Internal Energy (ideal Gas)

Question

Internal energy of 3 moles of a monatomic ideal gas at 400 K? (R = 8.3 J/mol·K)

RankGuru · Accepted Answer

1. **Ideal Gas U**: For an ideal gas, internal energy depends only on temperature.
2. **Monatomic Gas**: A monatomic gas has 3 translational degrees of freedom. By the law of equipartition of energy, each degree contributes $\frac{1}{2} RT$ per mole.
3. **Formula**: $U = n \left(\frac{f}{2}ight) RT$, where $f = 3$.
4. **Calculation**:
   - $n = 3 	ext{ mol}$
   - $R = 8.3 	ext{ J/mol\cdot K}$
   - $T = 400 	ext{ K}$
   - $U = 3 	imes \frac{3}{2} 	imes 8.3 	imes 400$
   - $U = 4.5 	imes 3320 = 14940$ J.
5. **Unit conversion**: $14940$ J $= 14.94$ kJ.

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Internal Energy (ideal Gas)

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