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

1. Feb 18, 2006

### QueenFisher

i'm given that p= $$\frac{1}{3}\rho\overline{c^2}$$

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

firstly, just from rearranging the original equation, you get

$$\overline{c^2}$$ = $$\frac{3p}{\rho}$$

square rooting both sides to get rms speed gives:

rms speed = $$\sqrt{\frac{3p}{\rho}}$$

which rearranges to rms speed = 9 $$\sqrt{\frac{p}{\rho}}$$

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

$$\overline{c^2}$$ = $$\frac{3p}{2\rho}$$

square rooting both sides to get rms speed gives:

rms speed = $$\sqrt{\frac{3p}{2\rho}}$$

which rearranges to rms speed = $$\frac{9}{4}$$ $$\sqrt{\frac{p}{\rho}}$$

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

Last edited by a moderator: Feb 18, 2006
2. Feb 18, 2006