Heat and Thermodynamics 4 Question 21
23. A gas mixture consists 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
(1999, 2M)
(a) $4 R T$
(b) $15 R T$
(c) $9 R T$
(d) $11 R T$
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Solution:
- Internal energy of $n$ moles of an ideal gas at temperature $T$ is given by
$$ U=n\left(\frac{f}{2} R T\right) $$
where, $\quad f=$ degrees of freedom.
$$ =5 \text { for } O _2 \text { and } 3 \text { for } Ar $$
Hence, $\quad U=U _{O _2}+U _{Ar}=2\left(\frac{5}{2} R T\right)+4\left(\frac{3}{2} R T\right)=11 R T$
