# Ideal Gases under Adiabatic Compression

1. Oct 14, 2012

### aa1607

I'm having trouble understanding what happens to the internal energy of an ideal gas being compressed adiabatically.

If DU = DQ + DW,

then as we do work PdV compressing the gas, since in adiabatic processes DQ=0, W the change in internal energy is non-zero, so U must increase.

But if we're talking about an ideal gas, as I keep hearing, (such as in this lecture where we're told an ideal gas shouldnt increase in temperature when we compress it in a bicycle pump:)

U is a function only of T, and so T ought not to vary as we increase the pressure, because it ought to be compensated for by a (countering) decrease in V, in accordance with the Ideal Gas Law: PV = nRT.

So should U stay constant or should it increase under adiabatic compression if the gas is ideal?

Can someone help me with this?

Thanks a lot!

2. Oct 14, 2012

### Staff: Mentor

U increases under adiabatic compression even if the gas is ideal. The change in U is equal to the work done on the gas. Air compressed in a bicycle pump is very close to an ideal gas. I found the discussion in the video very confusing. When the heated air passes from the pump through the valve into the tire, its higher temperature should remain nearly constant from one side of the value to the other, according to the Joule Thompson effect. You can look up the Joule Thompson parameter as a function of temperature and pressure for air (or calculate it from the non-ideal gas parameters for air), and you will find that the jt effect at bike tire pressures will be much smaller than the temperature change for adiabatic compression of air.

3. Oct 15, 2012

### aa1607

Thanks for the reply, I understand that now. The video is actually quite misleading.