A gaseous mixture has 2 moles of oxygen and 4 | vedclass

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

Vedclass · Accepted Answer

$11$

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(D) The internal energy $U$ of a gas is given by the formula $U = \frac{f}{2} nRT$,where $f$ is the degrees of freedom,$n$ is the number of moles,$R$ is the universal gas constant,and $T$ is the temperature.For oxygen $(O_2)$,which is a diatomic gas,the degrees of freedom $f_1 = 5$ (neglecting vibrational modes). The number of moles $n_1 = 2$.Internal energy of oxygen $U_1 = \frac{5}{2} 	imes 2 	imes RT = 5 RT$.For Argon $(Ar)$,which is a monatomic gas,the degrees of freedom $f_2 = 3$. The number of moles $n_2 = 4$.Internal energy of Argon $U_2 = \frac{3}{2} 	imes 4 	imes RT = 6 RT$.The total internal energy of the system is $U_{total} = U_1 + U_2 = 5 RT + 6 RT = 11 RT$.

$A$ gaseous mixture has $2$ moles of oxygen and $4$ moles of Argon at a temperature $T$. Neglecting all vibrational modes of the molecules,the total internal energy of the system is ($R$ = Universal gas constant). (in $RT$)

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