ever since I begun calculating thermodynamical cycles, I've had problems with determining the sign of the work along a particular bit of the cycle. Of course, I guess that an arbitrary cycle is 'bendy' and the sign of the work differential depends strongly on the coordinates, but usually the cycles I deal with consist of a couple of 'parts', for instance, adiabatics, isothermals, isochorics, etc. And whenever asked to calculate the total work done in a cycle (for instance to find the efficiency), I just kind of guessed the sign and managed to get by, but now when trying to understand this on a deeper level, this is coming back to haunt me.

So, suppose I have a thermodynamic cycle like this: LINK

Where:

(1)-adiabatic

(2)-isobaric

(3)-isothermal

(4)-isochoric

How do I know the sign of the work along each of these paths?