Do Path-Dependent Processes Affect Thermodynamic Quantities in Ideal Gases?

[painfive]

An ideal gas changes state from P=32, V=1 to P=1 V=8 via three different paths: first pressure then volume, first volume then pressure, and adiabatically. I need to calculate the change in heat energy, work done by the system, and change in internal energy for all three paths. Will these be the same for all the paths? What equations should I use? So far I found the heat change for the adiabatic system (zero) and the work done by the other two (only along the parts where the volume changes). I'm pretty sure the internal energy change is the same for all of them, so I need at least one more value before I can get the rest.

 

[Astronuc]

first pressure then volume, first (second?) volume then pressure, and adiabatically.

Does first pressure then volume mean first pressure changes (decreases) and then volume changes (increases)?

How about showing some equations.

e.g. W_{1 \rightarrow 2} = \int_{V_1}^{V_2} p\, dV

and for an adiabatic system pV^\gamma = const

and what is the relationship between energy and work in the gas?