A gas mixture consists of $2$ moles of oxygen and 4 moles of neon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system will be $...........\,RT$
A$8$
B$16$
C$4$
D$11$
JEE MAIN 2023, Medium
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D$11$
d $\left( C _{ v }\right)_{\operatorname{mix}}=\frac{ n _1 Cv _1+ n _2 Cv _2}{ n _1+ n _2}$
$\left( C _{ v }\right)_{\operatorname{mix}}=\frac{2 \times \frac{5}{2} R +4 \times \frac{3}{2} R }{2+4}=\frac{11 R }{6}$
$\Delta U = n \left( C _{ v }\right)_{\operatorname{mix}} RT =6 \frac{11 R }{6} \times RT =11 R$
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