A gas mixture consists of $8$ moles of argon and $6$ moles of oxygen at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is
JEE MAIN 2024, Diffcult
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$\mathrm{U}=\mathrm{nC}_{\mathrm{V}} \mathrm{T}$
$\Rightarrow \mathrm{U}=\mathrm{n}_1 \mathrm{C}_{\mathrm{V}_1} \mathrm{~T}+\mathrm{n}_2 \mathrm{C}_{\mathrm{V}_2} \mathrm{~T}$
$\Rightarrow 8 \times \frac{3 \mathrm{R}}{2} \times \mathrm{T}+6 \times \frac{5 \mathrm{R}}{2} \times \mathrm{T}$
$=27 \mathrm{RT}$
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