Question

A gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature$"\mathrm{t}"$. Neglecting all vibrational modes, the total internal energy of the system is?

Answer 1

Step 1: Given data

Moles of oxygen$=2\mathrm{mole}$

Moles of argon$=4\mathrm{moles}$

Step 2: Calculating total internal energy

Internal energy is given by$=\frac{{\mathrm{f}}_1}{2}\mathrm{nRT}$ where R is gas constant and T is temperature and n is moles of nitrogen and ${\mathrm{f}}_1$ is degree of freedom.

Oxygen is a diatomic gas, so its degree of freedom is $5$

Substituting value for moles of the oxygen we get,

Internal energy$=\frac{5}{2}\times 2\times \mathrm{T}$$\Rightarrow 5\mathrm{T}$ ….(i)

Now substituting value for argon which is a diatomic gas with a degree of freedom$=3$

Internal energy$=\frac{3}{2}\times 4\times \mathrm{T}\Rightarrow 6\mathrm{T}$ …(ii)

Total energy$=$Internal energy of oxygen$+$internal energy of argon

$=5\mathrm{T}+6\mathrm{T}\Rightarrow 11\mathrm{T}$

Therefore, the total energy of the system is$11\mathrm{T}$