Carnot cycle

Another use of idealisation in mechanical engineering is seen in the way a particular type of quasi-equilibrium processes, namely reversible processes, are handled in the mechanical engineering textbook in the discussion of the Carnot cycle: “A reversible process is… a process that can be reversed without leaving any trace on the surroundings … Reversible processes actually do not occur in nature. They are merely idealizations of actual processes” (p. 290, 291, emphasis in the original). Cengel and Boles give two reasons for “bothering with such fictitious processes … First, they are easy to analyse… [and secondly,] they serve as idealized models to which actual processes can be compared” (p.191).

23 _{Although quasi-equilibrium processes are considered across all of the disciplines, the mechanical} engineering authors are the only ones who justify the consideration of the idealised process as useful for the information it gives as a limiting case in comparison to real processes (see the discussion on efficiency in the following chapter).

Principal Mode: Physical realisability Secondary Modality: specialisation, Mode: particulars Secondary Modality: normativity, Mode: constitutive normativity

127 The Carnot cycle is a standard topic in any introductory thermodynamics course, and present in all the course textbooks under consideration. A Carnot heat engine is an idealised heat engine operating on the Carnot cycle. The cycle consists of four completely reversible processes, and gives the theoretical maximum efficiency of a heat engine that operates between two particular temperatures. These aspects are present in all discussions of the Carnot cycle in all of the texts. The mechanical engineering authors take this further.

A Carnot heat engine presents an example of Galilean idealisation as discussed by Weisberg (2007a) with ‘completeness’ as its goal. According to Weisberg ‘completeness’ has both an evaluative and regulative function as an idealisation, and both of these are present in the way the mechanical engineering authors use the Carnot cycle.

Firstly, by comparing real engines operating between the same two temperatures to the ideal Carnot heat engine, it becomes possible for the engineer to judge the performance of different real devices on the basis of how closely they correspond to the ideal. This is the evaluative function of the idealisation. Secondly, Galilean idealisation of this kind also has a regulative function. In the mechanical engineering textbook, the authors explain that knowledge of the maximum possible heat engine efficiency between two temperatures, is used by the engineer to direct the design of a real engine operating between the same temperatures towards lowering the irreversibilities in the device. The theoretical maximum efficiency is known and fixed, and any improvement of a real device has to be directed at improving the irreversibilities present in the real device.

As discussed in chapter two, with Galilean idealisation distortion is often temporary. This is not the case here: there is no attempt to re-introduce complexity of the irreversible processes at a later point. The ideal Carnot cycle is essentially a thinking tool for the engineer. The Carnot principles that follow from the Second Law of Thermodynamics give the engineer all she needs:

 Reversible (ideal) heat engines always have a higher efficiency than irreversible (real) ones operating between the same temperatures

 All reversible heat engines operating between the same two temperature reservoirs have the same efficiency

It is therefore possible to compare the performance of different devices designed to do the same task. The better device will be the one with fewer irreversibilities and with efficiencies closer to the theoretical limit set by the reversible processes. The purpose of considering the Carnot cycle here is to use it as a standard against which to compare real physical devices.

128 In the treatment of the Carnot cycle, the mechanical engineering textbook illustrates how the logic of the knowledge pushes the idealisation employed towards the physical realisability of engineering devices. Two secondary modalities are also present: the knowledge is specialised towards the particulars of specific engineering devices and processes, and the knowledge displays constitutive normativity in the decisions made possible for the design and comparison of different real devices to the upper limit of efficiency posed in the ideal Carnot cycle.

5.2.4 Approximation

The use of approximation is a form of idealisation: wittingly using an inexact or rough measure or estimate that introduces a form of distortion of reality. This is acceptable and even common in engineering, provided that the effect of the distortion is small enough not to compromise the functionality and safety of the device or process.

An instance of this can be seen in the mechanical engineering textbook when the authors caution students against using large numbers of significant figures in answers which implies greater empirical accuracy than instruments can measure. This is a common error that students are prone to make, and lecturers in science will give a similar caution. However, in a discussion on the use of significant digits in calculations, the mechanical engineering textbook authors extend the discussion, and point out that engineers will at times sacrifice accuracy (within reason) for ease of access to less accurate information. They give the example of using a value of 1000kg/m3 _{for the density of pure water at 0}0_{C when doing calculations of water with}

impurities at, say, 750_{C. The error of around 2.5% is considered acceptable, and students are}

encouraged to round off answers in sensible ways. “Besides, having a few percent uncertainty in the results of engineering analysis is usually the norm, not the exception” (Cengel & Boles, 2011, p. 38).

Another example of the use of approximation in mechanical engineering can be found in so- called unsteady-flow devices, where the mass flow rate varies over time (for example, the decrease in flow rate as a tank is emptied) The authors point out that unsteady-flow processes are typically transient but common in engineering. Examples are the charging of rigid vessels from supply lines (such as filling an air tank for deep-sea diving) and discharging of tanks (eg.

Principal Mode: Physical realisability Secondary Modality: specialisation, Mode: particulars Secondary Modality: normativity, Mode: constitutive normativity

129 driving a a gas turbine with pressurised air from a tank). Cengel and Boles (2011) recognise that real-life unsteady-flow processes are difficult to analyse, but propose a way forward:

Most unsteady-flow processes… can be represented reasonably well by the uniform-

flow process, which involves the following idealization: The fluid flow at any inlet or exit

is uniform and steady, and thus the fluid properties do not change with time or position over the cross section of an inlet or exit. If they do, they are averaged and treated as constants for the entire process. (Cengel & Boles, 2011, pp. 241-242, emphasis in the original)

The averaging of fluid properties is an idealisation for the purpose of solving a practical problem, and the authors follow this up with an evaluative statement that speaks to the normative nature of the engineering science knowledge:

Although both the steady-flow and uniform-flow processes are somewhat idealized, many actual processes can be approximated reasonably well by one of these with satisfactory results. The degree of satisfaction depends on the desired accuracy and the degree of validity of the assumptions made. (p. 242)

Cengel and Boles (2011) acknowledge that idealisation delivers approximate results, and emphasise that appropriate adequacy rather than absolute accuracy drives the approach. There is a normative condition for approximation: idealisation is constrained by the requirements of the ‘real’ world. The distortion has to be quantified and be judged to yield ‘acceptable’ results for the problem that needs to be solved. Therefore knowledge claims produced by

approximation are coded for the principal modality idealisation, mode physical realisability; the specific engineering setting of typical problems means that the secondary modality is

specialisation, mode particulars, and the normative constraint on the idealisation gives another secondary coding, mode constitutive normativity.

Principal Mode: Physical realisability Secondary Modality: specialisation, Mode: particulars Secondary Modality: normativity, Mode: constitutive normativity

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5.3

Physics

5.3.1 Modelling

Modelling is explained in the Preface to the first year physics textbook. The textbook

places a major emphasis on constructing and using physical models. A central aspect of science is the modelling of complex real-world phenomena. A physical model is based on what we believe to be fundamental principles; its intent is to predict or explain the most important aspects of an actual situation. Modelling necessarily involves making

approximations and simplifying assumptions in order that the model can be analysed in detail. (Chabay & Sherwood, 2011, p. v, emphasis added)

According to the authors of the first year physics textbook, idealisation is important in science, and its purpose is explanation of phenomena and prediction of behaviour, rather than physical realisability. Although ’approximation’ is mentioned in the description above, it is clear that the purpose is to allow analysis of the model, rather than a quantified deviation from reality, as was the case with the mechanical engineering text discussed earlier. The authors describe

idealisation as involving

simple, clean, stripped-down situations, free of messy complexities … idealized models allow us to investigate simple patterns…. and learn what factors are important in

determining these patterns. Once we understand these factors, we can revise and extend our models, including more interactions and complexities, to see what effects these have. (p. 82)

This description reminds us of the Galilean-type idealisation described by Weisberg (2007a): distortions in the form of simplifications are introduced in order to identify patterns as described above by Chabay and Sherwood. These distortions are revised only once

understanding is gained. The re-introduction of complexities is for further understanding and theory-building rather than physical realisability. In this context the authors refer to the use of computational tools, and suggest that computational modelling has now become “as important as theory and experiment in contemporary science…” (p. v). The principal mode is therefore coded as abstract-ideal theorisation with the secondary modality specialisation, mode universals because of the commitment to investigate patterns, as described above.

Principal Mode: Abstract-ideal theorisation

Secondary Modality:

131