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 . (0xygen has two rotational modes).

Answer 1

`O_(2)` is a diatomic gas having 5 degrees of freedom.
Energy (total internal) per mole of the gas `=(5)/(2) RT " " [underset(T = "temperature")(R = " Universal gas constant")]`
For 2 moles of the gas total intermal energy `=2 xx 5/2 RT =5RT " ".........(i)`
Neon (Ne) is a monoatomic gas having 3 degrees of freedom.
`:.` Energy per mole `=3/2 Rt`
We have 4 moles of Ne.
`"Hence"" ""Energy" =4 xx3/2 RT =6RT " " ......(ii) ["Using Eqs. (i) and (ii)"]`
`:. " " "Total energy "= 5RT +6RT`
`=11RT`