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Computing the work is easy: expansion work is defined to be the product of the force on the system times the distance through which the force moves. The negative sign is due to the fact that expansion work is done on the system by the surroundings. (If you want to compute the work done on the surroudings by the system, remove the - sign.)
w = -f*d
If we do the reaction in a piston where the piston moves up and down in response to pressure changes, then the force is just the pressure times the surface area of the piston, w = -P*a*d. In the same vein, for any expansion against a constant external pressure is just the change in volume times the pressure, w = -P*DV
Example: What is the work done on the system by the surroundings when 1 gram of liquid nitrogen converts to nitrogen gas at 77oK at a constant pressure of 1 atm? What is the work done by the system on the surroundings?
Solution: The expansion work is w = -P*DV.
The change in volume is Vgas - Vliquid. For liquid
nitrogen, the volume is much less than the volume of the gas so we can assume
that it is zero.