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Question

(A) The root mean square speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M

Vedclass · Accepted Answer

$(v_{rms})_1 < (v_{rms})_2 < (v_{rms})_3$ and $(\bar{K})_1 = (\bar{K})_2 = (\bar{K})_3$

Vedclass · Answer

(A) The root mean square speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M}}$.Given $m_1 > m_2 > m_3$,it follows that $(v_{rms})_1 The average kinetic energy of a gas molecule is given by $\bar{K} = \frac{3}{2}kT$. Since the temperature $T$ is the same for all gases in the mixture,the average kinetic energy depends only on the temperature and is independent of the molecular mass.Therefore,$(\bar{K})_1 = (\bar{K})_2 = (\bar{K})_3$.

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

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