Thermodynamics is a branch of physicswhich deals with the energy and work of a system.Thermodynamics deals only with thelarge scale responseof a system which we can observeand measure in experiments. As aerodynamicists, we are mostinterested in the thermodynamics of propulsionsystemsand high speed flows.The first law ofthermodynamics deals with the relationship betweenheat,energy, and work. We all have a basic understanding of work in general, butscientists have a more precise definition of work.
For scientists, work is the product of a force acting through adistance. As an example shown on the slide, an aircraft which isacted on by a force F from time equals zero to some later time tmoves some distance s. The work W done on the aircraft during thistime is:
W = F * s
The units of work is the Joule, which is equal toa Newton - meter. In the English system the unit of work is the foot- pound. In our simple example, the force is a constant valuealigned with the displacement of the aircraft. In most realapplications, the force varies along the flight path. Work is then theintegrated value of the force along the path. If we use the symbolS [ ] ds for the integral:
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W = S [F] d s
The force is avector quantitywhich changes in bothmagnitude and direction.The work is then equal to the integratedvalue of the component of the force in the direction of thedisplacement. If the angle between the force and displacement equals phi,then the work is given by:
W = S [F * cos(phi)] d s
where cos is thetrigonometric cosinefunction.
It is important to note that work is only done on, or by thecomponent of the force along the path. Using a cruisingaircraft as another example, the lift isdefined to be the force perpendicular to the flight path. Lift doesno work on a cruising aircraft because the displacement isperpendicular to the force. Similarly, if an aircraft was stopped atthe end of the runway with the brakes on and the engines at fullthrottle, the engines do no work on the aircraft because thedisplacement distance is zero.
In the previous examples, we have been concerned with the workdone on, or by a force applied to a solid object. For a gas,work is done when the volumeof a gas is changed at some pressuresince pressure represents a force per unit area and volumecan be related to the surface area and a distance. Notice that toproduce work, the volume must change.
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