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(C) The total internal energy of a gas is given by the formula:$U = \frac{n f R T}{2}$where $n$ is the number of moles and $f$ is the degree of freedo

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(C) The total internal energy of a gas is given by the formula:$U = \frac{n f R T}{2}$where $n$ is the number of moles and $f$ is the degree of freedom.Given,$n_{	ext{diatomic}} = n_{	ext{monoatomic}} = 2$.For a monoatomic gas,the degree of freedom $f_{	ext{monoatomic}} = 3$.For a diatomic gas,the degree of freedom $f_{	ext{diatomic}} = 5$.Calculating internal energy for each:$U_{	ext{monoatomic}} = \frac{2 	imes 3 	imes R T}{2} = 3 R T$$U_{	ext{diatomic}} = \frac{2 	imes 5 	imes R T}{2} = 5 R T$Therefore,the total internal energy of the mixture is:$U_{	ext{total}} = U_{	ext{monoatomic}} + U_{	ext{diatomic}} = 3 R T + 5 R T = 8 R T$.

$A$ gas mixture contains monoatomic and diatomic molecules of $2$ moles each. The mixture has a total internal energy of (symbols have usual meanings): (in $R T$)

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