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12.Kinetic Theory of Gases
normal
A gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $A_r$ at temperature $T.$ Neglecting all vibrational modes, the total internal energy of the system is
A
$4\, RT$
B
$15\, RT$
C
$9\, RT$
D
$11\, RT$
Solution
The internal energy of $n$ moles of a gas is $u =\frac{1}{2} nFRT$ where $F=$ number of degrees of freedom. The internal energy of $2$ moles of oxygen at temperature $T$ is $u _{ l }=\frac{1}{2} \times 2 \times 5 RT =5 RT ( F =5$ for oxygen molecule $)$
Total internal energy of $4$ moles of argon at temperature $T$ is $= u _2=\frac{1}{2} \times 4 \times 3 RT =6 RT$
Total internal energy $=u_1+u_2=11 R T$.
Standard 11
Physics
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