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 for the role it plays in
engine design.
The state of a gas is defined by
several properties including the
temperature, pressure,
and
volume
which the gas occupies. From our study of the
first law of thermodynamics, we have
found 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. These new variables will often make the analysis of a
system much simpler. For a gas, a useful additional state variable is
the enthalpy (H) which is defined to be the sum of the internal
energy (E) plus the product of the pressure (p) and volume (V),
H = E + p * V
How does one use this new variable called enthalpy? Let's consider the
first law
of thermodynamics applied to a gas system with both heat transfer (Q)
and work (W) done by the system in going from state 1 to state 2.
From our slide on
heat transfer,
we know that we can represent the amount of heat transfer by a constant (C),
called the
heat capacity,
times the difference in temperature (T):
Q = C * (T2 - T1)
From our slide on the
work
done by a gas, we know two things. First, the amount of work depends on the
process used to change the state. And second, that the work will be of the
form pressure times the change of volume. Let us select a constant pressure process.
Then the work is given by:
W = p * (V2 - V1)
The first law of thermodynamics tells us:
E2 - E1 = Q - W
Substitute the expression for the work:
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
Now substitute the value for "Q" which we talked about earlier:
(H2 - H1)p = Cp (T2 - T1)p
We have enclosed the terms of the equation in
parentheses with a "p" subscript to remind ourselves that this
equation is only true for a constant pressure process.
What good is all of this?
The internal energy of a gas is hard to measure, but the temperature of
a gas is easy to measure. Using the enthalpy for a gas lets us easily
solve problems involving the first law of thermodynamics by measuring
the temperature. The enthalpy is used in our derivation of the
conservation of energy for a gas.
We can apply the conservation of energy equation to determine the
work performed during the various strokes of a
four-stroke
engine.
The enthalpy is also used in our evaluation of the change of
entropy
as required by the
second law
of thermodynamics. Enthalpy is a very useful state variable when solving
gas dynamics problems.
There is also a "specific" form of the enthalpy equation, which is just
the derived form divided by the mass of the gas.
(h2 - h1)p = cp (T2 - T1)p
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 for a given gas. We can then use the tables of the results
to solve problems.
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