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  • A gas mixture consists of 2.0 moIes 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.)

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.)

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Degree of freedom is necessary to be known if we need to find the total energy of a particular molecule.

An oxygen molecule has 2 atoms, so the degree of freedom = 2 rotational + 3 translational = 5

Total internal energy for 2 moles of oxygen = 2\times \frac{5}{2} RT = 5RT

Neon gas has a degree of freedom equal to 3, since it is a monoatomic gas-only translational degree of freedom is present. So, the total internal energy  = \frac{3}{2} RT per mole.

For 4 moles of neon gas, total internal energy = 4\times \frac{3}{2} RT = 6RT

Hence total internal energy of 2 moles oxygen + 4 moles Neon = 5 + 6 = 11 RT

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