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Root mean square velocity for the molecules of a perfect gas (as $P \rightarrow 0$) is given by: $$c = \left( \frac{3RT}{M} \right) ^{\frac{1}{2}}$$

On dimensional analysis, RHS gives $\left( \frac{[L]^2}{[T]^2[mol]} \right) ^{\frac{1}{2}}$ which must be equal to $\frac{[L]}{[T]}$, is it dimensionally inconsistent?

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closed as unclear what you're asking by John Rennie, Jon Custer, Kyle Kanos, Bill N, Floris Sep 13 '17 at 0:48

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ It is my mistake, I mistook M's units to be that of mass instead $Mass * mol^{-1}$ $\endgroup$ – drake01 Sep 10 '17 at 12:13
  • $\begingroup$ You should delete the question since your premise for asking is flawed and recognized. It's not really about physics. $\endgroup$ – Bill N Sep 12 '17 at 21:39
  • $\begingroup$ I'm voting to close this question as off-topic because it was based on a mistake that was since recognized. $\endgroup$ – Floris Sep 13 '17 at 0:48
  • $\begingroup$ Sorry, but I can't find an option to delete the question $\endgroup$ – drake01 Sep 13 '17 at 2:18
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I would imagine that you forgot that $M$ is the mass per unit mol, which would solve your problem. However, since mol is a dimensionless number, it arguably doesn't need to appear in dimensional analysis (though can be helpful).

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Working in SI units (equivalent to dimensions) $$\text{m s}^{-1}=\sqrt{\frac{[\text{J}\ \text{K}^{-1}\ \text{mol}^{-1}] \ \ [\text{K}]}{[\text{kg}\ \text{mol}^{-1}]}}.$$ Alright?

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