Lesson 3C Heat Capacities Mempelajari 2 definisi kapasitas panas: kapasitas panas volume konstan dan kapasitas panas tekanan konstan.

Transkripsi

1 Chemical Engineering Thermodynamics Prepared by: Dr. NINIEK Fajar Puspita, M.Eng EngAugust August, Gs_III_Heat Effects 1 Lesson Topics Descriptions Lesson 3A Internal Energy & Enthalpy Mendiskusikan definisi energi dalam dan entalpi untuk real substances, gas-gas ideal, cairan dan padatan incompresible. Lesson 3B Thermo Properties: NIST WebBook Mempelajari bagaimana menggunakan NIST Webbook untuk mencapai data termodinamika. Lesson 3C Heat Capacities Mempelajari 2 definisi kapasitas panas: kapasitas panas volume konstan dan kapasitas panas tekanan konstan. Lesson 3D Hypothetical ti Mempelajari alur proses hipotetik tik untuk menentukan Process Paths perubahan sifat termal dari keadaan awal ke keadaan akhir. Lesson 3E Phase Changes Mempelajari bahwa alur proses hipotetik untuk alat yang bermanfaat dalam mempertimbangakan perubahan sifat terkait dengan perubahan fase. 2 1

2 Three Principle Phases, Revisited In Chapter 2, Lesson B, we discussed the difference between the three principle phases: gas, liquid, and solid. Just to refresh your memory, move the mouse pointer over the sketch of each phase to see a description of that phase. Molecules move randomly with three different types of motion: vibration, rotation and translation. Molecules are separated by large distances and travel a long way between collisions. We also learned that, in all the phases, molecules move randomly with three different types of motion: vibration, rotation and translation. Molecules move randomly with all three types of motion, but they are much closer together and cannot travel very far between collisions. The internal energy of the system is defined as the sum of the kinetic energies in the vibrational, rotational and translational motion of molecules. Atoms or molecules have all three types of motion, but they are very close together. As a result, they cannot travel far at all before they collide. Each molecule moves about within a small space and does not tend to wander. 3 U(T,P) for Real Substances Real Substances: Kenaikan T meningkatkan gerakan molekuler a.l. vibrasi, rotasi dan translasi, dan juga akan menaikkan U. Kenaikan P sedikit menurunkan U pada sebagian besar nilai T dan P. Fenomena ini terjadi karena interaksi molekuler yang kompleks. U Energi Internal sangat dipengaruhi oleh T U Energi Internal kurang dipengaruhi oleh P U = U(T, P) T 4 U as a Function of T at Constant P P U as a Function of P at Constant T 2

3 U(T) for Ideal Gases Ideal Gases: U = U(T) Kenaikan T meningkatkan gerakan molekuler vibrasi, rotasi dan translasi. Kenaikan T juga menaikkan U. Perubahan P tidak mempengaruhi U karena tidak adanya interaksi molekuler. 5 U(T) for Incompressible Liquids Incompressible Liquids & Solids : Kenaikan T meningkatkan gerakan molekuler secara vibrasi, rotasi and translasi. Kenaikan T juga meningkatkan U. Perubahan P tidak mempengaruhi U karena volume molar dari senyawa incompressible tidak dipengaruhi oleh perubahan tekanan. Konsekuensinya, tidak ada perubahan pada ekstensinya dan sifat interkasi molekuler dan karena itu, U tidak berubah juga. U = U(T) 6 3

4 Internal Energy_Energi dalam (E dalam ) adalah total energi kinetik (Ek) dan energi potensial (Ep) yang ada di dalam sistem. Formula E = Ek + Ep. Namun karena besar energi kinetik dan energi potensial pada sebuah sistem tidak dapat diukur, maka besar energi dalam sebuah sistem juga tidak dapat ditentukan, yang dapat ditentukan adalah besar perubahan energi dalam (E) suatu sistem. Perubahan energi dalam dapat diketahui dengan mengukur kalor (q) dan kerja (w), yang akan timbul bila suatu sistem bereaksi. Oleh karena itu, perubahan energi dalam dirumuskan dengan persamaan : E = q - w. q Jika sistem menyerap kalor, q +. Jika sistem mengeluarkan kalor q w Jika sistem melakukan kerja, w+ Jika sistem dikenai kerja oleh lingkungan, w- 7 Energi dalam Jadi bila suatu sistem menyerap kalor dari lingkungan sebesar 10 kj, dan sistem tersebut juga melakukan kerja sebesar 6 kj, maka perubahan energi dalam-nya akan sebesar 16 kj. q =+10 kj E = q - w SISTEM w = - 6 kj PERUBAHAN ENERGI DALAM BERNILAI 0 jika jumlah kalor yang masuk = jumlah kerja yang dilakukan, q + (masuk) SISTEM w + (dilakukan) dan jika jumlah kalor yang dikeluarkan = jumlah kerja yang dikenakan pada sistem. q (dikeluarkan) SISTEM w - (dikenakan) Artinya, tidak ada PERUBAHAN ENERGI DALAM yang terjadi pada sistem. 8 4

5 Enthalpy Entalpi adalah istilah dalam termodinamika yang menyatakan jumlah energi internal dari suatu sistem termodinamika ditambah energi yang digunakan untuk melakukan kerja. Entalpi tidak bisa diukur, tetapi nilai perubahannya bisa dihitung. Secara matematis, perubahan entalpi dapat dirumuskan sebagai berikut: ΔH = ΔU + PΔV di mana: H = entalpi sistem (joule) U = energi dalam (joule) P = tekanan dari sistem (Pa) V = volume sistem (m 3 ) 9 Enthalpy reaksi Entalpi = H = Kalor reaksi pada tekanan tetap Perubahan entalpi adalah perubahan energi yang menyertai peristiwa perubahan kimia pada tekanan tetap. a. Pemutusan ikatan membutuhkan energi (= endoterm) Contoh: H 2 2H - A kj ; ΔH= + A kj b. Pembentukan ikatan memberikan energi (= eksoterm) Contoh: 2H H 2 + A kj ; ΔH = - A kj

6 Entalpi Pembentukan Standar ( ΔH f ): ΔH untuk membentuk 1 mol persenyawaan langsung dari unsur-unsurnya yang diukur pada 298 o K dan tekanan 1 atm. Contoh: H 2 (g) + 1/2 O 2 (g) H 2 0 (l) ; ΔH f = kj 11 Entalpi Penguraian Standar: ΔH dari penguraian 1 mol persenyawaan langsung menjadi unsur-unsurnya (= Kebalikan dari ΔH pembentukan). Contoh: H 2 O (l) H 2 (g) + 1/2 O 2 (g) ; ΔH = kj 12 6

7 Entalpi Pembakaran Standar (ΔHc ): ΔH untuk membakar 1 mol suatu senyawa dengan O 2 dari udara yang diukur pada keadaan standar (298 o K dan tekanan 1 atm). Contoh: CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O(l) ; ΔHc = -802 kj 13 Entalpi Reaksi: ΔH dari suatu persamaan reaksi, di mana zat-zat yang terdapat dalam persamaan reaksi dinyatakan dalam satuan mol dan koefisien-koefisien persamaan reaksi kiharus bulat sederhana. Contoh: 2Al + 3H 2 SO 4 Al 2 (SO 4 ) 3 + 3H 2 ; ΔH = kj

8 Entalpi Netralisasi: ΔH yang dihasilkan (selalu eksoterm) pada reaksi penetralan asam atau basa. Contoh: NaOH(aq) + HCl(aq) NaCl(aq) + H 2 O(l) ; ΔH = kj/mol Hukum Lavoisier-Laplace: "Jumlah kalor yang dilepaskan pada pembentukan 1 mol zat dari unsurunsurya = jumlah kalor yang diperlukan untuk menguraikan zat tersebut menjadi unsur-unsur pembentuknya. Contoh: N 2 (g) + 3H 2 (g) 2NH 3 (g) ; ΔH = J 2NH 3 (g) N 2 (g) + 3H 2 (g) ; ΔH = J 15 Table: Enthalpy of Formation (ΔH f )

9 Table: Enthalpy of Formation (H f ), Gibbs Function (G), and Absolute Entropy (S) of Various Substances at 298 o K dan tekanan 1 atm Substance Formula H f G S H f dan G (kj/kmol) ; S (kj/kmol. o K) 17 Table: Enthalpy of Formation (H f ), Gibbs Function (G), and Absolute Entropy (S) of Various Substances at 298 o K dan tekanan 1 atm Substance Formula H f G S H f dan G (kj/kmol) ; S (kj/kmol. o K)

10 Determine the standard heat of each of the following reactions at K (25 C) 19 Ref. Smith V Ness p

11 21 Definition of Enthalpy Enthalpy, H, is a thermodynamic property, or state variable, and it is defined by: H = U + PV. Enthalpy (kj) Molar Enthalpy (kj/mole) Specific Enthalpy (kj/kg) Differential Form Integral Form 22 11

12 H(T,P) for Real Substances Real Substances U is a strong function of T U is a weak function of P H is a function of both T & P Note : At most, but not all values of T & P, H increases as P increases 23 H(T) for Ideal Gases Ideal Gases Molar enthalpy: Specific enthalpy: Since U of an ideal gas is a function of T only and R and MW are constants, H of an ideal gas is also a function of T only

13 H(T,P) for Incompressible Liquids and Solids U is a function of T only, but H is a function of T and also a weak function of P 25 Lesson Summary_Lesson 2A CHAPTER 3, LESSON A - INTERNAL ENERGY & ENTHALPY In this lesson we studied the functional dependence of internal energy, U, on both T and P. We considered three cases: real gases, ideal gases, and liquids and solids. Next, we defined a new state variable called enthalpy, H. We then considered and discussed the functional dependence of enthalpy on both T and P. The conclusions that we drew from these two studies are summarized in the table, below. REAL GASES - U is a strong function of T and a weak function of P. H is a function of both T and P. IDEAL GASES - U is a function of T only. H is a function of T only. Incompressible Liquids and Solids - U is a function of T only. H is a function of both T and P. In the next lesson, we will learn how to obtain values for both specific and molar internal energy and enthalpy from tables of data and databases

14 Sample Data from NIST WebBook 27 Thermophysical Properties of Fluid Systems Density Enthalpy Specific volume Entropy Cp Internal energy Cv Speed of Sound Choose the chemical species for which you want data. (Example: Water) Choose the system of units that you would like to use. (Example: K, MPa, kj...) Choose the type of thermodynamic data you want to obtain. (Example: Saturation Properties - Temperature Increments) Choose a standard state convention, which we call a reference state. (We will learn more about reference states later in this lesson.) When you have finished steps 1-4 click the "Press to Continue" button

15 Liquid phase data Data on saturation curve 29 What is a Reference State? Every table or graph of thermodynamic data has a standard state convention or a reference state associated with it. But why? It is not possible to determine the absolute value of U or H. We can only measure changes in U or H. In this regard, enthalpy and internal energy are much like altitude. The altitude of a mountain and the altimeters on airplanes are referenced to mean sea level. A reference state is also needed when tabulating the measured changes in U or H. A reference state is usually specified by the temperature, pressure, and the phase at which either U or H is zero. Then, U and H of every other state is equal to the change in U or H as the substance changes from the reference state to the state of interest 30 15

16 Review : U & H as Functions of T & P In this part of the lesson, we will plot enthalpy and internal energy data from the NIST WebBook. We will compare the results to what we expect for an incompressible liquid and for an ideal gas. Recall the conclusions we reached in the previous lesson: 31 Enthalpy & Internal Energy for Real Substances Now, we can obtain data from the NIST WebBook for water to show the trends observed for a real liquid. We will obtain two tables of data: 1. Units: o C, atm, kg/m 3, kj/kg Type of data: Isothermal properties Standard State: ASHRAE Convention T = 30 o C, P = 1 to 10 atm by 0.5 atm 2. Units: o C, atm, kg/m 3, kj/kg Type of data: Isobaric properties Standard State: ASHRAE Convention P = 1 atm, T = 5 to 95 o C by 5 o C If you like, go ahead and obtain the data from NIST WebBook and plot the data in Excel to see the expected trends. ASHRAE_American Society for Heating Refrigeration Air Conditioning Engineer 32 16

17 The enthalpy/pressure diagram The temperature/enthalpy diagram 33 NIST Thermodynamic Data for Subcooled Water Subcooled liquid tables for water obtained from the NIST WebBook The tables were imported into Excel and edited

18 U(P) & H(P) for Subcooled Water at Constant T 35 Comparison of Real and Incompressible Substances Real Liquid (water) Incompressible Liquid (no liquid id is completely l incompressible) ibl Incompressible Liquid: U at constant T is not a function of P. H increases as P increases. Real Liquid : U can increase slightly, or like water, U can decrease slowly as P increases. H increases as P increases

19 U(T) and H(T) for Liquid Water at Constant P Why does it seem like internal energy and enthalpy are the same here? 37 Comparison of U & H at Constant P 38 Why does it seem like internal energy and enthalpy are the same here? 19

20 Thermodynamic Properties of an Ideal Gas Ideal Gases U is a function of T only. H is a function of T only. Now let's obtain data from the NIST WebBook for hydrogen and compare the trends we observe to the behavior we would expect for an ideal gas. 1. Units: o C, atm, kg/m 3, kj/kg Type of data: Isothermal properties Standard State: ASHRAE Convention T = 30 o C, P = 1 to 10 atm by 0.5 atm 2. Units: o C, atm, kg/m 3, kj/kg Type of data: Isobaric properties Standard State: ASHRAE Convention P = 1 atm, T = 5 to 95 o C by 5 o C If you like, go ahead and obtain the data from NIST WebBook and plot the data in Excel to see the expected trends. 39 Thermodynamic Properties of Hydrogen Thermodynamic data for hydrogen obtained from the NIST WebBook, then imported into Excel and edited

21 U and H of Hydrogen at Constant T Hydrogen data obtained from NIST WebBook, then imported into Excel, edited, and plotted. 41 To an accuracy of three significant figures in and, hydrogen can be considered an ideal gas over this range of P. U and H of Hydrogen at Constant P Hydrogen data obtained from NIST WebBook, then imported into Excel, edited, and plotted. 42 Does this plot show the expected trends for an ideal gas at constant pressure? 21

22 Comparison of U & H at Constant P Does this plot show the expected trends for an ideal gas at constant pressure? Internal energy is a function of temperature. plus RT/MW gives the specific enthalpy 43 Does this plot show the expected trends for an ideal gas at constant pressure? The difference between the H and the U curves grows linearly as temperature increases. Conclusion: Hydrogen does behave like an ideal gas at 1 atm between 5oC and 95oC 44 22

23 Lesson Summary_Lesson 3B CHAPTER 3, LESSON B - THERMO PROPERTIES: NIST WEBBOOK In this lesson we learned that NIST WebBook is a valuable tool to determine thermodynamic properties. First we showed, step-by-step, how to locate the NIST website and the NIST WebBook within the website. Be sure to bookmark the link to the Thermophysical Properties of Fluid Systems at We considered how to specify what information we want to obtain such as the chemical species, phase, units for properties, and the reference state. We learned that a reference state is needed when tabulating the measured changes in internal energy or enthalpy. Often a reference state is fixed by the temperature, pressure, and phase. We then plotted enthalpy and internal energy data obtained from the NIST WebBook for an incompressible liquid, an ideal gas, and a real substance. From this we reinforced internal energy and enthalpy trends we learned in lesson B. We will be using NIST WebBook to obtain most of the data for this course. In the next lesson, we will learn how to use NIST WebBook to obtain data on a new property called heat capacity. 45 The Relationship Between Heat and Temperature When heating a substance, we must add a certain amount of heat to raise the temperature a specified amount. This capacity to take in heat is unique to each substance and is defined with the symbol C. Ch3, Lesson C, Page 1 - The Relationship Between Heat and Temperature If we add a Joule of energy to one gram of liquid water at 20oC it will raise the temperature to about 20.2oC. If we add 1 Joule of energy to one gram of liquid mercury at 20oC it will raise the temperature to about 27oC. If we add 1 Joule of energy to one gram of air at 20oC it will raise the temperature to about 21oC. This capacity for absorbing heat is called the heat capacity or the specific heat. Flip the page and we ll show you the formal definitions for heat capacity and specific heat. Then, we ll show you how to use them to solve problems 46 23

24 Definition of Constant V and P Heat Capacities The molar heat capacity of a substance is defined as the energy required to raise the temperature of a mole of a substance by one degree. The specific heat of a substance is defined as the energy required to raise the temperature of a unit mass of a substance by one degree. 47 Ideal Gas Specific Heats Recall from the previous lesson that the internal energy of an ideal gas is a function of T only: and Therefore, the heat capacities (or specific heats) for ideal gases reduce to: Often, ideal gas specific heats and heat capacities are approximated as polynomials in terms of T: 48 where a, b, c, and d are constants for a given substance 24

25 Gibbs Phase Rule o F = C - P + 2 where: of is the number of degrees of freedom or the number of intensive propertiesthat can be independently specified. All other intensive properties are then fixed and can be determined. C is the number of different chemical substances in the system. P is the number of distinct phases within the system. Intensive Properties: Do not depend on the size of the system. Examples include: Extensive Properties: Do depend on the size of the system. Examples include: Since we are dealing with pure substances that exist in a single-phase, (C = 1 and P =1), Therefore: o F = = 2 We only need to fix or specify 2 state variables in order to completely define the state of our system. 49 Change in U as a Function of Ideal-Gas Cv 50 25

26 Change in H as a Function of Ideal-Gas Cp 51 Cp and Cv Relationship for an Ideal Gas 52 26

27 Cp and Cv for Liquids & Solids 53 Ideal-Gas Cp Data from NIST WebBook Here is our heat capacity polynomial When you scroll down a bit farther on the Results Page of the NIST Webbook, you will find the constants for the heat capacity polynomial for Ammonia shown in a table like this: 54 27

28 3C-1 : Enthalpy Change of Ammonia Using the IG Heat Capacity Determine the enthalpy change and internal energy change of ammonia in J/mole, as it is heated from 350 o K to 600 o K, using the ideal gas heat capacity given by the Shomate Equation

29 57 Isothermal Vaporization of Water Example #3C-1 The temperature of 10 lbm of water is held constant at 205 F.The pressure is reduced from a very high value until vaporization is complete. Determine the final volume of the steam in ft3. 2C-1 : Specific Volume of Saturated Mixtures 4 pts Calculate the specific volume for the following situations: a.) Water at 200 o C and 80% quality b.) Freon 12 at -60 o C and 90% quality c.) Ammonia at 500 kpa and 85% quality Read : This is an exercise designed to drive home the meaning and use of the new concept of the quality of a saturated mixture. It is crucial to remember that if a quality is given, then the system contains a saturated mixture and you probably need to look up properties of both the saturated liquid and the saturated vapor

30 Given : a.) Water : T 200 o C x 0.80 kg vap/kg tot b.) R-12 : T -60 o C x 0.90 kg vap/kg tot c.) NH 3 : P 500 kpa x 0.85 kg vap/kg tot Find : V??? m 3 /kg for each of the three parts of this problem. 59 Solution Part a.) Data from the Saturation Temperature Table of the Steam Tables at 200 o C: V sat liq m 3 /kg V sat vap m 3 /kg P* 1554 kpa The key equation for this problem is the relationship between the properties of a saturated mixture and the properties of saturated liquid and vapor and the quality. Eqn 1 Now, we can plug numbers into Eqn 1 to answer this part of the question. V m 3 /kg Notice that I kept 4 significan figures in this answer istead of the usual 2 or 3 because there are 4 significant digits in the sat'd liquid and sat'd vapor values. Perhaps I should have only retained 2 significant digits because there only appear to be 2 significant digits in the quality. I have assumed that there are more than 2, really 4 or more, digits in the quality. This may not be a good assumption

31 Part b.) Data from the Saturation Temperature Table of the R-12 Tables at - 60 o C: V sat liq m 3 /kg V sat vap m 3 /kg P* 22.6 kpa Now, we can plug numbers into Eqn 1 to answer this part of the question. V m 3 /kg Significant figures are a bit tricky here. Part c.) Data from the Saturation Pressure Table of the Ammonia Tables at 500 kpa: V sat liq m 3 /kg V sat vap m 3 /kg T sat o CNow, we can plug numbers into Eqn 1 to answer this part of the question. V m 3 /kg Significant figures are a bit tricky here as well. 61 Lesson Summary_Lesson 3C CHAPTER 3, LESSON C - HEAT CAPACITIES In this lesson, we learned about new properties called heat capacity and specific heat. Heat capacity is the energy required to raise the temperature of a mole of a substance by one degree. Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree. Next, we studied the heat capacity of an ideal gas. We used the superscript o to identify heat capacities that apply only to ideal gases. We derived the following relationships for ideal gases: Ideal-gas heat capacities are often expressed as polynomials, such as: where a, b, c, and d are constants for a given substance. Next, we considered the heat capacities of liquids and solids. We found that over a moderate range of temperatures and pressures. Finally, we learned how to obtain heat capacity polynomials for a variety of substances from thenist WebBook

32 What is a State? Gibbs Phase Rule o F = C - P Initial State F = derajat kebebasan C = Jumlah senyawa kimia didalam At a given state all the properties sistem of a system are fixed and can be P = Jumlah fase dalam sistem measured or calculated Ch3, Lesson D, Page 1 - What is a State? Chapter 1 menjelaskan keadaan yang diberikan seluruh sifat materi didalam batasan sitsem yang ditetapkan Chapter 2 Gibbs Phase Rule untuk menetapkan berapa banyak sifat-sifat intensif untuk menspesifikasi keadaan sistem 63 What is a State? Untuk menggunakan Gibbs Phase Rule, harus tahu spesies kimia apa yang ada dalam sistem dan juga fase apa yang ada dalam sistem. Jika jumlah sifat-sifat intensif yang telah dispesifikasi= jumlah derajat kebebasan maka sifat-sifat intensif sistem tersebut dapat ditentukan. Jika air murni ada dalam sistem, maka C=air murni = 1 P = fase = cair = 1 F=C-P+2 =1-1+2 = 2 F=2 dapat dispesifikasiifik i 2 variabel iblintensif. if Yaitu T dan P Karena bermanfaat dan mudah untuk mengukur. Kemungkinan juga densitas dan entalpi spesifik karena juga sifat intensif

33 What Happens When a Property of a State Changes? Initial State 1 2 When the value of a property changes, the system is at a new state At a given state all the properties of a system are fixed and can be measured or calculated Ch3, Lesson D, Page 2 - What Happens When a Property of a State Changes? If any property of the system changes, then the system is in a different state. 65 What is a Process Path? Process Path: A process path is the actual series of states that the system passes through as it moves from the initial state to the final state during a process Initial State At a given state all the properties of a system are fixed and can be measured or calculated. 66 When the value of a property changes, the system is at a new state Ch3, Lesson D, Page 3 - What is a Process Path? A system can continue to change one or more of its properties. As it does so, it moves from one state to another. The series of states through which a system moves. During a process, a system moves from an initial state to a final state, but its properties do not abruptly jump from the values at the initial state and instantly take the values associated with the final state. The properties of the system change smoothly as the process progresses from the initial state to the final state. The series of states in which the system exists during the process is called the process path. 33

34 State Variables & Hypothetical Process Paths Process Path A process path is the actual series of states that the system passes through as it moves from the initial state to the final state during a process. The system occupies an infinite number of states between the initial state and the final state. We use a smooth curve to represent the smooth path. Final State Initial State 67 Changes in state variables are not path dependent. Therefore, when solving problems we can choose any path that connects the initial and final states. The trick is to choose a path that makes the problem easy to solve. This path is called a hypothetical process path (HPP). You Must Be Able to Final State Initial State 1. Ideal Gases 2. Liquids and solids for which 3. Real substances for which tables of thermodynamic properties are available

35 Ideal Gas: Change in H Using an HPP What hypothetical process path will allow us to easily calculate the change in enthalpy of the air? Let's consider a process in which air changes from the initial state to the final state, as shown in the diagram above. Determine the change in the molar enthalpy of the air for this process. 69 HPP for an Ideal Gas 70 35

36 Change in H for an Ideal Gas at Constant T Therefore, state 1 is an ideal gas state. From state 1 to state 2, the pressure decreases but we are at constant t temperature. Recall from Lesson A that for an ideal gas: 71 Change in H for an Ideal Gas at Constant T 72 From state 3 to state 4 the pressure increases but we are at constant temperature. Therefore, state 4 is also an ideal gas state 36

37 Change in H for an Ideal Gas at Constant P From state 2 to state 3, the temperature increases at constant pressure. Therefore: Step 2-3 involves an ideal gas being heated from 25oC to 125oC at a constant pressure. That s exactly like what we studied in the previous lesson! So, ΔH-wiggle 2-3 is just the integral of the ideal gas Cp from T2 to T3. Now, all we need to do is obtain ideal gas Cp data for air. Does that sound familiar? 73 Heat Capacity Polynomial Data from NIST WebBook 74 37

38 Summary of HPP for an Ideal Gas 75 Ideal Gas HPP Simplification Ch3, Lesson D, Page 13 - Ideal Gas HPP Simplification So, we figured out that for a process in which the initial and final states are both ideal gas states, changes in pressure have no affect on the change in enthalpy. Therefore, to determine ΔH-wiggle for these processes, all we need to do is integrate the ideal gas heat capacity from the initial temperature to the final temperature. Cool. That s not so hard. What do we do if one or more of our states is NOT an ideal gas state? Flip the page and we will begin to deal with that problem

39 Properties of Solids & Liquids 77 HPP's for Liquids and Solids 78 39

40 Heat Capacities of Solids and Liquids Solids and Liquids: If a polynomial for the heat capacity is available is is generally of the form: Often, just one value of use the known value as 79 is known. In this case Thermodynamic Properties of Real Substances The best way to determine a value for a change in any property is to look up the value of the property for the initial and final states in a thermodynamic table and calculate the difference between them. In this course, this is the only method presented that is applicable for non-ideal gases! Final State Use themodynamic tables for liquids whenever possible because they are more accurate than the methods discussed on the previous three pages How much error is involved if we assume a gas to be ideal when it is not? 80 Initial State 40

41 Change in H for a Real Gas: Steam Ch3, Lesson D, Page 18 - Change in H for a Real Gas: Steam Let s consider a process in which steam is compressed from 100 kpa to 1 MPa. During this process, the temperature of the steam rises from 100oC to 200oC. By now, you probably have some intuition t about the temperatures es and pressure e at which gases can be assumed to be ideal. If you check the molar volumes at the initial and final states, you will see that the initial state can be safely assumed to be an ideal gas state, but the final state CANNOT. The easiest way to determine ΔH-hat for this process is just to look up H-hat for the initial and final states in the NIST WebBook, and that is exactly what you should do in practice. But just to make a point, let s construct an HPP and do a little extra work on this problem. We might find something interesting. Flip the page and let s see. 81 HPP for a Real Substance 82 41

42 Summary of the Solution for a Real Substance 83 What If We Treated Steam as an Ideal Gas? 84 42

43 Error from the Ideal Gas Assumption 85 Lesson Summary_Lesson 3D CHAPTER 3, LESSON D - HYPOTHETICAL PROCESS PATHS We began this lesson by refreshing your memory about states and defined a process path as the actual series of states that the system passes through as it moves from the initial state to the final state during a process. We emphasized that state variables are not dependent on the actual process path and therefore a hypothetical process path (HPP) can be used to determine changes in thermodynamic properties during a process. We focused on determining the change in enthalpy and internal energy for processes. You must be able to determine and for: 1. Ideal Gases 2. Liquids id and solids for which h 3. Real substances for which tables of thermodynamic properties are available. For ideal gases, all you need to do is integrate Cv or Cp from T1 to T2 to determine ΔU or ΔH. We found that Cp data for solids and liquids is limited and Cv data is not available at all. For liquids, the Cp equation is often linear and for solids, a single Cv value is the norm

44 HPP's for Phase Changes In the previous lesson, we used hypothetical process paths to make it easier to determine the change in the properties of an ideal gas, liquids and solids for which is constant, and real substances for which we have thermodynamic tables. BUT only in one phase! Final State 87 Initial State PHASE CHANGE In this lesson, we will learn how to use hypothetical process paths to determine the change in properties associated with a phase change. What is Enthalpy of Vaporization? Vaporization (or boiling): Saturated Liquid Saturated Vapor Condensation: Saturated Vapor Saturated Liquid Enthalpy of Vaporization ( latent heat of vaporization): the amount of energy that must be added to the system to convert 1 mole of saturated liquid into 1 mole of saturated vapor 88 44

45 Is the Heat of Vaporization Constant Would it take the same amount of energy to boil 1 kg of water at sea level it would at an elevation of 14,000 ft? What is the Heat of Vaporization is at the critical point? Berapa banyak energi yang harus diberikan untuk menguapkan a kg cair jenuh jika proses terjadi pada T & P kritis? 89 Saturation, Vaporization and Vapor Pressure The latent heat of vaporization didefiniskan sebagai jumlah energi yang diinginkan untuk menguapkan cairan secara sempurna pada Tsat (temperatur jenuh) dan P* (uap atau tekanan jenuh). Tsat = Saturation temperature P* = Vapor pressure or saturation pressure 90 45

46 Heat of Vaporization from the NIST WebBook In Chapter 3, Lesson C we learned how to obtain data (including enthalpy) from NIST WebBook To determine the latent heat of vaporization we the difference between the two enthalpy values. 91 Vaporization of Subcooled Water Subcooled Liquid : T < Tsat or: P > P* 92 46

47 Heat Liquid Water to the Tsat Evaluated at: Integration using Excel, followed by a unit conversion, yields 93 Enthalpy Change for Vaporization of Subcooled Water We determined the latent heat of vaporization of water at 100 o C and 1 atm on page 5 of this lesson: On the previous page, we determined the enthalpy change associated with heating of water from 75 o C to 100 o C at a constant pressure of 1 atm: The total change in enthalpy associated with the change from State 1 to State 3 is the sum of these two values: 94 47

48 Vaporization of Subcooled Water: Shortcut Method Enthalpy of Vaporization Since we have NIST WebBook as a tool, we can determine the enthalpy at State 1 and State 3 and then determine the difference. We get the following values: The change in enthalpy is: This is the same answer obtained from using the hypothetical process path! 95 The Clapeyron Equation For many processes, such as distillation, it is very important to know how vapor pressure, P*, depends on temperature, T. The Clapeyron Equation provides such a thermodynamic relationship. Where: The equation also allows us to determine the the latent heat of vaporization 96 when we know, P*, and T for the phase change 48

49 The Clausius-Clapeyron Equation We will start with the Clapeyron Equation At moderate pressure, not close to the critica point, Therefore: If we also assume we have an ideal gs because we are at moderate pressure, we can substitute: A little algebra and calculus helps us put the equation into a form that we can easily integrate: Integrating, we obtain the Clausius-Clapeyron Equation : 97 Using The Clausius-Clapeyron Equation 98 49

50 Other Latent Heats This lesson has focused on vaporization because it is the most important phase change in this course. HPP's can be used in the same way to calculate the change in properties that occur when melting and sublimation phase changes occur in a process. Latent Heat of Vaporization amount of energy absorbed during vaporization amount of energy released during condensation Latent Heat of Fusion amount of energy absorbed during melting amount of energy released during freezing Latent Heat of Sublimation amount of energy absorbed during sublimation amount of energy released during desublimation 99 Lesson Summary_Lesson 3E CHAPTER 3, LESSON E - PHASE CHANGES Pada pelajaran ini, kami belajar bagaimana variabel keadaan berubah selama perubahan fase. Kami menggunakan alur proses hipotetik (hypothetical process paths_hpp's) untuk membantu menetapkan perubahan-perubahan p dalam sifat termodinamis selama proses perubahan fase. Kami menentukan perubahan dalam entalpi karena variabel tersebut merupakan variabel keadaan didalam proses perubahan fase. Kami fokus belajar pada proses penguapan. Panas laten penguapan yaitu jumlah energi yang harus menjadi input agar supaya menguapkan a mol atau a kg cairan. Sumber data panas penguapan yatiu NIST dll dan data dari NIST WebBook menunjukkan bahwa ΔHvap turun sebagaimana kenaikan temperatur terhadap Tc. Kami menggunakan HPP dan NIST WebBook untuk menghitung perubahan entalpi terkait dengan penguapan cair jenuh dan cair dingini dengan menggunakan 2 teknik kik yang berbeda. b Kemudian, kami mendiskusikan hubungan antara Tsat, P* dan ΔHvap. Kami mulai dari Clapeyron Equation dan turunan Clausius-Clapeyron Equation. Kami mendiskusikan penggunaan-penggunaan Clausius-Clapeyron Equation dan memperkenalkan perhitungan untuk memprediksi tekanan uap jenuh sebagai fungsi T. 2 perubahan fase yang umum : sublimation dan fusion