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(C) The internal energy $U$ of a gas is given by $U = \frac{f}{2}nRT$,where $f$ is the degrees of freedom,$n$ is the number of moles,$R$ is the univer

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$13.5$

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(C) The internal energy $U$ of a gas is given by $U = \frac{f}{2}nRT$,where $f$ is the degrees of freedom,$n$ is the number of moles,$R$ is the universal gas constant,and $T$ is the absolute temperature.For oxygen $(O_2)$,which is a diatomic gas,the degrees of freedom $f_1 = 5$ (neglecting vibrational modes).For argon $(Ar)$,which is a monatomic gas,the degrees of freedom $f_2 = 3$.The total internal energy $U_{total} = U_{O_2} + U_{Ar}$.$U_{total} = \frac{f_1}{2}n_1RT + \frac{f_2}{2}n_2RT$.Given $n_1 = 3$ moles and $n_2 = 4$ moles.$U_{total} = \frac{5}{2}(3)RT + \frac{3}{2}(4)RT$.$U_{total} = 7.5RT + 6RT = 13.5RT$.

If a gaseous mixture consists of $3$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$,then the total internal energy of the mixture is (neglect vibrational modes and $R$ - Universal gas constant). (in $RT$)

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