Question

a gas mixture consists of 2 mole of Oxygen and 4 mole organ at temperature t neglecting vibrational modes the total energy of the system is

Answer 1

We have to find the total energy of the system:-

we know that  f = degree of freedom
as oxygen is a diatomic gas 
diatomic gas degree of freedom  f₁ = 5
monoatomic gas degree of freedom f₂ = 3

These are the degree of freedom of oxygen & argon 

For a gas , the formula is :-

U = μN $\frac{1}{2} kt$ = μ $\frac{1}{2} RT$ 
 U = 2 × 5 ×$\frac{1}{2} RT$ + 4 × 3 ×$\frac{1}{2} RT$ 
U = 5RT + 6RT
U = 11 RT

Hence the total energy of the system is 11 RT .


Hope it Helps.

Answer 2

HEY!!

______________________________

▶▶Oxygen is diatomic and has five degree of the freedom whereas argon being monatomic has only three degrees of freedom.

✴For a gas,

✔U = UN × 1/2kT = U × 1/2 RT

✔N is the degrees of the freedom.

✔Therefore the total energy, 

✔U= 2 × 5 × 1/2 RT + 4 × 3 × 1/2RT = 11 RT

✔✔11 RT