Abstract
So far single component fluids, i.e. fluids of one chemical composition, have been treated. Part I has focused on ideal gases and incompressible liquids. In Chap. 18 fluids underlying a phase change have been investigated, i.e. a fluid can occur in solid, liquid and gaseous state—however, its chemical composition remains constant even when a phase change takes place.
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Notes
- 1.
- 2.
\({1\,\mathrm{ppm}\,}\equiv 1\times 10^{-4}\, {\text {Vol.-}\%}\).
- 3.
See Sect. 19.2.
- 4.
This process is called diffusion.
- 5.
However, reaching this equilibrium takes a while.
- 6.
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. 19.1.
- 7.
This is called partial pressure!
- 8.
To get a better understanding of the partial pressure: A pressure sensor measures the kinetic collisions of the molecules on its surface. The more collisions, the larger the pressure within the mixture. However, the sensor does not distinguish between the molecules of the different gases—it always shows the entire pressure. Nevertheless, the different molecules have a specific ratio on the total pressure. The partial pressures \(p_{i}\) represent the part of the pressure that is induced by component i.
- 9.
The entire work \(W=0\), since no energy is exchanged with the environment!
- 10.
The Gibb’s paradox claims, that if two identical gases are mixed, no generation of entropy occurs, i.e. \(S_{\text {i}}=0\), see Sect. 19.3.4.
- 11.
The proof is simple, as instead of 2 components n components have to be taken into account starting with Eq. 19.31.
- 12.
Kinetic as well as potential energies are ignored!
- 13.
Subject to the condition, that the specific heat capacity is temperature-independent!
- 14.
Kinetic as well as potential energies are ignored!
- 15.
Subject to the condition, that the specific heat capacity is temperature-independent!
- 16.
In this case, to keep it simple, two ideal gases are mixed. However, this approach can easily be extended to n components.
- 17.
This is just hypothetic, since mixing of different gases is always irreversible!
- 18.
Expansion means release of volume work!
- 19.
This requires a quasi-static change of state!
- 20.
According to the partial energy equation.
- 21.
See Fig. 13.13.
- 22.
Otherwise, it is not possible to get the same amount of initial entropy.
- 23.
Mind, that \(s_{0}\) is the specific entropy at an arbitrary reference level \(T_{0}\), \(p_{0}\).
- 24.
Mind, 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.
- 25.
In state (A) the total pressure is purely caused by air!
- 26.
Since the mixture is composed of ideal gases, the overall specific enthalpy purely is a function of temperature as well!
- 27.
Since no temperature dependencies are given!
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Schmidt, A. (2019). Mixture of Gases. In: Technical Thermodynamics for Engineers. Springer, Cham. https://doi.org/10.1007/978-3-030-20397-9_19
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DOI: https://doi.org/10.1007/978-3-030-20397-9_19
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