1. MAE 219: THERMODYNAMICS by Professor YVES NGABONZIZA MAE 219: THERMODYNAMICS I

2. Highlight  Syllabus Overview  Capstone course  Communication Platform (Blackboard, E-Portfolio)  E-Portfolio  Studio Hour  Term paper (Report Format)  Lab Experiment MAE 219: THERMODYNAMICS I

3. 1. CONCEPTS AND DEFINITIONS Closed system (control mass) consist of a fixed amount of mass, and no mass can cross its boundary Open system (control volume) involves mass flow Properties: Intensive: independent of the mass of the s/m e.g. : T, pressure, density Extensive: depend on system size e.g.: mass, volume MAE 219: THERMODYNAMICS I

4. Conservation of energy: potential energy + kinetic energy = constant (P.E.)(K.E.) Thermal equilibrium: Two bodies are in thermal equilibrium if they have the same temperature Otherwise, temperature moves from hot medium to cold medium MAE 219: THERMODYNAMICS I

5. Zeroth Law of Thermodynamics: If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other Source: http://www.grc.nasa.gov/WWW/K-12/airplane/Images/thermo0.gif MAE 219: THERMODYNAMICS I

6. Units SIUS Masskgslug ForceNlb Distancemft Velocitym/sft/s Accelerationm/s 2 ft/s 2 Densitykg/m 3 lb/ft 3 Temperature K 0 F MAE 219: THERMODYNAMICS I

7. Temperature Units Conversion T(K)=T( o C) + 273 T(R)=T( o F) + 460 T(R)=1.8T(K) T( o F)=1.8T( o C) + 32 MAE 219: THERMODYNAMICS I

8. Pressure: Normal force exerted by a fluid per unit area Unit: Pa (SI) or psi (US) Pgage = Pabs – Patm Pabs=actual (absolute) pressure Note: pressure measuring devices read 0 pressure in atmosphere MAE 219: THERMODYNAMICS I

9. p = f(z) +z p A =p B =p C =Patm+ Patm A B C h MAE 219: THERMODYNAMICS I

10. Example The pressure in a pressurized water tank is measured by a multi-fluid manometer. The gage pressure of air in the tank is to be determined. The densities of mercury, water, and oil are given to be 13,600, 1000, and 850 kg/m 3, respectively. Consider h1=0.2m, h2=0.3m and h3=0.46 H.W. 1 MAE 219: THERMODYNAMICS I

11. 2. PROPERTIES OF A PURE SUBSTANCE 2.1. Pure Substance A pure substance has a homogeneous and invariable chemical composition and may exist in more than one phase. 2.2. Phases of a pure substance Solid Phase: molecules are at relatively fixed position Liquid phase: groups of molecules move about each other Gas phase: molecules are far apart from each other. Molecules move randomly MAE 219: THERMODYNAMICS I

12. 2.3. Phase change processes Let's consider the results of heating liquid water from 20  C, 1 atm while keeping the pressure constant. As liquid water is heated while the pressure is held constant, the following events occur. Process 1-2: The temperature and specific volume will increase from the compressed liquid, or subcooled liquid, state 1, to the saturated liquid state 2. In the compressed liquid region, the properties of the liquid are approximately equal to the properties of the saturated liquid state at the temperature. MAE 219: THERMODYNAMICS I

13. Process 2-3: At state 2 the liquid has reached the temperature at which it begins to boil (100  C ), called the saturation temperature, and is said to exist as a saturated liquid. Properties at the saturated liquid state are noted by the subscript f and v 2 = v f. At state 3 the liquid and vapor phase are in equilibrium and any point on the line between states 2 and 3 has the same temperature and pressure. MAE 219: THERMODYNAMICS I

14. Process 3-4: At state 4 a saturated vapor exists and vaporization is complete. The subscript g will always denote a saturated vapor state. Note v 4 = v g. MAE 219: THERMODYNAMICS I

15. Process 4-5: If the constant pressure heating is continued, the temperature will begin to increase above the saturation temperature, 100  C in this example, and the volume also increases. State 5 is called a superheated state because T 5 is greater than the saturation temperature for the pressure and the vapor is not about to condense. MAE 219: THERMODYNAMICS I

16. This constant pressure heating process is illustrated in the following figure. Figure : T-ν diagram for the heating of water at constant pressure MAE 219: THERMODYNAMICS I

17. Thermodynamic properties at the saturated liquid state and saturated vapor state are given in Table A-4 as the saturated temperature table and Table A-5 as the saturated pressure table. These tables contain the same information. The saturation pressure is the pressure at which phase change will occur for a given temperature. In the saturation region the temperature and pressure are dependent properties; if one is known, then the other is automatically known. Thermodynamic properties for water in the superheated region are found in the superheated steam tables, Table A-6. MAE 219: THERMODYNAMICS I

18. 2.4. Property diagrams for phase-change processes In this section, we will discuss the T-V, P-V and P-T diagrams for pure substances T-V diagram MAE 219: THERMODYNAMICS I

19. P-V Diagram The P-V diagram of a pure substance is very much like the T-V diagram, but the T=constant line on this diagram have a downward trend. MAE 219: THERMODYNAMICS I

20. P-T Diagram This diagram is often called the phase diagram since all phases are separated. The triple point of water is 0.01 o C (= 273 K), 0.6117 kPa (See Table 3-3). The critical point of water is 373.95 o C, 22.064 MPa (See Table A-1). MAE 219: THERMODYNAMICS I

21. Saturated liquid-vapor mixture The analysis of the mixture is based on the proportion of the liquid and vapor phases in the mixture. Quality x is defined as The quality is zero for the saturated liquid and one for the saturated vapor (0 ≤ x ≤ 1). MAE 219: THERMODYNAMICS I

22. We note Recall the definition of quality x Then Note, quantity 1- x is often given the name moisture. The specific volume of the saturated mixture becomes MAE 219: THERMODYNAMICS I

23. The form that we use most often is It is noted that the value of any extensive property per unit mass in the saturation region is calculated from an equation having a form similar to that of the above equation. Let Y be any extensive property and let y be the corresponding intensive property, Y/m, then The term y fg is the difference between the saturated vapor and the saturated liquid values of the property y; y may be replaced by any of the variables v, u, h, or s. MAE 219: THERMODYNAMICS I

24. The enthalpy is a convenient grouping of the internal energy, pressure, and volume and is given by The enthalpy per unit mass is How to Choose the Right Table The correct table to use to find the thermodynamic properties of a real substance can always be determined by comparing the known state properties to the properties in the saturation region. Given the temperature or pressure and one other property from the group v, u, h, and s, the following procedure is used. For example if the pressure and specific volume are specified, three questions are asked: For the given pressure, MAE 219: THERMODYNAMICS I

25. The answer to one of these questions must be yes. If the answer to the first question is yes, the state is in the compressed liquid region, and the compressed liquid tables are used to find the properties of the state. If the answer to the second question is yes, the state is in the saturation region, and either the saturation temperature table or the saturation pressure table is used to find the properties. Then the quality is calculated and is used to calculate the other properties, u, h, and s. If the answer to the third question is yes, the state is in the superheated region and the superheated tables are used to find the other properties. Some tables may not always give the internal energy. When it is not listed, the internal energy is calculated from the definition of the enthalpy as MAE 219: THERMODYNAMICS I

26. Examples 1.A rigid tank contains 50 kg of saturated liquid water at 90 o C. Determine the pressure in the tank and the volume of the tank. 2.A piston-cylinder device contains 2 ft 3 of saturated water vapor at 50 psi pressure. Determine the temperature and the mass of the vapor inside the cylinder. MAE 219: THERMODYNAMICS I

27. Solution: 1.Using Table A-4, at 90 o C, P=70.183 kPa and ν=0.001036 m 3 /kg Then, the volume V = ν *m = 0.0518m 3 2. Using Table A5-E, at P=50psi, T=280.99 o F ν g =8.5175 ft 3 /lbm The mass MAE 219: THERMODYNAMICS I

28. 2.5. Equations of State The relationship among the state variables, temperature, pressure, and specific volume is called the equation of state. We now consider the equation of state for the vapor or gaseous phase of simple compressible substances. Ideal Gas Based on our experience in chemistry and physics we recall that the combination of Boyle’s and Charles’ laws for gases at low pressure result in the equation of state for the ideal gas as where R is the constant of proportionality and is called the gas constant and takes on a different value for each gas. If a gas obeys this relation, it is called an ideal gas. We often write this equation as MAE 219: THERMODYNAMICS I

29. The gas constant for ideal gases is related to the universal gas constant valid for all substances through the molar mass (or molecular weight). Let R u be the universal gas constant. Then, And we know The ideal gas equation of state becomes For fixed mass at 2 different phases MAE 219: THERMODYNAMICS I

30. Example: Determine the mass of the air in a room whose dimensions are 4m*5m*6m at 100 kPa and 25 o C Solution: Using Table A-1, R of the air is 0.287 kPa.m 3 /kg.K 25 o C = (25+273)K =298K V = (4*5*6) m 3 = 120m 3 MAE 219: THERMODYNAMICS I

31. The ideal gas equation of state is used when (1) the pressure is small compared to the critical pressure or (2) when the temperature is twice the critical temperature and the pressure is less than 10 times the critical pressure. 2.6. Compressibility Factor The compressibility factor Z determines how much the ideal gas equation of state deviates from the actual gas behavior. For an ideal gas Z = 1, and the deviation of Z from unity measures the deviation of the actual P-V-T relation from the ideal gas equation of state. or MAE 219: THERMODYNAMICS I

32. 2.7. Other Equations of State Many attempts have been made to keep the simplicity of the ideal gas equation of state but yet account for the intermolecular forces and volume occupied by the particles. Three of these are (a) Van der Waals: where accounts for intermolecular forces accounts for volume occupied by the gas molecules b MAE 219: THERMODYNAMICS I

33. (b) Beattie-Bridgeman: where The constants a, b, c, A o, B o for various substances are found in Table 3-4. ( c ) Benedict-Webb-Rubin: The constants for various substances appearing in the Benedict-Webb­-Rubin equation are given in Table 3-4. H.W. 2 MAE 219: THERMODYNAMICS I