states as it is a state function). In the current mathematical notation, the differential is an inexact differential. In another notation, is written (with a horizontal line through the d). This notation indicates that is not an exact one-form. The line-through is merely a flag to warn us there is actually no function (0-form) which is the potential of . If there were, indeed, this function , we should be able to just use Stokes Theorem to evaluate this putative function, the potential of , at the boundary of the path, that is, the initial and final points, and therefore the work would be a state function. This impossibility is consistent with the fact that it does not make sense to refer to the work on a point in the PV diagram; work presupposes a path. Other mechanical types of work There are several ways of doing mechanical work, each in some way related to a force acting through a distance. In basic mechanics, the work done by a constant force F on a body displaced a distance s in the direction of the force is given by If the force is not constant, the work done is obtained by integrating the differential amount of work, Rotational work Energy transmission with a rotating shaft is very common in engineering practice. Often the torque T applied to the shaft is constant which means that the force F applied is constant. For a specified constant torque, the work done during n revolutions is determined as follows: A force F acting through a moment arm r generates a torque T This force acts through a distance s, which is related to the radius r by The shaft work is then determined from: The power transmitted through the shaft is the shaft work done per unit time, which is expressed as Spring work When a force is applied on a spring, and the length of the spring changes by a differential amount dx, the work done is For linear elastic springs, the displacement x is proportional to the force applied where K is the spring constant and has the unit of N/m. The displacement x is measured from the undisturbed position of the spring (that is, when ). Substituting the two equations , where x1 and x2 are the initial and the final displacement of the spring respectively, measured from the undisturbed position of