A gas mixture consists of 2.0 moles of oxygen | vedclass

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(A) Oxygen $(O_{2})$ is a diatomic gas. Neglecting vibrational modes, its degrees of freedom $(f_{O_2})$ are $3$ (translational) $+ 2$ (rotational) $=

Vedclass · Accepted Answer

$11$

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(A) Oxygen $(O_{2})$ is a diatomic gas. Neglecting vibrational modes, its degrees of freedom $(f_{O_2})$ are $3$ (translational) $+ 2$ (rotational) $= 5$.The internal energy of $n$ moles of an ideal gas is given by $U = n \cdot \frac{f}{2} RT$.For $2.0$ moles of $O_{2}$:$U_{O_2} = 2.0 	imes \frac{5}{2} RT = 5 RT$.Neon $(Ne)$ is a monoatomic gas. Its degrees of freedom $(f_{Ne})$ are $3$ (translational).For $4.0$ moles of $Ne$:$U_{Ne} = 4.0 	imes \frac{3}{2} RT = 6 RT$.The total internal energy of the system is the sum of the internal energies of the individual components:$U_{total} = U_{O_2} + U_{Ne} = 5 RT + 6 RT = 11 RT$.

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

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