First Law of Thermodynamics - Isobaric Cooling

[chromium1387]

Homework Statement

An ideal monatomic gas has an initial pressure of 3 atm, an initial volume of 1 L, and is at an initial temperature of 90 degrees Celsius. It first expands isothermically to 2 L and is then cooled isobarically to a point where it is adiabatically compressed to its initial state. Calculate the total work done.

Homework Equations

w_2→3=∫PdV=P(V₂-V₁

The Attempt at a Solution

Alright. I think I pretty much know what to do, but I am still a little confused. So, I've found the work done after the transition from state 1 to state 2. From there, can I calculate the new pressure at state 2 with P₁V₁=P₂V₂? And then, once I have my second pressure, this will be the pressure I use in my integral above. However, I do not know the volume the gas will be after the transition to the third state, which is what I need to find the value of the integral, correct? Or am I missing something?

 

[LawrenceC]

"...where it is adiabatically compressed to its initial state."