Thermodynamics is a branch of physics
which deals with the energy and work of a system.
Thermodynamics deals only with the
large scale response
of a system which we can observe
and measure in experiments. As aerodynamicists, we are most
interested in the thermodynamics of propulsion
systems
and high speed flows.
The first law of
thermodynamics deals with the relationship between
heat,
energy, and work. We all have a basic understanding of work in general, but
scientists have a more precise definition of work.
For scientists, work is the product of a force acting through a
distance. As an example shown on the slide, an aircraft which is
acted on by a force F from time equals zero to some later time t
moves some distance s. The work W done on the aircraft during this
time is:
W = F * s
The units of work is the Joule, which is equal to
a Newton  meter. In the English system the unit of work is the foot
 pound. In our simple example, the force is a constant value
aligned with the displacement of the aircraft. In most real
applications, the force varies along the flight path. Work is then the
integrated value of the force along the path. If we use the symbol
S [ ] ds for the integral:
W = S [F] d s
The force is a
vector quantity
which changes in both
magnitude and direction.
The work is then equal to the integrated
value of the component of the force in the direction of the
displacement. 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 the
trigonometric cosine
function.
It is important to note that work is only done on, or by the
component of the force along the path. Using a cruising
aircraft as another example, the lift is
defined to be the force perpendicular to the flight path. Lift does
no work on a cruising aircraft because the displacement is
perpendicular to the force. Similarly, if an aircraft was stopped at
the end of the runway with the brakes on and the engines at full
throttle, the engines do no work on the aircraft because the
displacement distance is zero.
In the previous examples, we have been concerned with the work
done on, or by a force applied to a solid object. For a gas,
work is done when the volume
of a gas is changed at some pressure
since pressure represents a force per unit area and volume
can be related to the surface area and a distance. Notice that to
produce work, the volume must change.
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