1 Thermo., Lesson 2: Properties of Pure SubstancesMECE-251 Thermo., Lesson 2: Properties of Pure Substances A pure substance must have the same molecular composition throughout. Water is a pure substance. Air is not a pure substance. In some cases “dry air” may be treated like a pure substance. Moist air is a mixture of water and dry air – we’ll come back to this later. Read Sections 2.1 – 2.6 Solve Problems View Lectures and Case Studies Solve Case Study Complete On-line Lesson Quiz Mon Tue Wed Thu Fri Sat or Sun During this lesson we will explore the dependence of the specific volume of pure substances as a function of Temperature and Pressure. As before, the lesson is organized into a series of tasks. The tasks are ordered by the days of the week. You may choose to spend about 30 minutes each day to keep up with the tasks, or you may set aside a few hours one on day to go through the tasks in order. Prior to viewing this lecture, it is expected that the student has read Sections 2.1 through 2.6 of the textbook “Schaum’s Outline of Thermodynamics for Engineers” and completed the assigned chapter problems. Keep in mind that we are limiting our discussion to the consideration of pure substances, such as water, nitrogen, carbon dioxide, R134A or any number of other pure substances. We must keep in mind that “Air” is not a pure substance. Even though air is a mixture of pure substances, if we were to cool air down at a given pressure, we would observe that the different components of air would condense at different temperatures from one another, and thus its molecular composition would not be uniform. R·I·T MECE-251 1

2 Phase Equilibrium 2 1 3 4 5 In our prior lesson, we studied the phase change of water as it moved from a pure liquid phase at to a pure vapor, as illustrated in the left figure. The temperature is plotted as a function of specific volume for various pressures in the Figure on the right. Note that the horizontal axis has a logarithmic scale. State 1 is called a “compressed liquid” or a “sub-cooled liquid”. In this condition, the temperature of the water is less than the saturation temperature at the given pressure. Stated another way, this also means that at a given temperature, the pressure of the water is greater than the saturation pressure at the given temperature. State 2 is called the “saturated liquid” point, with a quality of 0%. As the pressure (isobars) increase from a very small value to a very high value, the locus of points having 0% quality is called the “Saturated Liquid Line”. At an isobar of 100kPa (constant atmospheric pressure), the specific volume changes very little from state 1 to state 2, reflecting the fact that we often consider water to be incompressible. In reality, liquid water is indeed compressible, and we often need to account for this in engineering applications State 3 is an equilibrium mixture of equal parts liquid and gaseous phases, and is said to have a quality of 50%. The quality reflects the mass fraction of the water which is in the vapor phase. State 4 is called the “saturated vapor” point, with a quality of 100%. As the pressure (isobars) increases from a very small value to a very high value, the locus of points having 100% quality is called the “Saturated Vapor Line”. The line connecting states 2, 3 and 4 is called the saturation temperature of water at 100kPa. This is commonly called the “boiling point” of water. The region to the right of the saturated vapor line is called a “superheated vapor” region. State 5 represents a superheated vapor state. At very high pressures, the saturated liquid line and saturated vapor line collapse to a point, called the “critical point”, and the distinction between liquid and vapor/gas phase ceases to exist. The region above is called the trans-critical region. Water is contained in a sealed cylinder under a pressure of 1 atmosphere (100 kPa). As heat is added, the temperature increases and phase change takes place. Reference: Engineering Thermodynamics - A Graphical Approach by Israel Urieli Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 2

3 The p v T Diagram for a substance that contracts upon freezing NIST Thermodynamics Research Center International Association for the Properties of Water and Steam IAPWS Steam Calculator (Paid Subscription) The three-dimensional relationship between pressure, specific volume, and temperature is shown in the Figure. This figure is typical of many engineering substances which contract upon solidification (unlike water, which expands). Each colored region of the 3-d surface represents a different type of phase equilibrium. The horizontal P=constant line is an isobar. The vertical T=constant line is an isotherm. It is common practice to represent thermodynamic cycles on a two dimensional view of the 3-d space. The T-v view and the P-v view are commonly used. Many engineers rely upon tabulated values of thermodynamic property data. It is increasingly common for software tools to be used to provide thermodynamic property data. However, great care must be taken to ensure the validity of property data from software applications. There is a great deal of BAD DATA presented in thermodynamic property software. It is essential that the engineer rely upon trusted data sources for property software. Excellent data is available from the National Institute of Standards and Technology at a nominal cost. Reference: Engineering Thermodynamics - A Graphical Approach by Israel Urieli Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 3

4 Thermodynamic Properties of Water (aka Steam Tables) Schaum’s Appendix C.“The Vapor Dome” Saturation Temperature (boiling point) of Water is 100C at kPa. Saturation Temperature (boiling point) of Water is 180C at 1 MPa (10 atm.) The saturated liquid-vapor mixture region of the steam dome is presented in the data tables in Appendix C-1 and C-2. The pure substance is an equilibrium mixture of liquid and vapor phases throughout the vapor dome. The quality describes the mass fraction of the equilibrium mixture that is in the vapor phase. When the temperature is 100C and the steam has a quality of x=0, then the specific volume of the steam is m3/kg. This is referred to as v_f. When the temperature is 180C and the steam has a quality of x=1.0, then the specific volume of the steam is m3/kg. This is referred to as v_g. When the temperature is C, the pressure is MPa, and we see that v_f = v_g. This is the peak of the steam dome and is called the critical point. Water above this condition is called a “supercritical fluid”. Critical Point of Water is T = 374C and P = 22.1 MPa Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 4

5 Thermodynamic Properties of Water (aka Steam Tables) Schaum’s Appendix C.“Superheat Region” Saturated Steam (boiling point of Water , x= 1.00) T = C and P 1.00 MPa v = m3/kg Superheated Steam T = 500C and P = 1 MPa v = m3/kg The superheated region of the steam dome is presented in the data tables in Appendix C-3. Throughout the superheat region, the pure substance is completely in the vapor, or gaseous, phase. At the vapor line, water is a saturated steam. This means that the quality of the steam is x = 1.0, and that both the temperature and pressure are at the saturation (or boiling point). Saturation means that the steam is an equilibrium mixture of liquid a vapor phases. The superheated steam tables always “start out” from the saturation point. As the temperature rises above the saturation temperature, and the pressure remains constant at 1 megapascal, the specific volume of the steam increases significantly. As the pressure increases to 1.2 megapascals and the temperature rises to 1200 C, the specific volume increases to m3/kg. Superheated Steam T = 1200C and P = 1.20 MPa v = m3/kg Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 5

6 Thermodynamic Properties of Water (aka Steam Tables) Schaum’s Appendix C.“Compressed Liquid” Compressed Liquid T = 0 C and P 5.00 MPa v = m3/kg Compressed Liquid T = 120 C and P = 5 MPa v = m3/kg The compressed liquid region of the steam dome is presented in the data tables in Appendix C-4. Throughout the compressed liquid region, the pure substance is completely in the liquid phase. At the liquid line, water is a saturated liquid. This means that the quality of the steam is x = 0.0, and that both the temperature and pressure are at the saturation (or boiling point). As the pressure increases above the saturation pressure, say from 0.1 to 5 MPa, there is relatively little change in specific volume. At pressures well above saturation pressures, water can remain in the liquid phase even at elevated temperatures. For example, water remains a liquid at 120C when the environmental pressure is 5 MPa. Water remains a compressed liquid at 260C when the environmental pressure is 5 or 10 MPa. There is very little change in specific volume at these pressures, but water is indeed compressible. Compressed Liquid T = 260 C and P = 10 MPa v = m3/kg Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 6

7 The Compressibility Factor – Real GasesFor Dry Air TC = 133K PC = 37.7 Bar ≈ 547 psia M = kg/kmol For Truck Brake Systems 233K < Tenvir range < 340K Ptyp ≈ 8-10 bar (abs) The compressibility chart is a good tool to decide if the ideal gas equation of state is a reasonable engineering approximation. If the compressibility factor is above Z = 0.95, we’re usually safe from an engineering perspective. This chart is presented in terms of reduced temperature and reduced pressure. The reduced temperature is the ratio of the absolute temperature over the absolute critical temperature (at the peak of the vapor dome). The reduced pressure is the ratio of the absolute pressure over the critical pressure. For dry air the critical temperature is 133 Kelvin, and the critical pressure is 37.7 bar or 547 psi (absolute). Let’s consider that a truck braking system has to operate over extreme temperature ranging from -40F (-40C) up to 140F (60C) , or in absolute values, 233Kelvin to 340 Kelvin. The extreme outside air temperature of -40F luckily corresponds to very low reduced pressure. The maximum temperature is assumed to be a combination of a hot environment and temperature rise due to the work of compression on the air. A typical operating range for compressed air storage on truck brake systems is 8 to 9 bars (gage) or 9 to 10 bars (absolute). This corresponds to a reduced temperature range of 1.75 to 2.56 and a reduced operating pressure of less than 0.27. As we can see from the compressibility chart, dry air has a compressibility factor in excess of 0.95 in these conditions. The ideal gas equation is a reasonable, but not perfect engineering assumption in these cases. At extreme environmental conditions, it is quite possible that some components of dry air (such as CO2) will cause problems. We’ll leave the detailed analysis to the ME’s who work on these systems… but our EE’s should have an appreciation of these issues. For Truck Brake Systems < Tr < 2.56 Pr ≈ 0.27 For Truck Brake Systems The ideal gas law is a fairly reasonable assumption. It will help us understand key ideas. Reference: "A Generalized Thermodynamic Correlation based on Three-Parameter Corresponding States", B.I.Lee & M.G.Kesler, AIChE Journal, Volume 21, Issue 3, 1975, pp Reference: R·I·T MECE-251 7

8 Equations of State for Dry AirTC = 133 K = 239 R PC = 37.7 Bar ≈ 547 psia M = kg/kmol = lbm/lbmol R = kJ/Kg·K = 53.3 ft·lbf / lbm·R For pneumatically actuated mechatronic systems, we need a good understanding of both water and dry air. Later, we will mix water and dry air to consider moist air – the real gas used in most pneumatic actuators. The key properties for dry air are given here. The ideal gas equation of state will be sufficient for most of our applications. The ideal gas equation of state can be algebraically expressed in several forms as shown here. The compressible gas equation of state can be used for extreme (low temperature or high pressure) operating conditions. Ideal Gas, Z ≈ 1 P v = R T P V = m R T P = ρ RT P V = Nmoles Runiversal T Compressible Gas, Z < 1 Z = P v R T Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 8

9 Next Steps L2 Task 3B: Please review the example problems on line.L2 Task 3C: Then, solve the review problem. L2 Task 4A: Please review the lecture on line. L2 Task 4B: Please review the example problems on line. L2 Task 4C: Then, solve the review problem. L2 Task 5: Solve and TURN IN the case study problem. L2 Task 6: Take the Lesson 2 quiz. Now, its time to solve some review problems, move on to the next lecture, and finish the lesson. Please proceed to the next lecture after solving the review problems. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 9

10 Extra slides after this point

11 The Compressibility Factor – Real GasesFor Dry Air TC = 133K PC = 37.7 Bar ≈ 547 psia M = kg/kmol For Truck Brake Systems Ttyp ≈ 133K Ptyp ≈ 8-10 bar (abs) Now, its time to solve some review problems, move on to the next lecture, and finish the lesson. Please proceed to the next lecture after solving the review problems. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 11

12 The Compressibility Factor – Real GasesNow, its time to solve some review problems, move on to the next lecture, and finish the lesson. Please proceed to the next lecture after solving the review problems. Reference: Moran, Shapiro, Boettner, Bailey: Fundamentals of Engineering Thermodynamics, 7th Edition, Dec 2010, © 2011, Wiley. Reference: R·I·T MECE-251 12

13 The Ideal Gas Equation of StateNow, its time to solve some review problems, move on to the next lecture, and finish the lesson. Please proceed to the next lecture after solving the review problems. Reference: Moran, Shapiro, Boettner, Bailey: Fundamentals of Engineering Thermodynamics, 7th Edition, Dec 2010, © 2011, Wiley. Reference: R·I·T MECE-251 13

14 The Compressibility Factor – Real GasesFor Dry Air TC = 133K PC = 37.7 Bar ≈ 547 psia M = kg/kmol For Truck Brake Systems 233K < Tenvir range < 340K Ptyp ≈ 8-10 bar (abs) The compressibility chart shown here is a good tool to decide if the ideal gas equation of state is a reasonable engineering approximation. If the compressibility factor is above Z = 0.95, we’re usually safe from an engineering perspective. This chart is presented in terms of reduced temperature and reduced pressure. The reduced temperature is the ratio of the absolute temperature over the absolute critical temperature (at the peak of the vapor dome). The reduced pressure is the ratio of the absolute pressure over the critical pressure. For dry air the critical temperature is 133 Kelvin, and the critical pressure is 37.7 bar or 547 psi (absolute). Let’s consider that a truck braking system has to operate over extreme temperature ranges from -40F (-40C) up to 140F (60C) and at pressure up to 10 bar (absolute). The extreme outside air temperature of -40F luckily corresponds to very low reduced pressure. The maximum temperature is assumed to be a combination of a hot environment and temperature rise due to the work of compression on the air. Let’s consider the full range of ambient temperatures ranging from negative 40F to positive 140F, or in absolute values, 233Kelvin to 340 Kelvin. A typical operating range for compressed air storage on truck brake systems is 8 to 9 bars (gage) or 9 to 10 bars (absolute). This corresponds to a reduced temperature range of 1.75 to 2.56 and a reduced operating pressure of less than 0.27. As we can see from the compressibility chart, dry air has a compressibility factor of about 0.8 in these conditions. The ideal gas law is not a great engineering assumption in these cases. At extreme environmental conditions, it is quite possible that some components of dry air (such as CO2) will cause problems. We’ll leave the detailed analysis to the ME’s who work on these systems… but our EE’s should have an appreciation of these issues. For Truck Brake Systems < Tr < 2.56 Pr ≈ 0.27 For Truck Brake Systems The ideal gas law is not a great assumption. But it will help us understand key ideas. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill R·I·T MECE-251 14