A gas mixture coinsists 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 (jee 1999)
(a) 4 RT (b) 15 RT ( c) 9 RT (d) 11 RT.

Options

A. 4 RT
B. 15 RT
C. 9 RT
D. 11 RT

Answer

D

Explanation

The internal energy of n moles of a gas is `u = 1/2 nFRT`, where F = number of degrees of freedom.
The internal energy of 2 moles of oxygen at temperature T is `u_1 = 1/2 xx 4 xx 5 RT = 5 RT` (F = 5 of oxygen molecule)
Total internal energy of 4 moles of argon at temperature T is = `u_2 = 1/2 xx 4 xx 3RT= 6RT`.
Total internal energy ` u_1 + u_2 + 11RT`.