Question 273: Thermodynamics & KTG

Question

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

Accepted Answer

The internal energy (U) of a gas depends on its degrees of freedom (f).
For a monatomic gas like neon, the degrees of freedom are f = 3 (translational). For a diatomic gas like oxygen, the degrees of freedom are f = 5 (3 translational + 2 rotational).
The internal energy for each component of the gas mixture can be calculated using the formula:
$$U = \frac{f}{2}nRT$$
where n is the number of moles, R is the universal gas constant, and T is the temperature.
For the 4 moles of neon (monatomic):
$$U_{Ne} = \frac{3}{2} \cdot 4RT = 6RT$$
For the 2 moles of oxygen (diatomic):
$$U_{O_2} = \frac{5}{2} \cdot 2RT = 5RT$$
Now, to find the total internal energy, we sum the internal energies of the individual components:
$$U_{total} = U_{Ne} + U_{O_2} = 6RT + 5RT = 11RT$$
Thus, the total internal energy of the system is 11RT.

Answer

4RT

Answer

16RT

Answer

8RT

Answer

11RT

Thermodynamics & KTG

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

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