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For a proof, imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2, i.e., the work is independent of the path followed, as long as it goes from A to B.
For conservative forces, path independence can be interpreted to mean that the work done in going from a point to a point is independent of the moving path chosen (dependent on only the points and ), and that the work done in going around a simple closed loop is :
The work per unit of charge is defined as the movement of negligible test charge between two points, and is expressed as the difference in electric potential at those points. The work can be done, for example, by electrochemical devices (electrochemical cells) or different metals junctions [clarification needed] generating an electromotive force.
The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: = If the force is variable, then work is given by the line integral:
As an example, mechanical work and heat are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include work, heat and arc length.
Thermodynamic work is one of the principal kinds of process by which a thermodynamic system can interact with and transfer energy to its surroundings. This results in externally measurable macroscopic forces on the system's surroundings, which can cause mechanical work, to lift a weight, for example, [1] or cause changes in electromagnetic, [2] [3] [4] or gravitational [5] variables.
The dependence of work on the path of the thermodynamic process is also unrelated to reversibility, since expansion work, which can be visualized on a pressure–volume diagram as the area beneath the equilibrium curve, is different for different reversible expansion processes (e.g. adiabatic, then isothermal; vs. isothermal, then adiabatic ...
For example, if two slits are separated by 0.5 mm (d), and are illuminated with a 0.6 μm wavelength laser (λ), then at a distance of 1 m (z), the spacing of the fringes will be 1.2 mm. If the width of the slits b is appreciable compared to the wavelength, the Fraunhofer diffraction equation is needed to determine the intensity of the ...