Question

A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is:
(A) 15 RT (B) 12 RT
(C) 4 RT (D) 20 RT

Answer 1

Given:

A gas mixture consist of 3 moles of oxygen and 5 moles of argon at temperature T.

To Find:

Total internal energy of the system

Solution:

Mixture consist of 3 moles of oxygen and 5 moles of argon.

Internal energy of the system is a function of temperature only.

Oxygen is a Di-atomic gas whereas Argon is a Mono- atomic gas

Internal energy is represented by U

$U = nc_{v}T$

n = moles of oxygen + moles of argon

$c_{v}$ for Mono-atomic gases= $\frac{3R}{2}$

$c_{v}$ for Di-atomic gasses = $\frac{5R}{2}$

U = $3(\frac{5R}{2} )T + 5\frac{3R}{2} T$

$U = 15RT$

Total Internal energy of the system is 15RT .