1. 1 Units and Key Constants

2. 2 Conventional Units ParameterEnglish UnitsSI Units –DistanceFeet, InchesMeters, M –Time SecondsSeconds, s –ForcePounds (force), lbf4.448 Newton, N –Pressurepsf, psiPascal, Pa (1N/1m 2 ) bar (10 5 Pa) 1 ft H 2 O2.989 kPa –MassPounds (mass), lbm0.4536 kilogram –EnergyBtuJoule, J –Power1 Hp0.7457 kWatt

3. 3 Equivalent Systems of Units

4. 4 Important Constants for Air

5. 5 Useful Equivalents

6. 6 For Liquid Water : U.S. Standard Atmosphere - 1976

7. 7 Standard Atmosphere Stratosphere >65,000 ft 59 F Temperature Altitude 3.202 psia 14.696 psia Pressure 36,089 ft Altitude 36,089 ft

8. 8

9. 9

10. 10 Thermodynamics Review

11. 11 Thermodynamics Review Thermodynamic views –microscopic: collection of particles in random motion. Equilibrium refers to maximum state of disorder –macroscopic: gas as a continuum. Equilibrium is evidenced by no gradients 0 th Law of Thermo [thermodynamic definition of temperature]: –When any two bodies are in thermal equilibrium with a third, they are also in thermal equilibrium with each other. –Correspondingly, when two bodies are in thermal equilibrium with one another they are said to be at the same temperature.

12. 12 Thermodynamics Review 1 st Law of Thermo [Conservation of energy]: Total work is same in all adiabatic processes between any two equilibrium states having same kinetic and potential energy. –Introduces idea of stored or internal energy E – dE = dQ - dW dW = Work done by system [+]=dW out = - pdV Some books have dE=dQ+dW [where dW is work done ON system] dQ = Heat added to system [+]=dQ in –Heat and work are mutually convertible. Ratio of conversion is called mechanical equivalent of heat J = joule

13. 13 Review of Thermodynamics Stored energy E components –Internal energy (U), kinetic energy (mV 2 /2), potential energy, chemical energy Energy definitions –Introduces e = internal energy = e(T, p) –e = e(T)  de = Cv(T) dT thermally perfect –e = Cv T calorically perfect 2 nd law of Thermo –Introduces idea of entropy S –Production of s must be positive –Every natural system, if left undisturbed, will change spontaneously and approach a state of equilibrium or rest. The property associated with the capability of systems for change is called entropy.

14. 14 Review of Thermodynamics Extensive variables – depend on total mass of the system, e.g. M, E, S, V Intensive variables – do not depend on total mass of the system, e.g. p, T, s,  (1/v) Equilibrium (state of maximum disorder) – bodies that are at the same temperature are called in thermal equilibrium. Reversible – process from one state to another state during which the whole process is in equilibrium Irreversible – all natural or spontaneous processes are irreversible, e.g. effects of viscosity, conduction, etc.

15. 15 Thermodynamic Properties Primitive Derived

16. 16 1st Law of Thermodynamics For steady flow, defining: We can write: and

17. 17 1st Law of Thermodynamics Substituting back into 1 st law: –Height term often negligible (not for hydraulic machines) Defining total or stagnation enthalpy: The first law for open systems is:

18. 18 Equation of State The relation between the thermodynamic properties of a pure substance is referred to as the equation of state for that substance, i.e. F(p, v, T) = 0 Ideal (Perfect) Gas –Intermolecular forces are neglected –The ratio pV/T in limit as p  0 is known as the universal gas constant (R). p  /T  R = 8.3143e 3 – At sufficiently low pressures, for all gases p  /T = R or Real gas: intermolecular forces are important

19. 19 Real Gas

20. 20 Real Gas

21. 21 1 st & 2 nd Law of Thermodynamics Gibbs Eqn. relates 2 nd law properties to 1 st law properties :

22. 22 Gibbs Equation Isentropic form of Gibbs equation: and using specific heat at constant pressure:

23. 23 Thermally & Calorically Perfect Gas Also, for a thermally perfect gas Cp[T]: Calorically perfect gas - Constant Cp

24. 24 Isentropic Flow For Isentropic Flow [if dQ=0, Adiabatic Gas Law]: Precise gas tables available for design work Thermally Perfect Gas good flows at moderate temperature.

25. 25 Common Gases Gas  Argon1.67 Helium1.67 Air1.40 Hydrogen1.40 Nitrogen1.40 Oxygen1.39 Water vapor1.33 Carbon dioxide1.29 Sulfur dioxide1.29 Butane1.10 monatomic diatomic polyatomic

26. 26 Important Constants for Air

27. 27 Gibbs Equation Rewriting Gibbs Equation:

28. 28 Gibbs Equation Rewriting Gibbs Equation:

29. 29 Isobars are not parallel

30. 30 Mollier for Static / Total States ss Poin Poout V 2 /2 h 02i h 02 h 01 We will soon see