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2022 | OriginalPaper | Chapter

19. Mixture of Ideal Gases

Author : Achim Schmidt

Published in: Technical Thermodynamics for Engineers

Publisher: Springer International Publishing

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Abstract

So far, single-component liquids have been treated, i.e. fluids with an unchanging chemical composition. Part I of the book has focused on ideal gases and incompressible fluids, which are typical representatives of single-component fluids.

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Footnotes
1
At sufficiently low pressure, gas mixtures can also be considered ideal, cf. [5].
 
2
However, chemical reactions are treated in Chaps. 23 and 24.
 
3
\({1}\,{\text {ppm}}\equiv {1 \times 10^{-4}}\, {{\text {vol}}.-\%}\).
 
4
The entire mass of component i in Fig. 19.1.
 
5
The entire amount of particles i in Fig. 19.1.
 
6
The total volume of particles i in Fig. 19.1 if all particles could be separated and sorted. However, the particles in thermodynamic equilibrium occupy the entire volume, see Sect. 19.2.
 
7
See Sect. 19.2.
 
8
This process is called diffusion and is based on a chemical potential.
 
9
However, reaching this equilibrium takes a while.
 
10
There is no heat crossing the system boundary, since the system is supposed to be adiabatic. Furthermore, no work passes the system boundary, see Fig. 19.2.
 
11
This is denoted partial pressure: Let us theoretically assume that a pressure sensor sensitive to gas 1 is immersed in state (B). The pressure correlates with the number of particles impinging on the sensor. Due to the decreasing particle number density in (B) compared to (A), the impacts of gas 1 are reduced. This is expressed by the partial pressure \(p_{1}\). The same applies accordingly to gas 2.
 
12
A real pressure sensor does not distinguish between the particles of the different gases—it always shows the entire pressure. Nevertheless, the different particles have a specific ratio on the total pressure. The partial pressures \(p_{i}\) represent the part of the pressure caused by the component i.
 
13
The entire work \(W=0\), since no energy is exchanged with the environment.
 
14
Gibb’s paradox states that when two identical gases mix, there is no entropy generation, i.e. \(S_{\text {i}}=0\), see Sect. 19.3.4.
 
15
The proof is simple, since instead of 2 components n components have to be considered, starting with Eq. 19.31.
 
16
Kinetic as well as potential energies are ignored.
 
17
Subject to the condition, that the specific heat capacity is temperature-independent.
 
18
Kinetic as well as potential energies are ignored.
 
19
Subject to the condition, that the specific heat capacity is temperature-independent.
 
20
In this case, two ideal gases are mixed for simplicity. However, this approach can easily be extended to n components.
 
21
This is just hypothetic, since mixing of different gases is always irreversible.
 
22
Expansion means release of volume work.
 
23
This requires a quasi-static change of state.
 
24
According to the partial energy equation.
 
25
The equivalent model investigates an isothermal mixing.
 
26
See Fig. 13.​13.
 
27
Otherwise, it is not possible to get the same amount of initial entropy.
 
28
Note that \(s_{0}\) is the specific entropy at an arbitrary reference level \(T_{0}\), \(p_{0}\).
 
29
Note that the effective work, see Sect. 9.​2.​3, does not play a role, since the pistons are encapsulated from the environment—except for the negligible cross sections of the two rods.
 
30
In state (A), the total pressure is caused exclusively by air.
 
31
This is true because the mixture consists of ideal gases.
 
32
Since the mixture consists of ideal gases, the total specific enthalpy is exclusively a function of temperature.
 
33
Since no temperature dependencies are given.
 
Metadata
Title
Mixture of Ideal GasesMixtureideal gases
Author
Achim Schmidt
Copyright Year
2022
Book
Technical Thermodynamics for Engineers

Print ISBN: 978-3-030-97149-6

Electronic ISBN: 978-3-030-97150-2

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-97150-2_19

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