Sandler (2006) explains the approach followed in the chemical engineering textbook to solve problems, and the importance of identifying the system boundaries in each case:
In many thermodynamics problems one is given information about the initial
equilibrium state of a substance and asked to find the final state if the heat and work flows are specified…. Since we use thermodynamic balance equations to get the
information needed to solve this sort of problem, the starting point is always the same: the identification of a convenient thermodynamic system… The seemingly most
arbitrary step in thermodynamic problem solving is the choice of the system … some system choices may result in less effort being required to obtain a solution. (p. 70) Tank-filling problems represent an important class of problems in the chemical engineering textbook. This example refers to two tanks joined by a valve, one with an ideal gas under
142 Final Tank 1 Initial Tank 1 Initial Tank 1 Tank 2 Vacuum Final Tank 1 Tank 2
particular conditions, the other evacuated. The process is assumed to be adiabatic. The problem to be solved is to determine the final conditions in both tanks.
In order to solve the problem, a choice has to be made about what constitutes the “system”, i.e. where the boundaries are that distinguishes the system from the surroundings.
There are three possible approaches to the problem.
1. SYSTEM = Both Tanks (as enclosed by the dotted line below)
With the system as indicated, some implications follow:
The system is CLOSED.
No expansion work is done (on/by the system as a whole), so the total volume of the system remains constant.
The two balance equations (mass and energy) that can be developed from this are not enough to solve the problem, and a further set of equations needs to be developed, now considering a different system: the changes in tank 1, considered by itself.
143 Initial
Tank 1
Final
Tank 1
This system is now no longer closed, but open, and the differential forms of the equations have to be used, since the amount of gas between the initial and final states changes. After a
considerable amount of mathematical manipulation (p. 77-79), an answer is reached.
Once the Second Law of thermodynamics has been introduced and entropy is developed as a third type of balance equation for problem solving, Sandler returns to the same problem. The approach to the system definition is different: again the focus is on Tank 1, but now a different part of Tank 1:
3. SYSTEM = the portion of the gas in tank 1 that remains behind when the pressures in the two tanks have been equalised.
To draw the initial system, the student has to imagine “only that portion of the contents of the first cylinder that remains in the cylinder when the pressures have equalized” (Sandler, 2006, p. 128).
In this case the system is closed, but the volume changes. By introducing the entropy balance as a third balance, the problem now becomes simple to solve.
The interest here lies in the idealisation as a distortion that is introduced in the approach to solving this problem; the ideal gas model does not allow for the conceptualisation of the gas in this way. For this approach to the problem to be effective, the portion of the contents of the gas (a fraction of the actual gas molecules) that does not move into tank 2 has to be imagined as occupying a fraction of the volume of tank 1 in the initial state. This conceptualisation of the system is a completely virtual construct, but essential to the solution, because without this the expansion of the gas portion in the closed system cannot be accounted for. This flies in the face of the ideal gas model that insists that a gas will fill the volume it occupies as a result of the continuous motion of its particles.
144 Although the system choice is an unusual one, it is one that leads quickly to a useful result. This demonstrates that sometimes a clever choice for the thermodynamic system can be the key to solving a thermodynamic problem with minimum effort. (Sandler, 2006, p. 129)
In terms of Weisberg’s categorisation, this is an example of the pragmatic Galilean idealisation where problem solving is the central concern. The orientation to knowledge demonstrated in this example is the physical realisability of the solution rather than allegiance to the abstract theory of the ideal gas model. In fact, it can be seen as another instance (see Approximation under mechanical engineering in paragraph 5.2.4 earlier in this chapter) where the physical realisibility of the solution constrains the amount of idealisation the engineering scientist is willing to entertain in the use of the Ideal Gas model.
The approach to the problem in the chemical engineering text effectively suspends the tenets of the ideal gas model for the purpose of solving the problem. The ideal gas model is implied in the mathematical equations employed, but the model’s requirements are suspended when the amount of gas left behind in the original tank is conceived of as an identifiable (virtual) amount of gas at the start of the problem. This speaks to the suggestion made by Houkes (2009) as he explores what empirical evidence could possibly account for a (weak) “epistemic emancipation” of engineering science. Houkes proposes that if scientific theories are valued in engineering science not only for their explanatory value, but also for their “usefulness”, one might expect to see instances where changes to the theory will be made in the engineering science for practical “usefulness” purposes. The problem-solving approach described here is an example of what Laymon (1989a) calls a “fictional-as-if theory” (p.364): the gas in tank 1 is taken to behave as if it is possible to isolate the portion of the gas that remains behind in the tank. This is acceptable (and even desirable) in the engineering science text because it allows for a simple way to solve the problem at hand. The ‘adjustment’ made to the Ideal Gas theory in this example reflects a shift away from the fundamental value in the sciences as discussed in chapter two (explanation and description of phenomena) towards the fundamental value in engineering (responding to needs and problems identified). I argue that this represents an example of empirical evidence for Houkes’ construct of weak emancipation of engineering science knowledge.
145 The principal modality for this aspect of the thermodynamics knowledge in the chemical
engineering text is therefore idealisation (mode physical realisability as the driver), with the secondary modality specialisation (mode particulars) because of the typical engineering environment, and the strong association with the fundamental engineering values of problem- solving present in this example.