## Conclusions

In this chapter, the precise teaching of thermodynamics has been emphasized since these topics are used in other fields of science and technology. The textbooks must be correct giving the precise description of systems, equations, and conclusions. Otherwise the students learn the wrong information and apply it in the same fashion. It has also been shown that methodologies exist for physical interpretation of mathematical expressions in thermodynamics by eliminating nonmea-surable quantities such as entropy, designing thermodynamic experiments, and investigating various applications in other fields of science and technology that use thermodynamic principles. The emphasis has been on correct and precise work, a quality that we must impose on our students. This type of instruction would ultimately affect students who are aware of the nature, the effect of everyday usage of energy on the environment, and what needs to be done within the restrictions of nature to be sustainable at least at the levels that we enjoy today. Of course, these must be done in all aspects of education not only in the education of engineers, in general, and thermodynamics education, in particular. Success in this will make life better now and forever.

The previous pages have emphasized undergraduate work. It is indeed very important to extend this into statistical and non-equilibrium thermodynamics for graduate students. The challenges of energy use, pollution, and sustainability all depend on clear, precise, and correct study of these and appropriate applications. It can and should be pursued very aggressively throughout.

### Acknowledgment

The view expressed herein are those of the author and do not purport to reflect the position of the Unites States Military Academy, the Department of the Army, or the Department of Defense.

Nomenclature

B Any extensive thermodynamic property b Any intensive thermodynamic property, b=Blm c Specific heat (kJ/(kg-K) ); also speed of sound (m/s)

e specific energy (kJ/kg)

F Helmholtz potential (kJ)

G Gibbs free energy (kJ)

H Enthalpy (kJ)

h Specific enthalpy (kJ/kg)

k Ratio of specific heats, k=(cp/cv)

M Molecular mass (kmol); also arbitrary function m Mass (kg)

N Arbitrary function n Unit vector p Pressure (kPa)

T Temperature (K)

U Internal energy (kJ)

u Specific internal energy (kJ/kg)

v Specific volume (m3/kg)

X Arbitrary function

V Arbitrary function

Z Arbitrary function; also compressibility factor (-)

z Elevation (m)

Greek symbols a Coefficient of thermal expansion (1/K)

ß Coefficient of performance for a refrigerator y Coefficient of performance for a heat pump

A Difference

ö Increment q Efficiency for an engine

kt Isothermal compressibility (1/kPa)

^ Joule-Thomson coefficient (K/kPa)

4 Arbitrary thermodynamics property p Density (kg/m3)

a Entropy generation (kJ/K)

Subscripts g

CE CV f fg

Engine Carnot engine Control volume Liquid phase

Phase change from liquid to vapor Vapor phase

High p o v

Low Volume Pressure Atmospheric

References

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