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
A.
$$4\, RT$$
B.
$$15\, RT$$
C.
$$9\, RT$$
D.
$$11\, RT$$
Answer :
$$11\, RT$$
Solution :
The internal energy of n moles of a gas is
$$U = \frac{1}{2}\,nFRT$$
where $$F$$ = number of degrees of freedom. Internal energy of 2 moles of oxygen at temperature $$T$$ is
$${U_1} = \frac{1}{2} \times 2 \times 5\,RT$$ [$$F$$ = 5 for oxygen molecule]
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 = $$11 \,RT$$
Releted MCQ Question on Heat and Thermodynamics >> Thermodynamics
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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