Let overline{V}, V_{text{rms}}, and V_{p} den | vedclass

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(C, D) The expressions for the speeds are:$V_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$$\overline{V} = \sqrt{\frac{8RT}{\pi M}}$$V_{p} = \sqrt{\frac{2RT}{M}

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Average kinetic energy of a molecule is $\frac{3}{4} m V_{p}^{2}$

Vedclass · Answer

(C, D) The expressions for the speeds are:$V_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$$\overline{V} = \sqrt{\frac{8RT}{\pi M}}$$V_{p} = \sqrt{\frac{2RT}{M}}$Comparing these values, we find $V_{p} For the average kinetic energy of a molecule:$K.E. = \frac{1}{2} m V_{	ext{rms}}^{2} = \frac{1}{2} m \left( \frac{3RT}{M} ight)$.Since $V_{p}^{2} = \frac{2RT}{M}$, we have $\frac{RT}{M} = \frac{V_{p}^{2}}{2}$.Substituting this, $K.E. = \frac{1}{2} m \cdot 3 \cdot \left( \frac{V_{p}^{2}}{2} ight) = \frac{3}{4} m V_{p}^{2}$.Thus, option $D$ is also correct.

Let $\overline{V}$, $V_{\text{rms}}$, and $V_{p}$ denote the mean speed, root mean square speed, and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?

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