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A gas mixture consists of 2 moles of oxygen and 4 moles argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is
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The correct answer is:
$11 R T$
For an ideal gas, the internal energy is given by,
$\mathrm{U}=\frac{\mathrm{f}}{2} \mathrm{nRT}$.
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,
$\mathrm{U}=2 \times \frac{5}{2} \times \mathrm{RT}+4 \times \frac{3}{2} \mathrm{RT}=11 \mathrm{RT}$
$\mathrm{U}=\frac{\mathrm{f}}{2} \mathrm{nRT}$.
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,
$\mathrm{U}=2 \times \frac{5}{2} \times \mathrm{RT}+4 \times \frac{3}{2} \mathrm{RT}=11 \mathrm{RT}$
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