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2022 | OriginalPaper | Buchkapitel

12. Caloric Equations of State

verfasst von : Achim Schmidt

Erschienen in: Technical Thermodynamics for Engineers

Verlag: Springer International Publishing

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Abstract

In the previous chapters, the law of conservation of energy, which enables thermodynamic systems to be energetically evaluated, has been discussed in detail. A distinction has been made between closed and open systems.

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Vorheriges Kapitel First Law of Thermodynamics

Nächstes Kapitel Meaning and Handling of Entropy

Such as \(\left[ u\right] ={1}\,{\frac{\mathrm{kJ}}{\mathrm{kg}}}\) and \(\left[ h\right] ={1}\,{\frac{\mathrm{kJ}}{\mathrm{kg}}}\).

If two independent state values unambiguously define the thermodynamic state, all other state values must also unambiguously belong to this state and be determinable.

The indices at the brackets indicate that this variable is kept constant.

At constant specific volume v.

At constant pressure p.

The thermodynamic proof is given in Sect. 12.3.2.

Note that the system is adiabatic, i.e. \(Q_{12}=0\), and that no work is exchanged across the system boundary, i.e. \(W_{12}=0\). The work to open the valve is neglected.

Yet this would violate Eq. 12.17.

If T remains constant, the specific internal energy does not change. This is exactly what was observed in the experiment.

Frankly, it is even difficult to find a physical meaning for the inner energy. Even though you have probably accepted its existence by now.

Also known as integrating factor.

Similar to the first law of thermodynamics: The state value internal energy is influenced by the process values work and heat.

For the Gibbs free energy there is a physical motivation for chemical reactive systems, e.g. fuel cells or Lithium Ion batteries. This is treated in Part III of this book, see Sect. 24.3.

No path information is required to solve the integral.

A constant specific heat capacity is assumed here. How to proceed if the specific heat capacity is not constant is shown in Sect. 12.4.4.

Assuming that \(c_{v}=\text {const.}\) and \(c_{p}=\text {const.}\)

This is indicated by the index v.

This is indicated by the index p.

Very slow is a synonym for no turbulence inside, see also Theorem 7.16.

The acceleration due to gravity g is not relevant because the piston is operated horizontally.

The change in kinetic energy can be neglected because the change of state is quasi-static. Furthermore, there is no change in potential energy because the cylinder is horizontal.

According to \(V=\frac{mRT}{p}\).

Note that \(H=mh\).

Fluid movement would have to be triggered by a moving piston, for example.

Note that \(U=mu\).

This part is intended for advanced readers who are already familiar with the T, s-diagram, see Sect. 13.4.

Assuming, that \(c_{p}=\text {const.}\)

Including arithmetic and logarithmic averaged values.

A temperature difference is needed for the calculation, so it makes no difference whether one takes \(\varDelta \vartheta \) or \(\varDelta T\), see Eq. 12.183.

The specific enthalpy remains constant.

Titel: Caloric Equations of State
verfasst von: Achim Schmidt
Verlag: Springer International Publishing
Buch: Technical Thermodynamics for Engineers
Print ISBN: 978-3-030-97149-6

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

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-030-97150-2_12

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