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If a gas mixture contains 2 moles of $\mathrm{O}_{2}$ and 4 moles of Ar at temperature $T$, then what will be the total energy of the system (neglecting all vibrational modes)
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The correct answer is:
$11 R T$
Total energy
$\mathrm{U}=2\left(\frac{\mathrm{n}_{1}}{2} \mathrm{RT}\right)+4\left(\frac{\mathrm{n}_{2}}{2} \mathrm{RT}\right)$
For $\mathrm{O}_{2}, \mathrm{n}=5$ and for $\mathrm{Ar}, \mathrm{n}_{2}=3$
$\therefore \mathrm{U}=2\left(\frac{5}{2} \mathrm{RT}\right)+4\left(\frac{3}{2} \mathrm{RT}\right)=11 \mathrm{RT}$
$\mathrm{U}=2\left(\frac{\mathrm{n}_{1}}{2} \mathrm{RT}\right)+4\left(\frac{\mathrm{n}_{2}}{2} \mathrm{RT}\right)$
For $\mathrm{O}_{2}, \mathrm{n}=5$ and for $\mathrm{Ar}, \mathrm{n}_{2}=3$
$\therefore \mathrm{U}=2\left(\frac{5}{2} \mathrm{RT}\right)+4\left(\frac{3}{2} \mathrm{RT}\right)=11 \mathrm{RT}$
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