Question

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.)

Answer 1

Given,

Number of moles of oxygen gas $=2.0$ moles

Number of moles of neon gas $=4.0$ moles

A diatomic gas has $3$ translational degree of freedom and two rotational degree of freedom. Thus, a diatomic gas molecule can have $5$ degree of freedom if we neglect vibrational mode which generally occurs at high temperature.

Internal energy of oxygen(diatomic) gas

$=\frac{5}{2}\times 2\times R\times T=5RT$

A monoatomic gas has $3$ translational degree of freedom and zero rotational degree of freedom.

Internal energy of neon(monoatomic) gas $=\frac{3}{2}\times 4\times R\times T=6RT$

Total internal energy of mixture
$=5RT+6RT=11RT$.

$\text{Final Answer}:11RT$.