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 aerodynamics, the thermodynamics
of a gas obviously plays an important role in the analysis of
propulsion systems.
The
first law
of thermodynamics defines the relationship between the various forms of
kinetic and potential energy present in a system, the
work
which the system
can perform and the transfer of
heat.
The law states that energy is conserved in all thermodynamic processes.
However, we can imagine thermodynamic processes which would conserve energy
but which never occur in nature. For example, if we bring a hot object into
contact with a cold object, the hot object cools down and the cold object
heats up until an equilibrium is reached. The transfer of heat goes from the
hot object to the cold object. We could imagine a system in which the
heat would instead be transferred from the cold object to the hot object, and
such a system would not violate the first law of thermodynamics. The cold
object would get colder and the hot object would get hotter but energy would
be conserved. Obviously we don't encounter such a system in nature and to
explain this and similar observations, thermodynamicists proposed a second
law of thermodynamics. Clasius, Kelvin, and Carnot proposed various forms
of the second law to describe the particular physics problem that each was
studying. The description of the second law stated on this slide was taken
from Halliday and Resnick's textbook, "Physics". It begins with the definition
of a new state variable called
entropy.
Entropy has a variety of
physical interpretations, including the statistical disorder of the system,
but for our purposes, let us consider entropy to be just another property
of the system, like
enthalpy
or
temperature.
The second law states that there exists a useful state variable called entropy.
The change in entropy (delta S) is equal to the heat transfer (delta Q) divided
by the temperature (T).
delta S = (delta q) / T
For a given physical process, the entropy of
the system and the environment will remain a constant if the process can be
reversed.
If we denote the initial and final states of the system by "i" and "f",
then:
Sf = Si (reversible process)
An example of a reversible process would be ideally forcing a
flow through a constricted pipe. (Ideal means no boundary layer losses).
As the flow moves through the constriction, the pressure, temperature and
velocity would change, but these variables would return to their original
values downstream of the constriction. The
state
of the gas would return to its original conditions and the change of entropy
of the system would be zero.
The second law states that
if the physical process is irreversible, the entropy of the system
and the environment must increase; the final entropy must be greater than
the initial entropy.
Sf > Si (irreversible process)
An example of an irreversible process is the problem
discussed in the second paragraph where a hot object is put in contact with a cold object.
Eventually, they both achieve the same equilibrium temperature. If we then
separate the objects they
do not naturally return to their original (different) temperatures. The
process of bringing them to the same temperature is irreversible.
The application of the second law describes why heat is transferred from the
hot object to the cool object. Let us assume that the heat is transferred from the
hot object (object 1) at temperature T1 to the cold object (object 2) at temperature T2.
The amount of heat transferred is Q and the final equilibrium
temperature for both objects we will call Tf. The temperature of the hot object changes
as the heat is transferred away from the object.
The average temperature of the hot object during
the process we will call Th and it would be the average of T1 and Tf.
Th = (T1 + Tf) / 2
Similarly, for the cold object, the final temperature is Tf and the average
temperature during the process is Tc which is the average of Tf and T2.
Tc = (T2 + Tf) / 2
Th will always be greater than Tc, because T1 is greater than T2.
Th > Tc
The entropy change for the hot object will be (-Q/Th), with the minus sign
applied because the heat is transferred away from the object.
delta Sh = -Q / Th
For the cold object,
the entropy change is (Q/Tc), positive because the heat is transferred into the object.
delta Sc = Q / Tc
So the total entropy change for the whole system would be given by the equation
Sf = Si - Q / Th + Q / Tc
with Si and Sf being the final and initial values
of the entropy.
The term (Q/Tc) will always be greater than (-Q/Th) because Th is greater than
Tc. Therefore,
Sf will be greater than Si, as the second law predicts. If, instead, we had
assumed that the heat was being transferred from the cold object to the hot object, our
final equation would be
Sf = Si + Q / Th - Q / Tc
The signs on the terms would
be changed because of the direction of the heat transfer.
This would result in Sf being less than Si and the entropy of the system
would decrease which would violate the second law of thermodynamics.
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