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 thermodynamics in the study of propulsion
systems
and understanding high speed flows.
The state of a gas is defined by
several properties including the
temperature,
pressure,
and
volume
which the gas occupies. From a study of the
first law of thermodynamics, we
find that the internal energy of a gas is also a state variable,
that is, a variable which depends only on the state of the gas and
not on any process that produced that state. We are free to define
additional state variables which are combinations of existing state
variables. The new variables often make the analysis of a
system much simpler. For a gas, a useful additional state variable is
the enthalpy which is defined to be the sum of the internal
energy E plus the product of the pressure p and volume V.
Using the symbol H for the enthalpy:
H = E + p * V
The enthalpy can be made into an
intensive, or specific , variable by
dividing by the mass. Propulsion engineers use
the specific enthalpy in engine analysis more than the enthalpy
itself.
How does one use this new variable called enthalpy? Let's consider the
first law
of thermodynamics for a gas. For a system with heat transfer Q and
work W, the change in internal energy E from state 1
to state 2 is equal to the difference in
the heat transfer into the system and the work done by the system:
E2  E1 = Q  W
The
work and
heat transfer
depend on the process used to change the state. For the special case of
a constant pressure process, the work done
by the gas is given as the constant pressure p times the change in
volume V:
W = p * [V2  V1]
Substituting into the first equation, we have:
E2  E1 = Q  p * [V2  V1]
Let's group the conditions at state 2 and the conditions at state 1
together:
(E2 + p * V2)  (E1 + p * V1) = Q
The (E + p * V) can be replaced by the enthalpy H.
H2  H1 = Q
From our
definition of the heat transfer, we can represent
Q by some heat capacity coefficient Cp times the temperature T.
(H2  H1) = Cp * (T2  T1)
At the bottom
of the slide, we have divided by the mass of gas to produce the
specific enthalpy equation version.
(h2  h1) = cp * (T2  T1)
The
specific heat capacity
cp is called
the specific heat at constant pressure and is related to the
universal gas constant of the equation of state. This final equation
is used to determine values of specific enthalpy for a given
temperature. Enthalpy is used in the energy
equation for a fluid. Across
shock waves,
the total enthalpy of the gas remains a constant.
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