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Question

A gas mixture consists of $$2$$ moles of oxygen and $$4$$ moles of argon at temperature $$T$$. Neglecting all vibrational modes, the total internal energy of the system is


A
4RT
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B
5RT
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C
15RT
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D
11RT
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Solution

The correct option is A $$11 RT$$
For an ideal gas, the internal energy is given by,

$$ U = \dfrac {f}{2} n R T$$.

For a monoatomic gas, there are only 3 translational degrees of freedom and for a diatomic gas there are 3 translational + 2 rotational degrees of freedom.

So, 
$$ U = 2 \times \dfrac{5}{2} \times RT + 4 \times \dfrac {3}{2} RT = 11 RT$$

Physics

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