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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:
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.
If the system has such rigid walls that pressure–volume work cannot be done, but the walls are adiabatic (Q = 0), and energy is added as isochoric (constant volume) work in the form of friction or the stirring of a viscous fluid within the system (W < 0), and there is no phase change, then the temperature of the system will rise.
An example of such an exchange would be an isentropic expansion or compression that entails work done on or by the flow. For an isentropic flow, entropy density can vary between different streamlines. If the entropy density is the same everywhere, then the flow is said to be homentropic.
The net work equals the area inside because it is (a) the Riemann sum of work done on the substance due to expansion, minus (b) the work done to re-compress. Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a P-V diagram.
The value of work done (VOWD) is a project management technique for measuring and estimating the project cost at a point in time. It is mainly used in project environments of the Petroleum industry and is defined as the value of goods and services progressed, regardless of whether or not they have been paid for or received.
Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows. The gradient theorem also has an interesting converse: any path-independent vector field can be expressed as the gradient of a scalar field. Just like the gradient theorem itself, this converse has many ...
The diagram enables calculation of the work performed and thus can provide a measure of the power produced by the engine. [ 4 ] To exactly calculate the work done by the system it is necessary to calculate the integral of the pressure with respect to volume.