Which Gas Shows Greater Pressure Increase When Compressed Adiabatically?

[raitozx]

Gas, pressure, physics, what??

Question: Consider two cylinders of gas identical in all respects except that one contains O2 and the other He. Both hold the same volume of gas at STP and are closed by a movable piston at one end. Both gases are now compressed adiabatically to one-third their original volume. Which gas will show the greater pressure increase?

The "answer" is apparently that He shows the greater pressure increase since it is lighter. Gases with lower molecular masses will travel at a faster rate. Therefore, their pressure will increase at a faster rate.

Using the ideal gas law PV = nRT, I assumed that V, n, R, and T were all identical since the question mentions "identical in ALL RESPECTS". So just through this, I figured that the pressure has to be identical. Did I do something wrong?

Also, if the "answer" is actually correct, which equation would prove it?

 

[Jack the Stri]

For an ideal gas, this is true. However, you're not dealing with ideal gases, so you need to use the http://en.wikipedia.org/wiki/Van_der_Waals_equationVan .

 

[nasu]

This ia an adiabatic process. You can find the final pressure from the equation for this process:

pV^gamma=constant.

The adiabatic exponent gamma is different for the two gases. The reason is not the atomic weight but the fact that He is mono-atomic whereas O2 is diatomic.
For ideal gas, gamma = Cp/Cv where Cp and Cv are the specific heats at constant pressure and constant volume, respectively.