A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T . Neglecting all vibrational modes we calculated the total internal energy of the system to be x R T . What is the value of x ?

Step-by-step solution

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 × 2 × 5 RT = 5 RT (F = 5 for oxygen molecule) The total internal energy of 4 moles of argon at temperature T is U 2 = 1 2 × 4 × 3 RT = 6 RT (F = 3 for argon molecule) Total internal energy = U 1 + U 2 = 1 1 RT ⇒ x = 11