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Question

A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational degrees of freedom, the total internal energy of the system is

A
4RT
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B
15RT
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C
9RT
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D
11RT
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Solution

The correct option is D 11RT
Let μ be the number of moles of a gas.
By neglecting vibrational degrees of freedom,
Number of degrees of freedom of Ar f1=3
Number of degrees of freedom of O2 f2=5
Internal energy of 2 moles of oxygen
UO2=μ(f22RT)=2×52RT=5RT
Internal energy of 4 moles of Argon
UAr=μ(f12RT)=4×32RT=6RT
Total internal energy of the mixture of two gases is
U=Uo2+UAr=11RT
Thus, option (d) is the correct answer.

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