question_answer 32)

                  A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system (Oxygen has two rotational modes.)    

Answer:

                  Total energy of a system per mole \[u=\,\frac{f}{2}RT\]                 For oxygen, \[f=5\] and number of moles \[=2\]                 \[\therefore \] Total energy of 2 moles of oxygen                 \[{{u}_{1}}=2\times \frac{5}{2}\,RT=\,5RT\]                 Neon is a monoatomic gas, so f = 3 and number of moles = 4                 \[\therefore \] Total energy of 4 moles of neon,                 \[{{u}_{2}}=4\times \,\frac{3}{2}\,RT\,=\,6\,RT\]                 Hence, total energy of system, \[u={{u}_{1}}+{{u}_{2}}=11\,RT\].