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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:
A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. This is illustrated in the figure to the right: The work done by the gravitational force on an object depends only on its change in height because the ...
For a quasi-static adiabatic process, the change in internal energy is equal to minus the integral amount of work done by the system, so the work also depends only on the initial and final states of the process and is one and the same for every intermediate path. As a result, the work done by the system also depends on the initial and final states.
This suggests path-independence of work done on the staircase; equivalently, the force field experienced is conservative (see the later section: Path independence and conservative vector field). The situation depicted in the print is impossible.
Energy gained by the system, through work done on it, is lost to the bath, so that its temperature remains constant. An adiabatic process is a process in which there is no matter or heat transfer, because a thermally insulating wall separates the system from its surroundings. For the process to be natural, either (a) work must be done on the ...
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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.