First slide

Internal energy

Question

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature ‘T’. Neglecting all vibrational mode, the total internal energy of the system is

Moderate

A

4RT
B

15RT
C

9RT
D

11RT

Solution

Total Internal Energy of System = $U_{oxygen} + U_{argon}$
$\begin{array}{l} = μ \frac{f_{1}}{2} R T + μ_{2} \frac{f_{2}}{2} R T \\ (f = degree of fredom) \\ = 2 \frac{5}{2} R T + 4 \frac{3}{2} R T \\ = 5 R T + 6 R T \\ = 11 R T \end{array}$
$A s f_{1} = 5 (for oxygen) and f_{2} = 3 (for Argon)$
Therefore, the correct answer is (D).

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