Abstract
The main purpose of this chapter is to briefly recapitulate what is learned in a first course in classical thermodynamics (Only those portions of a typical undergraduate curriculum that are relevant to combustion calculations are given emphasis). As defined in Chap. 1, thermodynamics is the science of relationships among heat, work, and the properties of the system. Our first task, therefore, will be to define the keywords in this definition: system, heat, work, and properties. The relationships among these quantities are embodied in the First and the Second laws of thermodynamics. The laws enable one to evaluate the change in the states of the system, as identified by the changes in its properties. In thermodynamics, this change is called a process, although, in common everyday language, the processes maybe identified with terms such as cooling, heating, expansion, compression, phase change (melting, solidification, evaporation, condensation), or chemical reaction (such as combustion, catalysis, etc.). As such, it is important to define two additional terms: state and process.
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Notes
- 1.
Only those portions of a typical undergraduate curriculum that are relevant to combustion calculations are given emphasis.
- 2.
Sometimes it is also possible to experience the process for oneself. After all, thermodynamics is a science that is very much built on the observations and experiences of everyday life.
- 3.
In this sense, the everyday statement heat contained in a body has no meaning in thermodynamics.
- 4.
This type of reference to surroundings will be made later in defining universe (see Sect. 2.7.2).
- 5.
This is also called a control volume.
- 6.
Here, constant implies constancy with time, whereas uniform implies spatial uniformity. That is, p, T, and composition of the system are same in every part of the system.
- 7.
At very high temperatures, the system (gas) will turn into plasma, when the gas will shed electrons and become ionized. The gas will then be a mixture of neutral atoms, ionized atoms, and electrons. Such ionized state is not of interest in this book.
- 8.
Van der Waals was awarded the Nobel Prize in 1910 for this discovery.
- 9.
In this sense, the van der Waals Eq. 2.4 is simply a modification of the ideal gas law \(p\, \overline{v} = R_{u}\, T\) via gas-specific constants a and b. Constant b represents the volume occupied by molecules per mole of gas, which is subtracted from the container molar volume \(\overline{v}\). The estimate of this unavailable volume is, therefore, related to the hard-sphere molecular diameter d. The constant a, on the other hand, is related to the idea that intermolecular forces are appreciable only between a molecule and its nearest neighbors. Molecules are attracted equally in all directions, but the molecules in the outer layers will experience only a net inward force. A molecule approaching the container wall is thus slowed down by the inward force and the pressure exerted on the wall is somewhat smaller than what it would have been in the absence of attractive forces. This reduction in pressure is estimated to be proportional to \( n^{2}\) where n is the number of molecules (\(N = n \times N_{Avo} \)) per unit volume. Thus constants a and b are given by
$$\begin{aligned}\,\,\,\,\,\,\,\,\, b \,\,\, =\,\,\, \frac{2}{3}\,N_{Avo}\, d^{3},\qquad \qquad {(2.9)} \end{aligned}$$$$\begin{aligned} \text {and}\,\,\, a \,\,\, =\,\,\, \alpha n^{2} \overline{v}^{2},\qquad \qquad {(2.10)} \end{aligned}$$where \(\alpha \) is constant of proportionality and \(N_{Avo}\) is Avogadro’s number (\(6.02 \times 10^{26}\) molecules/kmol).
- 10.
Collision properties determine the rates of chemical reactions, as discussed in Chap. 5.
- 11.
In mechanics, formal definition of work is given by \(\text {work (J)} = \text {force (N) } {\times } \text { displacement (m) in the direction of the force} \). The thermodynamic definition of work done by a system is consistent with this definition if and when it can be demonstrated that the sole effect external to the system could be reduced to raising (or lowering) of a weight. In carrying out this demonstration, one is free to change the surroundings.
- 12.
Alternatively, the law can also be stated as
$$\oint _{path}\,(d\,Q - d\, W) = 0.$$ - 13.
The reader will now appreciate why a loose statement such as heat contained in body (meaning system) is unacceptable in thermodynamics. A system does not contain heat. It contains energy.
- 14.
Other possibilities include magnetic, electrical, or capillary energies, although we are not concerned with these in this book.
- 15.
Because E can have any value, to facilitate calculations, E is assigned a datum value at some reference state. Thus, PE may be assigned a zero value at the mean-sea-level (say) or U may be assigned zero value at zero degrees C or K. These deductions apply only to a pure substance or to the components of an inert mixture. Later, in Chap. 4, however, we will find that for a reacting mixture, ChE cannot be assigned a datum value in this way and special treatment becomes necessary.
- 16.
In some books, Eq. 2.19 is written as \(d^{'}Q - d^{'}W = dU\) to remind us that dQ and dW, being path functions, are inexact differentials, whereas dU (or dE) is an exact differential. In this book, it is assumed that the reader is aware of this difference.
- 17.
Joule evaluated work in lbf-ft and heat in Btu. Thus, \(W_{1}/Q_{2} = J\) (a constant) had units of lbf-ft/Btu and J \(=\) 778 has come to be known as Joule’s mechanical equivalent of heat. In SI units, however, work is evaluated in N-m and heat in Joules. As 1 N-m \(=\) 1 Joule, the mechanical equivalent of heat in SI units is 1 N-m/Joule.
- 18.
This state of affairs will prevail when the gas molecules are sufficiently far apart so that the molecular force field plays no part. As such, a perfect gas at very low pressures and high temperatures will behave as an ideal gas.
- 19.
If there were more than one (say, three) outlet, the mass-conservation equation will read as
$$\frac{d\, m_{CV}}{dt} = \sum _{k=1}^{k=2}\,\dot{m}_{k, in} - \sum _{l=1}^{l=3}\,\dot{m}_{l, out}.$$ - 20.
This manner of writing the First law is an acknowledgment that as long as our interest lies in determining state change (\(\Delta E\) or \(\Delta U\)), the real irreversible process can always be replaced by a reversible one. We have already noted that to replace an irreversible process by a quasi-static reversible process, the former process may have to be modified.
- 21.
However, this does not imply that \(dq_{rev} = dq_{irrev}\) or \(dw_{rev} = dw_{irrev}\).
- 22.
Recall that steam does not the obey ideal gas relation. However, a fuel vapor mixed with air is assumed to behave as an ideal gas.
- 23.
In Chap. 5, it will be inferred that hard-sphere diameters are functions of temperature.
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Date, A.W. (2020). Thermodynamics of a Pure Substance. In: Analytic Combustion. Springer, Singapore. https://doi.org/10.1007/978-981-15-1853-9_2
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