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. In rocket science, we are most
interested in the thermodynamics of
high speed flows, and in
propulsion systems
which produce thrust by
accelerating a gas. To understand how thrust is created, it is useful
to study the basic thermodynamics of gases.
The state of a gas is determined by the
values of certain measurable properties
like the pressure,
temperature,
and
volume
which the gas occupies. The values of these variables and
the state of the gas can be changed. On this figure we show a gas
confined in a blue jar in two different states. On the left, in State
1, the gas is at a higher pressure and occupies a smaller volume than
in State 2, at the right. We can represent the state of the gas on a graph
of pressure versus volume, which is
called a
pV diagram
as shown at the right.
To change the state of the gas from State 1 to
State 2, we must change the conditions in the jar, either by heating
the gas, or physically changing
the volume by moving a piston, or by changing the pressure by adding or removing
weights from the piston. In some of these changes, we do work
on, or have work done by the gas, in other changes we add, or
remove heat. Thermodynamics helps us determine the amount of work
and the amount of heat necessary to change the state of the gas.
Notice that in this example we have a fixed mass of gas. We can
therefore plot either the
physical volume
or the
specific volume, volume divided by mass,
since the change is the same for a constant mass. On the figure,
we use physical volume.
Scientists define work W to be the product
of force F acting through a distance s :
W = F * s
For a gas, work is the product of
the pressure p and the volume V during a change of volume.
W = p * V
We can do a
quick units check to see that pressure force / area times volume
area * length gives units of force times length which are the units of work
W = (force / area) * (area * length) = force * length
In the metric system the unit of work is the Joule, in the English system
the unit is the footpound.
In general, during a change of state both the volume
and the pressure change. So it is more correct to define the work as
the integrated, or summed variable pressure times the change of volume
from State 1 to State 2. If we use the symbol S [ ] ds for integral, then:
W = S [p] dV
On a graph
of pressure versus volume, the work is the area under the curve that
describes how the state is changed from State 1 to State 2.
As mentioned above, there are several options for changing the state of
a gas from one state to another. So we might expect that the amount of
work done on, or by a gas could be different depending on exactly how the state
is changed. As an example, on the graph on the figure, we show a curved
black line from State 1 to State 2 of our confined gas.
This line represents a change brought about by removing weights
and decreasing the pressure and allowing the volume to adjust according
to Boyle's law with no heat addition. The line
is curved and the amount of work done on the gas is shown by the red
shaded area below this curve. We could, however, move from State 1
to State 2 by holding
the pressure constant and increasing the volume by
heating the gas using Charles' law. The
resulting change in state proceeds from State 1 to an intermediate
State "a" on the graph. State "a" is at the same pressure as State 1,
but at a different volume. If we then remove the weights, holding a
constant volume, we proceed on to State 2. The work done in this
process is shown by the yellow shaded area. Using either
process we change the state of the gas from State 1 to State
2. But the work for
the constant pressure process is greater than the work for the curved
line process. The work done by a gas not only depends on the initial
and final states of the gas but also on the process used to change
the state. Different processes can produce the same state, but
produce different amounts of work.
Notice that not only does the work done by the gas depend on the process, but
also the heat transferred to the gas. In the first process, the curved line from
State 1 to State2, no heat was transferred to the gas; the process was adiabatic.
But in the second process, the straight line from State 1 to State "a" and then
to
State 2, heat was transferred to the gas during the constant pressure process.
The heat transferred to a gas not only depends on the initial
and final states of the gas but also on the process used to change
the state.
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