Force work done

Mole fraction of liquid phase Work of friction forces Work done on a unit mass of gas Distance between device of preliminary condensation (DPC) and separator... 

Work done Work done is dependent upon the force applied times the distance moved in the direction of the force. Work done = Force x Distance moved in the direction of the force (J). The SI unit of work done is the newton metre or joule (symbol J). 

If one assumes (p °°) = 0, then = qcp, therefore, (pj = A Jq. This means that the potential is numerically equal to the force work done on the displacement of the unit positive point charge from the given point to infinity. 

If we consider the case of a gas in adsorption equilibrium with a surface, there must be no net free energy change on transporting a small amount from one region to the other. Therefore, since the potential represents the work done by the adsorption forces when adsorbate is brought up to a distance x from the surface, there must be a compensating compressional increase in the free energy of the adsorbate. Thus... 

There are several different fomis of work, all ultimately reducible to the basic definition of the infinitesimal work Dn =/d/ where /is the force acting to produce movement along the distance d/. Strictly speaking, both/ and d/ are vectors, so Dn is positive when the extension d/ of the system is in the same direction as the applied force if they are in opposite directions Dn is negative. Moreover, this definition assumes (as do all the equations that follow in this section) that there is a substantially equal and opposite force resisting the movement. Otiierwise the actual work done on the system or by the system on the surroundings will be less or even zero. As will be shown later, the maximum work is obtained when tlie process is essentially reversible . 

The fluctuation dissipation theorem relates the dissipative part of the response fiinction (x") to the correlation of fluctuations (A, for any system in themial equilibrium. The left-hand side describes the dissipative behaviour of a many-body system all or part of the work done by the external forces is irreversibly distributed mto the infinitely many degrees of freedom of the themial system. The correlation fiinction on the right-hand side describes the maimer m which a fluctuation arising spontaneously in a system in themial equilibrium, even in the absence of external forces, may dissipate in time. In the classical limit, the fluctuation dissipation theorem becomes / /., w) = w). 

In the limit of very slow change (quasi-static process) the frictional component is zero and then the work done by the external force equals the free energy change, i.e.. 

It is necessary to establish some conventions concerning signs before proceeding further. When the applied force is a tensile force and the distortion is one of stretching, F, dL, and dw are all defined to be positive quantities. Thus dw is positive when elastic work is done on the system. The work done by the sample when the elastomer snaps back to its original size is a negative quantity. 

The above representation for the shell energy contains three different terms describing the bending energy of the shell, the deformation energy of the middle surface, and the work done by the exterior force /, respectively. 

Eneigy. The SI unit of energy is the joule which is the work done when the point of appHcation of a force of one newton is displaced a distance... 

The first integral on the right-hand side is the rate of work done on the fluid in the control volume by forces at the boundaiy. It includes both work done by moving solid boundaries and work done at flow entrances and exits. The work done by moving solid boundaries also includes that by such surfaces as pump impellers this work is called shaft work its rate is Ws-... 

Over the time increment dt, the force applied on the left-hand side of the element acts over a distance u dt, so the work done on the element from the left is Pu dt. The force on the right-hand boundary of the element k P + (dPIdh), dh, and it travels a distance (u + (dufdh), dh) dt, so the work done by the element on the surrounding fluid to the right is (P + (dP/dh), dh)(u + (dujdh), dh) dt. The net work done on the fluid element is the difference... 

If the work assumption is made, i.e., if it is assumed that the external work done by surface and body forces on a finite region in the reference configuration of a body undergoing homogeneous closed cycles of deformation is nonnegative, then an inequality may be deduced paralleling (5.37) by arguments essentially the same as those of Section 5.2.4. 

When metals are rolled or forged, or drawn to wire, or when polymers are injection-moulded or pressed or drawn, energy is absorbed. The work done on a material to change its shape permanently is called the plastic work- its value, per unit volume, is the area of the cross-hatched region shown in Fig. 8.9 it may easily be found (if the stress-strain curve is known) for any amount of permanent plastic deformation, e. Plastic work is important in metal- and polymer-forming operations because it determines the forces that the rolls, or press, or moulding machine must exert on the material. 

We prove this by a virtual work calculation. We equate the work done by the applied stress when the dislocation moves completely through the crystal to the work done against the force / opposing its motion (Fig. 9.12). The upper part is displaced relative to the lower by the distance b, and the applied stress does work (7/1/2) moving... 

As we press a flat indenter into the material, shear takes place on the 45° planes of maximum shear stress shown in Fig. 11.4, at a value of shear stress equal to k. By equating the work done by the force F as the indenter sinks a distance u to the work done against k on the shear planes, we get ... 

Fig. 6.7. How pearlite grows from undercooled y during the eutectoid reaction. The transformation is limited by diffusion of carbon in the y, and driving force must be shared between all the diffusionol energy barriers. Note that AH is in units of J kgn2 is the number of carbon atoms that diffuse from or to Fe3C when 1 kg of y is transformed. (AH/njKfT - 7]/TJ is therefore the free work done when a single carbon atom goes from or to Fe,C.

As shown by Eq. (6) the PME is the reversible work done by the average force. It is possible to express relative values of the PME between different solute configurations X i and X2 using Eq. (6) and the reversible work theorem [4] ... 

Working design equations for each of these flow rates follow. Hemeon developed equations for estimating the volumetric flow rate of induced air based on the power generated by the stream of falling particles (i.e., the work done per unit time by the drag force over the distance... 

The analysis to find the fiber buckling load in each mode is based on the energy method described by Timoshenko and Gere [3-31], The buckling criterion is that the change in strain energy for the fiber, AUf, and for the associated matrix material, AUf, is equated to the work done by the fiber force, AW, during deformation to a buckled state, that is,... 

Finally, the work done by the external force P during buckling is... 

In the transmission of energy by these simple machines, the conseiwation law always applies The work input equals the work output. Wlien work is done by a system, energy is transferred out of it and when work is done on a system, energy is transferred into it. When two objects interact by way of a machine (e.g. a lever), the work out of one object equals the work into the other. The work done by a person forcing one end of a lever downward equals the work done lifting a load at the other end as the lever moves upward. In any practical situation, the frictional forces resisting motion will always increase the amount of force (and work) required to do ajob. 

The amount of work done on an object is determined by the force exerted on it multiplied by the distance it moves in the direction of the force. Therefore the key to figuring out how much the force is magnified by a simple machine is to compare distances moved. For example, if the end of a lever under a stone weighing 2,000 newtons moves upward 1 meter, the amount of work done lifting the stone is 1 meter X... 

An increase of speed corresponds to an increase of kinetic energy. This increase of kinetic energy is a result of the net force acting in the direction ol motion through some distance. Net force times distance is the work done on the object ... 

U is the net work done on the system and is defined as the sum of the work done hy external forces and external moments. 

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