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I have studied Maxwell's velocity distribution curve for same gas in different temperatures. I tried to plot the graph for gases of different molar mass. I understood that the most probable speed will be less for gases of higher molar mass will have lesser value of Most Probable Speed but I am not able to understand what will be the change in the Y coordinates of the graph (Fraction of molecules).

I will be grateful if you explain me this.

Thanks $:)$

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  • $\begingroup$ What do you mean by "what will be the change in the Y coordinate"? $\endgroup$
    – RC_23
    Jul 27, 2022 at 1:49
  • $\begingroup$ @RC_23 In Maxwell's graph, X axis represents velocity and Y axis represents fraction of molecules which possess that speed. If there are two elements of masses M1 and M2 (M1> M2). Then for any point in the graph, whose Y coordinate will be greater? $\endgroup$ Jul 27, 2022 at 4:23

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The Maxwell Boltzmann speed distribution is:

$$ f(v)= \left( \frac{m}{2 \pi kT} \right)^{3/2} e^{-\left(\frac{m}{kT} \frac{v^2}{2}\right)} 4 \pi v^2 $$

This curve is parameterized by the factor $\sqrt{\frac{m}{T}}$.

As you can see, decreasing the mass $m$ has exactly the same effect on the shape of the curve as increasing the temperature $T$. For example, you would expect helium at room temperature to have the same distribution of speeds as air at a higher temperature.

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