For a gas at a temperature T,the root-mean-sq | vedclass

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(B) The expressions for the three speeds of a gas at temperature $T$ are given by:${v_{rms}} = \sqrt{\frac{3RT}{M}}$${v_{av}} = \sqrt{\frac{8RT}{\pi M

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${v_{rms}} > {v_{av}} > {v_{mp}}$

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(B) The expressions for the three speeds of a gas at temperature $T$ are given by:${v_{rms}} = \sqrt{\frac{3RT}{M}}$${v_{av}} = \sqrt{\frac{8RT}{\pi M}}$${v_{mp}} = \sqrt{\frac{2RT}{M}}$Comparing the coefficients:${v_{rms}} = \sqrt{3} \cdot \sqrt{\frac{RT}{M}} \approx 1.732 \cdot \sqrt{\frac{RT}{M}}$${v_{av}} = \sqrt{\frac{8}{3.14}} \cdot \sqrt{\frac{RT}{M}} \approx \sqrt{2.546} \cdot \sqrt{\frac{RT}{M}} \approx 1.596 \cdot \sqrt{\frac{RT}{M}}$${v_{mp}} = \sqrt{2} \cdot \sqrt{\frac{RT}{M}} \approx 1.414 \cdot \sqrt{\frac{RT}{M}}$Thus,the relationship is ${v_{rms}} > {v_{av}} > {v_{mp}}$.

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

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