11text{ }RT$
$13text{ }RT$
$15text{ }RT$
$9text{ }RT$

Solution Explained:

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

Internal energy $U = sum n_i frac{f_i}{2} RT$. For diatomic $text{O}_2$, $f=5 implies U_1 = 5RT$. For monatomic $text{He}$, $f=3 implies U_2 = 6RT$. Total $U = 11RT$.

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