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EEJ MAIN Physics QUESTION #7020
Question 1
A vessel contains $15\text{ g}$ of Nitrogen gas at $27^\circ\text{ C}$. How much heat must be transferred to the gas so that the $rms$ velocity of the molecules is doubled? (Use $R = 8.3\text{ J/K mole}$)
  • $0.9\text{ kJ}$
  • $6\text{ kJ}$
  • $10\text{ kJ}$
  • $14\text{ kJ}$✔️
Correct Answer Explanation
To double the $rms$ velocity, the absolute temperature $T$ must increase four times because $v_{rms} \propto \sqrt{T}$. Initial $T = 300\text{ K}$, final $T = 1200\text{ K}$, so $\Delta T = 900\text{ K}$. Heat $Q = n C_v \Delta T$. For $N_2$ (diatomic), $C_v = \frac{5}{2}R$. Number of moles $n = \frac{15}{28}$. $Q = (\frac{15}{28}) \times (\frac{5}{2} \times 8.3) \times 900 \approx 10,000\text{ J}$ or $10\text{ kJ}$.