1. Dec 12, 2011

### UCstudent

1. The problem statement, all variables and given/known data

Explain why the rms velocity of a gas increases when it is adiabatically compressed.

2. Relevant equations

None

3. The attempt at a solution

I know that compressing a gas decreases the volume, but I don't know details on how it would effect rms velocity

2. Dec 12, 2011

### netgypsy

Do you understand what adiabatically compressed means? If you don't, google it :-)

3. Dec 12, 2011

### gnulinger

If you compress a gas adiabatically, no heat is transferred from the gas to its surroundings. You know that compressing a gas increases the temperature (and you can calculate by how much using your adiabatic relations).

$T*V^{γ-1} = constant$
$T_{0}*V_0^{γ-1} = T_1*(V_0 + ΔV)^{γ-1}$
Thus
$T_1 = T_{0}*(V_0/(V_0 + ΔV))^{γ-1}$
And
$ΔT = T_1 - T_0$

Then
$ΔE = (3/2)N k_b ΔT= (1/2)N m (Δv)^2$
Or
$Δv = \sqrt{(3/2) (k_b ΔT)/m}$

Last edited: Dec 12, 2011
4. Dec 12, 2011