A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

Question

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

Tardigrade Admin · Accepted Answer

For two moles of diatomic oxygen with no vibrational mode. U1 = 2× (5/2) RT = 5RT For four moles of monoatomic Argon, U2 = 4× (3/2) RT = 6RT ∴ U=U1+ U2 = 5RT+6RT=11RT

Q. A gas mixture consists of $2$ moles of oxygen and $4$ moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

$4 RT$

$9 RT$

$11 RT$

$15 RT$

For two moles of diatomic oxygen with no vibrational mode.
$U_{1} = 2 \times \frac{5}{2} RT = 5 RT$
For four moles of monoatomic Argon,
$U_{2} = 4 \times \frac{3}{2} RT = 6 RT$
$∴ U = U_{1} + U_{2} = 5 RT + 6 RT = 11 RT$

Q. A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

4RT

9RT

11RT

15RT