i'm given that p= [tex]\frac{1}{3}\rho\overline{c^2}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

without calculation, what happens to rms speed if pressure halved, temperature constant?

firstly, just from rearranging the original equation, you get

[tex]\overline{c^2}[/tex] = [tex]\frac{3p}{\rho}[/tex]

square rooting both sides to get rms speed gives:

rms speed = [tex]\sqrt{\frac{3p}{\rho}}[/tex]

which rearranges to rms speed = 9 [tex]\sqrt{\frac{p}{\rho}}[/tex]

then, using original equation, when pressure halved, you get:

[tex]\overline{c^2}[/tex] = [tex]\frac{3p}{2\rho}[/tex]

square rooting both sides to get rms speed gives:

rms speed = [tex]\sqrt{\frac{3p}{2\rho}}[/tex]

which rearranges to rms speed = [tex]\frac{9}{4}[/tex] [tex]\sqrt{\frac{p}{\rho}}[/tex]

so is it ok to say that the rms speed is quartered?

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# Kinetic theory of gases - can someone check this please?

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