# Work transfer in thermodynamics
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Mechanical work
There are several ways of doing work, each in some way related to a force acting through
a distance.
W =F.s (kJ )
There are two requirements for a work interaction:
there must be a force acting on the boundary
the boundary must move
Therefore, the displacement of the boundary without any force to oppose or drive this
motion (such as expansion of a gas into evacuated space) is not a work interaction, W=0.
Also, if there are no displacements of the boundary, even if an acting force exists, there
will be no work transfer W = 0 (such as increasing gas pressure in a rigid tank).
Moving Boundary Work
The expansion and compression work is often called moving boundary work, or simply
boundary work.
We analyze the moving boundary work for a quasi‐equilibrium process. Consider the gas
enclosed in a piston‐cylinder at initial P and V. If the piston is allowed to move a distance
ds in a quasi‐equilibrium manner, the differential work is:
The quasi‐equilibrium expansion process. On this diagram, the
differential area dA under the process curve in P‐V diagram is equal to PdV, which is the
differential work.
Note: a gas can follow several different paths from state 1 to 2, and each path will have a
different area underneath it (work is path dependent).
The net work or cycle work is shown in Fig. 5. In a cycle, the net change for any properties
(point functions or exact differentials) is zero. However, the net work and heat transfer
depend on the cycle path.
ΔU = ΔP = ΔT = Δ(any property) = 0 for a cycle
