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Question
A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.)
Solution
O2 is a diatomic gas having 5 degrees of freedom
Energy (total internal) per mole of the gas = `5/2` RT ....`[(R = "Universal gas constant"),(T = "Temperature")]`
For 2 moles of the gas total internal energy = `2 xx 5/2` RT = 5 RT .....(i)
Neon (Ne) is a monoatomic gas having 3 degrees of freedom
∴ Energy per mole = `3/2` RT
We have 4 moles of Ne
Hence, Energy = `4 xx 3/2` RT = 6 RT .....(ii) [Using equations (i) and (iii)]
∴ Total energy = 5 RT + 6 RT
= 11 RT
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