The conservation of energy is a fundamental concept of physics
along with the
conservation of mass
and the
conservation of momentum.
Within some problem domain, the amount of energy remains constant
and energy is neither created nor destroyed. Energy can be converted from
one form to another (potential energy can be converted to kinetic
energy) but the total energy within the domain remains fixed.
On some separate slides, we have discussed
the state of a static gas, the properties
which define the state, and the
first law
of thermodynamics as applied to any system, in general.
On this slide we derive a useful form of the energy conservation equation
for a gas beginning with the first law of thermodynamics.
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. Like the Wright brothers, we are most
interested in thermodynamics in the study of propulsion
systems.
Aeronautical engineers usually simplify a thermodynamic analysis
by using intensive variables; variables that do not depend on
the mass of the gas. We call these variables specific
variables, and many of the state properties listed on this slide,
such as the work, internal energy, and volume are specific quantities;
the value of the quantity divided by the mass of the quantity.
Engineers usually use the lower case letter for the "specific"
version of a variable.
Let us look at the state variables present in a sample problem.
The figure shows a piston in a cylinder of the Wright
1903 engine. As the piston moves
from position 1 to position 2, it compresses the gas present in the cylinder.
Work (w) is performed on the gas.
Some of the work, called the shaft work (wsh), opposes
the motion of the cylinder, while the rest of the
work goes into changing the state of the
gas.
The work performed to change the state of the gas is equal to the
difference in the
pressure (p)
times the
specific volume (v) from state 1 to state 2.
w = wsh + p2 * v2  p1 * v1
The specific internal energy (e) is defined by the
first law of thermodynamics.
Although it is not present in this problem,
heat (q)
may also be transferred
to the gas.
From the first law of thermodynamics, the change in internal energy is equal
to heat transfer minus the work.
e2  e1 = q  w
A useful
additional variable, called the specific
enthalpy (h),
is the sum of the internal energy and the pressurevolume term used
to define the work on the gas.
h = e + p * v
If we perform a little algebra on the first law of thermodynamics,
we can begin to group some terms of the equations. In particular, the
enthalpy of the gas can be used to simplify the equation
into its final form:
h2  h1 = q  wsh
For the compression stroke and
power stroke of a fourstroke engine,
there is no external heat
flow into the gas and the "q" term is set equal to zero. During
combustion, no work is performed and the "wsh"
term is set to zero.
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