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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 modes, the total internal energy of the system is?


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Solution

Step 1: Given data

Moles of oxygen=2mole

Moles of argon=4moles

Step 2: Calculating total internal energy

Internal energy is given by=f12nRT where R is gas constant and T is temperature and n is moles of nitrogen and f1 is degree of freedom.

Oxygen is a diatomic gas, so its degree of freedom is 5

Substituting value for moles of the oxygen we get,

Internal energy=52×2×T5T ….(i)

Now substituting value for argon which is a diatomic gas with a degree of freedom=3

Internal energy=32×4×T6T …(ii)

Total energy=Internal energy of oxygen+internal energy of argon

=5T+6T11T

Therefore, the total energy of the system is11T


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