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There are many kinds of work, including mechanical work, electrical work, and work against a gravitational or a magnetic field. Here we will consider only mechanical work, focusing on the work done during changes in the pressure or the volume of a gas. To describe this pressure–volume work (PV work), we will use such imaginary oddities as friction less pistons, which involve no component of resistance, and ideal gases, which have no attractive or repulsive interactions.
Imagine, for example, an ideal gas, confined by a friction less piston, with internal pressure Pint and initial volume Vi (Figure 18.3). If Pext = Pint, the system is at equilibrium; the piston does not move, and no work is done. If the external pressure on the piston (Pext) is less than Pint, however, then the ideal gas inside the piston will expand, forcing the piston to perform work on its surroundings; that is, the final volume (Vf) will be greater than Vi. If Pext > Pint, then the gas will be compressed, and the surroundings will perform work on the system.
If the piston has cross-sectional area A, the external pressure exerted by the piston is, by definition, the force per unit area: Pext = F/A. The volume of any three-dimensional object with parallel sides (such as a cylinder) is the cross-sectional area times the height (V = Ah). Rearranging to give F = PextA and defining the distance the piston moves (d) as Δh, we can calculate the magnitude of the work performed by the piston by substituting into Equation 18.2:
Equation 18.3w = Fd = PextAΔh
Figure 18.3 PV Work
Using a frictionless piston, if the external pressure is less than Pint (a), the ideal gas inside the piston will expand, forcing the piston to perform work on its surroundings. The final volume (Vf) will be greater than Vi. Alternatively, if the external pressure is greater than Pint (b), the gas will be compressed, and the surroundings will perform work on the system.
The change in the volume of the cylinder (ΔV) as the piston moves a distance d is ΔV = AΔh,The work performed is thus
Equation 18.4w = PextΔV
The units of work obtained using this definition are correct for energy: pressure is force per unit area (newton/m2) and volume has units of cubic meters, so
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