1) For a reversible adiabatic process, the ideal gas law can be written also as

or equivalently

where

and

are the initial and final temperature of the gas, and

and

are its initial and final volume.

is the adiabatic index, given by

where f is the number of degrees of freedom of the molecule. For helium, which is monoatomic gas, we have f=3, therefore

Instead, for oxigen (

) which is a diatomic gas, we have f=5, therefore

2) Using the initial relationship written at point 1), we can now calculate the increase in temperature for both gases. First of all, let's rewrite the initial equation as:

And since we know that both gases are compressed to one-third of their original volume, i.e.

this means

So now we can calculate the final temperature for each gas, since we know the initial temperature:
- For helium:

- For oxigen:

So, helium shows the greater temperature increase.