Thermodynamics and Propulsion  
Subsections
2.3 Example Applications of the First Law to motivate the use of a property called ``enthalpy''
2.3.1 Adiabatic, steady, throttling of a gas (flow through a valve or other restriction)Figure 2.5 shows the configuration of interest. We wish to know the relation between properties upstream of the valve, denoted by ``1'' and those downstream, denoted by ``2''.
To analyze this situation, we can define the system (choosing the appropriate system is often a critical element in effective problem solving) as a unit mass of gas in the following two states. Initially the gas is upstream of the valve and just through the valve. In the final state the gas is downstream of the valve plus just before the valve. The figures on the left of Figure 2.6 show the actual configuration just described. In terms of the system behavior, however, we could replace the fluid external to the system by pistons which exert the same pressure that the external fluid exerts, as indicated schematically on the right side of Figure 2.6. The process is adiabatic, with changes in potential energy and kinetic energy assumed to be negligible. The first law for the system is therefore
The work done by the system is
Use of the first law leads to
In words, the initial and final states of the system have the same value of the quantity . For the case examined, since we are dealing with a unit mass, the initial and final states of the system have the same value of . We define this quantity as the ``enthalpy,'' usually denoted by ,
In terms of the specific quantities, the enthalpy per unit mass is
It is a function of the state of the system. has units of Joules, and has units of Joules per kilogram. The utility and physical significance of enthalpy will become clearer as we work with more flow problems. For now, you may wish to think of it as follows (Levenspiel, 1996). When you evaluate the energy of an object of volume , you have to remember that the object had to push the surroundings out of the way to make room for itself. With pressure on the object, the work required to make a place for itself is . This is so with any object or system, and this work may not be negligible. (The force of one atmosphere pressure on one square meter is equivalent to the force of a mass of about .) Thus the total energy of a body is its internal energy plus the extra energy it is credited with by having a volume at pressure . We call this total energy the enthalpy, .
When is enthalpy the same in initial and final states? (MP 2.3)
2.3.2 QuasiStatic Expansion of a GasConsider a quasistatic process of constant pressure expansion. We can write the first law in terms of the states before and after the expansion as
By grouping terms we can write the heat input in terms of the enthalpy change of the system:

The final temperature is thus roughly hotter than the outside air!
It may be helpful to recap what we used to solve this problem. There were basically four steps:
A message that can be taken from both of these examples (as well as from a large number of other more complex situations, is that the quantity occurs naturally in problems of fluid flow. Because the combination appears so frequently, it is not only defined but also tabulated as a function of temperature and pressure for a number of working fluids.
Muddy Points
In the filling of a tank, why (physically) is the final temperature in the tank higher than the initial temperature? (MP 2.4)
can be differentiated (applying the chain rule to the term) to produce
 
or
 
Douglas Quattrochi 20060806