Question

A gas mixture consists of $2$ moles of nitrogen and $4$ moles of xenon at temperature "t". neglecting all vibrational modes, the total internal energy of the system is

Answer 1

Step 1: Given data

Moles of nitrogen$=2\mathrm{moles}$

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

Step 2: Calculating total internal energy of the system

Internal energy$=\mathrm{moles}\times \frac{\mathrm{Degree}\mathrm{of}\mathrm{freedom}}{2}\times \mathrm{RT}$

Degree of freedom for nitrogen i.e. a diatomic gas$=5$

Degree of freedom for xenon i.e. a monoatomic gas$=3$

Substituting value we get,

The internal energy of nitrogen$=2\times \frac{5}{2}\times \mathrm{RT}\Rightarrow 5\mathrm{RT}$

The internal energy of xenon$=4\times \frac{3}{2}\times \mathrm{RT}\Rightarrow 6\mathrm{RT}$

The total internal energy of the system$=$internal energy of nitrogen$+$internal energy of xenon

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

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