Why Does RMS Velocity Increase During Adiabatic Compression?

[UCstudent]

rms velocity and compression. Please help!

Homework Statement

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

Homework Equations

None

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

 

[netgypsy]

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

 

[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
$Δv = \sqrt{(3/2) (k_b ΔT)/m}$

 

[netgypsy]

And I was going to make you figure it out yourself. :-(