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# 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?

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Solution

## Step 1: Given dataMoles of oxygen$=2\mathrm{mole}$Moles of argon$=4\mathrm{moles}$Step 2: Calculating total internal energyInternal 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}×2×\mathrm{T}$$⇒5\mathrm{T}$ ….(i)Now substituting value for argon which is a diatomic gas with a degree of freedom$=3$Internal energy$=\frac{3}{2}×4×\mathrm{T}⇒6\mathrm{T}$ …(ii)Total energy$=$Internal energy of oxygen$+$internal energy of argon$=5\mathrm{T}+6\mathrm{T}⇒11\mathrm{T}$Therefore, the total energy of the system is$11\mathrm{T}$

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