Question

A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational moles, the total internal energy of the system is
A.) 4RT
B.) 15RT
C.) 9RT
D.) 11RT

Answer 1

Hint: The description and formula and properties of diatomic and monatomic gases must be considered for addressing these types of questions. Inner energy of the formula for gases must also be understood.

Complete step-by-step answer:

Diatomic gases are gases in which two atoms of the same form are the molecules which create it. Oxygen a gas, for example, may consist of molecules containing two oxygen atoms.
Monatomic gasses consist of single-atom ions, such as helium or sodium vapor, etc.

Here we know f = degree of freedom

As oxygen is a diatomic gas the degree of freedom for the diatomic gas ${f_1}$= 5 and the argon is monoatomic gas with its monoatomic degree of freedom ${f_2}$ = 3

Internal energy of 2 moles of oxygen is given by

${U_{oxygen}} = \mu \left( {\dfrac{5}{2}RT} \right)$
${U_{oxygen}} = 2 \cdot \dfrac{5}{2}RT$
${U_{oxygen}} = 5RT$

Internal energy of 4 moles of argon is given by

${U_{\arg on}} = \mu \left( {\dfrac{3}{2}RT} \right)$
${U_{\arg on}} = 4 \cdot \dfrac{3}{2}RT$
${U_{\arg on}} = 6RT$

Total internal energy =${U_{Total}} = {U_{oxygen}} + {U_{\arg on}}$
$U = 5RT + 6RT$
$U = 11RT$

Hence our answer is option D which states that the total internal energy of the system is $11RT$.

Note: It is very important to remember the properties of diatomic and monatomic gases. In this question we saw how internal energy of diatomic and monatomic gases varies. Also, how the degree of freedom of diatomic and monatomic gases are different.