One form of mechanical work frequently encountered in practice is associated with the expansion or compression of a gas in a piston–cylinder device. During this process, part of the boundary (the inner face of the piston) moves back and forth. Therefore, the expansion and compression work is often called moving boundary work, or simply boundary work.
It is also called PdV work. Moving boundary work is the primary form of work involved in automobile engines. During their expansion, the combustion gases force the piston to move, which in turn forces the crankshaft to rotate.
A quasi-equilibrium process is a process during which the system remains nearly in equilibrium at all times. A quasi-equilibrium process, also called a quasi static process, is closely approximated by real engines, especially when the piston moves at low velocities. Under identical conditions, the work output of the engines is found to be a maximum, and the work input to the compressors to be a minimum when quasi-equilibrium processes are used in place of non quasi-equilibrium processes.
The boundary work in the differential form is equal to the product of the absolute pressure P and the differential change in the volume dV of the system. This expression also explains why the moving boundary work is sometimes called the P dV work. Here, P is the absolute pressure, which is always positive. However, the volume change dV is positive during an expansion process (volume increasing) and negative during a compression process (volume decreasing). Thus, the boundary work is positive during an expansion process and negative during a compression process.
The integral of pdv can be evaluated only if we know the functional relationship between P and V during the process. That is, P = f (V) should be available. Note that P = f (V) is simply the equation of the process path on a P-V diagram.
The area under the process curve on a P-V diagram is equal, in magnitude, to the work done during a quasi-equilibrium expansion or compression process of a closed system. (On the P-v diagram, it represents the boundary work done per unit mass.)
Note that work is a mechanism for energy interaction between a system and its surroundings, and boundary work represents the amount of energy transferred from the system during an expansion process (or to the system during a compression process).
Note: Problem (Boundary work for a constant Pressure process) solved has been taken from following book:
Thermodynamics an Engineering Approach by Yunus A Cengel
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