Question:
The total internal energy of a mixture of 6 moles of nitrogen, 4 moles of oxygen and 2 moles of hydrogen at temperature \(T\) is
\[
(R=\text{Universal gas constant})
\]
The total internal energy of a mixture of 6 moles of nitrogen, 4 moles of oxygen and 2 moles of hydrogen at temperature \(T\) is
\[
(R=\text{Universal gas constant})
\]
Show Hint
For an ideal diatomic gas (neglecting vibrational modes),
\[
\boxed{
U=\frac{5}{2}nRT
}
\]
where \(n\) is the total number of moles.
Updated On: Jul 15, 2026
- \(24RT\)
- \(36RT\)
- \(30RT\)
- \(20RT\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use the internal energy formula for diatomic gases.
Nitrogen (\(\mathrm{N_2}\)), oxygen (\(\mathrm{O_2}\)), and hydrogen (\(\mathrm{H_2}\)) are all diatomic gases.
At ordinary temperatures,
\[
U=\frac{5}{2}nRT.
\]
Step 2: Calculate the total number of moles. \[ n=6+4+2=12. \]
Step 3: Compute the total internal energy. \[ U = \frac{5}{2}(12)RT = 30RT. \] Hence, \[ \boxed{30RT} \] Therefore, \[ \boxed{(C)} \] is the correct answer.
Step 2: Calculate the total number of moles. \[ n=6+4+2=12. \]
Step 3: Compute the total internal energy. \[ U = \frac{5}{2}(12)RT = 30RT. \] Hence, \[ \boxed{30RT} \] Therefore, \[ \boxed{(C)} \] is the correct answer.
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