Thermodynamics is a branch of physics
which deals with the energy and work of a system.
Thermodynamics deals 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.
To understand how a propulsion system works, we must
study the basic thermodynamics of
gases.
Gases have various
properties that we can observe with our
senses, including the gas
pressure p,
temperature T,
mass, and
volume V
that contains the gas.
Careful, scientific observation has determined that these
variables
are related to one another, and the values of these
properties determine the
state
of the gas.
A thermodynamic process, such as
heating or
compressing the gas,
changes the values of the state variables in a
manner which is described by the
laws of thermodynamics. The
work done by a gas
and the
heat transferred to a gas
depend on the beginning and ending states of the gas and
on the process used to change the state.
It is possible to perform a series of processes, in which the state
is changed during each process, but the gas eventually
returns to its original state. Such a series of processes is
called a cycle and forms the basis for understanding
engines. The
Carnot Cycle
is one of the fundamental thermodynamic cycles and is described on
this web page. We will use a
p-V diagram
to plot the various processes in the Carnot Cycle. The cycle begins
with a gas, colored yellow on the figure, which is confined in a cylinder,
colored blue. The volume of the cylinder is changed by a moving red piston,
and the pressure is changed by placing weights on the piston. We have two
heat sources; the red one is at a nominal 300 degrees, and the purple one
is at 200 degrees. Initially, the gas is in State 1 at high temperature,
high pressure, and low volume.
-
The first process performed on the gas is an isothermal expansion.
The 300 degree heat source is brought into contact with the cylinder,
and weight is removed, which lowers the pressure in the gas. The
temperature remains constant, but the volume increases. During the
process from State 1 to State 2 heat is transferred from
the source to the gas to maintain the temperature. We will note the
heat transfer by Q1 into the gas.
-
The second process performed on the gas is an adiabatic expansion.
During an adiabatic process no heat is transferred to the gas.
Weight is removed, which lowers the pressure in the gas. The
temperature decreases and the volume increases as the gas
expands to fill the volume. During the
process from State 2 to State 3 no heat is transferred.
-
The third process performed on the gas is an isothermal compression.
The 200 degree heat source is brought into contact with the cylinder,
and weight is added, which raises the pressure in the gas. The
temperature remains constant, but the volume decreases. During the
process from State 3 to State 4 heat is transferred from
the gas to heat source to maintain the temperature. We will note the
heat transfer by Q2 away from the gas.
-
The fourth process performed on the gas is an adiabatic compression.
Weight is added, which raises the pressure in the gas. The
temperature increases and the volume decreases as the gas is
compressed. During the
process from State 4 to State 1 no heat is transferred.
At the end of the fourth process, the state of the gas has returned to
its original state and the cycle can be repeated as often as
you wish. During the cycle,
work W has been produced by the gas, and the
amount of work is equal to the area enclosed by the process curves.
From the
first law
of thermodynamics, the amount of work produced is equal to the net
heat transferred during the process:
W = Q1 - Q2
The Carnot Cycle has performed as an engine, converting the heat transferred
to the gas during the processes into useful work. A similar
Brayton Cycle
explains how a
gas turbine engine works, and an
Otto Cycle
explains how an
internal combustion engine works.
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