solution: part a.

Before we start the main Math process, let's convert the initial pressure and temperature to SI units:

eqnarray8

Since the process is adiabatic, you can use the equation:

eqnarray10

From this we know that the inital states and the final states when plugged into this formula must be equal:

eqnarray13

Now we just plug in what we know: the initial pressue, and the fact that the final volume is four times the initial volume, as well as gamma.

eqnarray19