Question:
A gaseous 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 mixture is
A gaseous 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 mixture is
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Use $U = nC_vT$, and remember diatomic = $\dfrac{5}{2}R$, monatomic = $\dfrac{3}{2}R$ when vibrational modes are ignored.
Updated On: Jun 4, 2025
- $4RT$
- $15RT$
- $9RT$
- $11RT$
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The Correct Option is D
Solution and Explanation
Oxygen (diatomic): $C_v = \dfrac{5}{2}R$, Energy = $2 \cdot \dfrac{5}{2}RT = 5RT$
Argon (monatomic): $C_v = \dfrac{3}{2}R$, Energy = $4 \cdot \dfrac{3}{2}RT = 6RT$
Total internal energy $= 5RT + 6RT = 11RT$
Argon (monatomic): $C_v = \dfrac{3}{2}R$, Energy = $4 \cdot \dfrac{3}{2}RT = 6RT$
Total internal energy $= 5RT + 6RT = 11RT$
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