Thermodynamics

68 | Thermodynamicsx 1 = 1 mmxFIGURE 2–32Solid bars behave as springs under theinfluence of a force.bF 1 = 300 NRigid wire frameSurface of filmxF 2 = 600 NFIGURE 2–33Stretching a liquid film with amovable wire.FRestpositionx 2 = 2 mmFIGURE 2–31The displacement of a linear springdoubles when the force is doubled.MovablewireFdxthe work associated with the expansion or contraction of an elastic solid barby replacing pressure P by its counterpart in solids, normal stress s n F/A,in the work expression:22W elastic F dx s n A dx1kJ21(2–30)where A is the cross-sectional area of the bar. Note that the normal stresshas pressure units.Work Associated with the Stretching of a Liquid FilmConsider a liquid film such as soap film suspended on a wire frame(Fig. 2–33). We know from experience that it will take some force to stretchthis film by the movable portion of the wire frame. This force is used toovercome the microscopic forces between molecules at the liquid–air interfaces.These microscopic forces are perpendicular to any line in the surface,and the force generated by these forces per unit length is called the surfacetension s s , whose unit is N/m. Therefore, the work associated with thestretching of a film is also called surface tension work. It is determined from2W surface s s dA1kJ21(2–31)where dA 2b dx is the change in the surface area of the film. The factor 2is due to the fact that the film has two surfaces in contact with air. The forceacting on the movable wire as a result of surface tension effects is F 2bs swhere s s is the surface tension force per unit length.Work Done to Raise or to Accelerate a BodyWhen a body is raised in a gravitational field, its potential energy increases.Likewise, when a body is accelerated, its kinetic energy increases. The conservationof energy principle requires that an equivalent amount of energymust be transferred to the body being raised or accelerated. Remember thatenergy can be transferred to a given mass by heat and work, and the energytransferred in this case obviously is not heat since it is not driven by a temperaturedifference. Therefore, it must be work. Then we conclude that(1) the work transfer needed to raise a body is equal to the change in thepotential energy of the body, and (2) the work transfer needed to acceleratea body is equal to the change in the kinetic energy of the body (Fig. 2–34).Similarly, the potential or kinetic energy of a body represents the work thatcan be obtained from the body as it is lowered to the reference level ordecelerated to zero velocity.This discussion together with the consideration for friction and otherlosses form the basis for determining the required power rating of motorsused to drive devices such as elevators, escalators, conveyor belts, and skilifts. It also plays a primary role in the design of automotive and aircraftengines, and in the determination of the amount of hydroelectric power thatcan be produced from a given water reservoir, which is simply the potentialenergy of the water relative to the location of the hydraulic turbine.1