Editing Working fluid (section)

==Work==
The working fluid can be used to output useful [[work (physics)|work]] if used in a [[turbine]]. Also, in thermodynamic cycles energy may be input to the working fluid by means of a [[compression (physical)|compressor]]. The mathematical formulation for this may be quite simple if we consider a cylinder in which a working fluid resides. A piston is used to input useful work to the fluid. From mechanics, the work done from state 1 to state 2 of the process is given by:
:<math> W = -\int_{1}^{2} \mathbf{F} \cdot \mathrm{d}\mathbf{s}</math>

where ''ds'' is the incremental distance from one state to the next and ''F'' is the force applied. The negative sign is introduced since in this case a decrease in volume is being considered. The situation is shown in the following figure:

[[File:Piston cylinder.jpg|frame|none|Work input on a working fluid by means of a cylinder–piston arrangement]]

The force is given by the product of the pressure in the cylinder and its cross sectional area such that
:<math>\begin{align}
W &= -\int_{1}^{2} PA \cdot \mathrm{d}\mathbf{s} \\
&= -\int_{1}^{2} P \cdot \mathrm{d}V
\end{align}</math>

Where ''A&sdot;ds = dV'' is the elemental change of cylinder volume. If from state 1 to 2 the volume increases then the working fluid actually does work on its surroundings and this is commonly denoted by a negative work. If the volume decreases the work is positive. By the definition given with the above integral the work done is represented by the area under a [[pressure–volume diagram]]. If we consider the case where we have a constant pressure process then the work is simply given by
:<math>\begin{align}
W &= -P \int_{1}^{2} \mathrm{d}V \\
&= -P \cdot \left(V_2 - V_1\right)
\end{align}</math>

[[File:Isobaric-process.svg|thumb|none|Constant pressure process on a p–V diagram]]