# Technical Thermodynamics

Size: px
Start display at page:

Transcription

1 Technical Thermodynamics Chapter 2: Basic ideas and some definitions Prof. Dr.-Ing. habil. Egon Hassel University of Rostock, Germany Faculty of Mechanical Engineering and Ship Building Institute of Technical Thermodynamics January 12, 2011 / 1

2 Contents 1) Introduction 2) Basic ideas and some definitions 3) First law of thermodynamics and energy 4) Second law and entropy 5) Cyclic processes 6) Exergy 7) Equations of state of real gases 8) Mixtures 9) Combustion 10) Heat transfer 11) Energy conversion: heat work 2

3 What is Technical Thermodynamics? Thermodynamics has to do with or is the science of the 5 e s (five-e): energy: energy conversion, transformation, storage entropy: only with entropy we can understand equilibrium, the time arrow and thermal efficiency exergy: is the (technical) availability of work economy: the products an engineer creates must be sold environment: to minimize the effects of the (industrial) techniques on environment is crucial for survival 3

4 Thermodynamic System A thermodynamic system is a certain volume or a certain mass under monitoring. This volume or mass is separated from the surrounding (environment) by a boundary. Mass flow B 4

5 Thermodynamic System II The (imaginary) systems boundary, a.k.a control boundary, allows the quantitative determination of the inward or outward flow of material, Energy, entropy, exergy and momentum in and out of the system. The area outside the considered system is called Environment". Examples of systems: One complete steam power plant; the water in the steam cycle, the content of a cylinder in a combustion engine, all the Electrons of an electrical discharge, a spatially fixed voxel (volume element) 5

6 Thermodynamic System III A system which is completely isolated from the environment, with neither mass or energy transfer is called totally closed or isolated system dm = 0, de = 0. If there is no mass transfer but a transfer of energy is possible, then it is called closed system dm = 0. If both mass and energy transfer is possible, then it is called open system. If no heat goes in or out, then it is called adiabatic system. 6

7 Thermodynamic System IV Distinctions according to system properties: homogeneous system same properties at all locations inhomogeneous oder heterogeneous system properties change with local position Homogeneous System (properties are locally constant) 7

8 boundary Thermodynamic System V Cylinder, Closed System Mass flow A Mass flow B Heat exchange flow process, Open System heat loss 8

9 Thermodynamic System VI The choice of a system or system boundaries is arbitrary. You can solve the problem skillfully or clumsily, but not wrongly. If you choose the system clumsily, you will not arrive at the desired result. However, you will also not going to arrive at the wrong result. 9

10 State and State Variable I The state of a system is characterized through state variables. We distinguish internal and external quantities. External quantities are the location in space and the velocity of the system. An unambiguous description of the state of a thermodynamic system is Usually possible through a few independent state variables, e.g. pressure p, volume V, mass m. All measurable properties of the system depend only on these state variables, That is, any property Prop of the system Syst can be described as a unique function of these independent state variables Z1, Z2, Z3,... Prop(Syst) = f (Z1,Z2, Z3...). 10

11 State and State Variable II To describe a state, we need a certain number of independent state variables. We usually need to choose between different state variables. They have to be (mathematically, functionally) independent. Example (to show the opposite) : Density, Volume and Mass are not Independent, because 11

12 State and State Variable III Difference in intensive and extensive state variables: Intensive state variable is independent of the quantity of the substance in the system e.g.: Pressure, Temperature, Density System 1, System 2 and the overall system have the same p, T, 12

13 State and State Variable IV Extensive state variables are those that are proportional to the quantity of material in the system e.g. : Volume V, Internal Energy U, Entropy S (will be defined later). Total system 3 13

14 State and State Variable Extensive state variable: The internal energy U, not defined yet, is the sum of the internal energies of the subsystems, as tank, battery, etc tank battery 14

15 State and State Variable V Specific state variable is defined as the ratio of the extensive state variable by the mass (This applies to homogeneous systems): Specific Volume Specific Internal Energy Specific Entropy 15

16 State and State Variable VI Molar state variables are defined as ratio of extensive state variable by mol-number (1 mol = *10 23 molecules or atoms) (for homogeneous Systems) Molar Volume Molar Internal Energy Molar Entropy 16

17 State and State Variable VII by integration of specific state variables over volume, we obtain an extensive state variable For homogenous systems (like in the definition): 17

18 State and State Variable VIII External state variables indicate the "external" (mechanical) state of the system, the spatial coordinates and the system velocity relative to a reference system. Thermodynamic Equilibrium A System is in thermodynamic equilibrium if its state variables do not change in time when the system is in isolation (from the environment). Counter-example is a fluid in turbulent motion. The unambiguous description of just the equilibrium states, requires only a few state variables 18

19 thermodynamic equilibrium Thermodynamic Equilibrium A System is in thermodynamic equilibrium if its state variables do not change in time when the system is in isolation (from the environment). 19

20 State and State Variable IX Application of Technical Thermodynamics is limited to systems in (thermodynamic) equilibrium and the transitions of a system from one equilibrium state to another. This is also called Quasi-static process. Counter-example: System which consists of iron and wet air Phase: Each homogenous area of a system is called a phase One homogenous system consists of exactly one phase 20

21 Thermodynamic process Processes cause a change in the condition of systems. A certain state change can be caused be different processes. c = velocity acceleration = process The process description is broader than the description of the effect of State change. 21

22 Thermodynamic process Cycle - Modifies a system state such that from State 1, via intermediate 2, 3, 4,... n, goes back to State 1. That is called a cycle process For cycle: Other definition for state variable: A variable g is a state variable if for any circular integration:! dg = 0 22

23 Thermodynamic process A Natural Process runs by itself without external assistance. Example: Cooling of hot body, dissolution of a substance in a solvent (ex: piece of sugar in a coffee), combustion, corrosion. Conclusion: In an isolated system, a natural process changes the internal State of the system only to certain final point, then the system stays stable, this is the equilibrium state. This state is characterized by the fact that the system is not capable of further changes itself without interference from the outside. 23

24 Thermodynamic process Equilibriums (to balance) : Mechanical equilibrium: Pressure 1 = Pressure 2 Concentration equilibrium: Concentration 1 = Concentration 2 Thermal equilibrium: Temperature 1 = Temperature 2 Total system 3 To adjust the thermal equilibrium, an energy flow between the systems takes place System 1 system 2 24

25 Definition of Temperature From this we come to an empirical Definition of temperature: Systems in thermal equilibrium show this temperature. Zeroth law of thermodynamics: If system S3 (thermometer) is in thermal equilibrium with system S2 (some material) and system S3 is in thermal equilibrium with system S1 (some other body), then system S2 and system S1 are also in thermal equilibrium with each other. This constitutes the Basics of Temperature Measurement of the two systems S1 and S2. We want to know if they have the same temperature. Therefore we use a third system (S3) to find that out. S3 is a Thermometer. 25

26 Temperature measurement gas thermometer Atmospheric pressure p_out e.g. Fluid e.g. Hg or H2O lhs balance area rhs balance area 26

27 Balancing We have 5 terms for all balance equations: G = quantity to be under scrutiny G syst = quantity within the system G in = inflow G out = outflow G source = creation of G G destruct = destruction of G G syst (t) G syst (t 0 ) = + G in G out + G source G destruct Content of G in system at time t minus content of G at time t 0 equals Plus inflow minus outflow plus creation minus destruction 27

28 Balancing Notation: Finite change of a State variable U: ΔU Differential change: du Integration: Finite Process variable: W, Q Differential variable: δw, δq Integration: 28

29 29

30 Apple Balance 29

31 Apple Balance The Apple Balance: 29

32 Apple Balance The Apple Balance: System: System boundary: Control time: Collection of terms: what is important?: Result: 29

33 Apple Balance The Apple Balance: System: System boundary: Control time: Collection of terms: what is important?: Result: Change of Number of apples = input - output + production - destruction in the system 29

34 Balances The Apple Balance Change of Number of apples = + input output + production - destruction in the system => General form of the balance : Change of Quantity within System = + input output + production destruction 30

35 Balances General form of the balance : Change within System = input - output + production destruction signs: + means benefit for the system - means loss for the system 31

36 Mass-Balance Mass balance: Change within System = input - output + production destruction Mass conservation Mass is conserved. And Einstein's E=mc 2 does not alter this. 32

37 Mass-Balance Mass balance: Change within System = input - output + production destruction Mass conservation Mass is conserved. And Einstein's E=mc 2 does not alter this. 32

38 Mass-Balance Mass balance: Change within System = input - output + production destruction Mass conservation Mass is conserved. And Einstein's E=mc 2 does not alter this. 32

39 Energy-Balance Energy balance: Change within System = input - output + production destruction Energy conservation First law of thermodynamics Energy is strictly conserved. Best explanation to be found in the famous Feynman lectures, part I. Quantum mechanics uncertainty principle does Not alter this law. 33

40 Energy-Balance Energy balance: Change within System = input - output + production destruction Energy conservation First law of thermodynamics Energy is strictly conserved. Best explanation to be found in the famous Feynman lectures, part I. Quantum mechanics uncertainty principle does Not alter this law. 33

41 Energy-Balance Energy balance: Change within System = input - output + production destruction Energy conservation First law of thermodynamics Energy is strictly conserved. Best explanation to be found in the famous Feynman lectures, part I. Quantum mechanics uncertainty principle does Not alter this law. 33

42 Entropy-Balance Entropy (S) balance: Change within System = input - output + production destruction Second law of thermodynamics Entropy can be be produced in an isolated system, or spontaneously Increased. 34

43 Entropy-Balance Entropy (S) balance: Change within System = input - output + production destruction Second law of thermodynamics Entropy can be be produced in an isolated system, or spontaneously Increased. 34

44 Exergy-Balances Exergy (Ex) balance: Change within System = input - output + production destruction Exergy (Ex) is also called availability (of work). E.g. from 1 ton of coal We could get a certain amount of electricity theoretically, this is The exergy of the coal. In reality we get much less, due to exergy Destruction or exergy loss due to the process. 35

45 Exergy-Balances Exergy (Ex) balance: Change within System = input - output + production destruction Exergy (Ex) is also called availability (of work). E.g. from 1 ton of coal We could get a certain amount of electricity theoretically, this is The exergy of the coal. In reality we get much less, due to exergy Destruction or exergy loss due to the process. 35

46 Money Balance: Money-Balance Change of Money in account = inflow expenses + money production - money destruction Typically there is no money production, exception money press of state. Also money destruction happens seldom, fortunately. Maybe if we loose a coin in sand dunes, we would like to count it as destruction. (Or loss?). Different kinds of money: interest, coins, ruble, dollar,... Also different kinds of energy (z.b. Internal energy U, Enthalpy H, Kinetic energy E_kin, Heat,... 36

47 Forms of Energy Energy Energy supply Energy content Work Heat Energy Internal Kinetic Potential Input Energy Energy Energy 37

48 Temperature measurement gas thermometer System homogeneous V=constant Atmospheric pressure p_out e.g. 1 bar V Fluid e.g. Hg or H 2 O gravity 38

49 Triple point of water Triple point of water: At p = 611,657 Pa and T= 273,16 K ( t = 0,01 C) water exists simultaneously in three phases: solid, liquid and gas Here T = K has been defined. Such natural occurring certain points have been used as fix points for Temperature scales. 39

50 Temperature Fix Points Definition: Absolute zero Triple point of water Zero Celsius scale = 0 K = K = K 40

51 Definition of Ideal Gas: Ideal Gas Large number of molecules or atoms (6*10^23) No interaction of individual molecules or atoms among themselves (pressure should be small) Molecules or atoms are to be considered small mass points The net volume of molecules or atoms should be small against the volume of the reference vessel Though molecules or atoms of an ideal gas need to have impact and exchange energy and momentum in order to establish a thermodynamic equilibrium (e.g. to show a Maxwell Boltzmann velocity distribution and an entropy maximum in an infinite period of time) the molecules and atoms must be very small in comparison to the total container volume, that is an infinitesimal limit. 41

52 Ideal Gas From experiments and statistical thermodynamics : Thermal state equation for ideal gases, in the molar form pv = n molecules kt p = Pressure in bar, V = Volume in m^3, n_molecules = Number of molecules, k = Boltzmann constant = 1.38E-23 J/K, T = Temperature in K, R_m = Universal Gas constant = J/(mol K), R-m applies for all ideal gases. 42

53 Ideal Gas L= Loschmidt number = 6.022* /mol (Avogadro-Number) From now on we will write n instead of just n_mole, n means number of moles. 43

54 Ideal Gas Thermal state equation of ideal gases in specific form: Ideal Gas equation M=Mol mass 44

55 Ideal Gas Examples of molecular weight (from the periodic table of elements): 45

56 Ideal Gas Examples of molecular weight (from the periodic table of elements): Why is it, that we find in the periodic table of elements M O = and M C = and not integer numbers? 46

57 Ideal Gas T This is a qualitative sketch like in literature. If we plot this eqn Quantitatively it looks like the one on the next slide. 47

58 Ideal Gas Quantitative plot T 48

59 pv = mrt! pv = RT! p " = RT! p = RT 1 v 49

60 Ideal Gas pv = mrt! pv = RT! p " = RT! p = RT 1 v 49

61 Ideal Gas Density pv = mrt! pv = RT! p " = RT! p = RT 1 v 49

62 Ideal Gas Density Specific Volume pv = mrt! pv = RT! p " = RT! p = RT 1 v 49

63 Ideal Gas pv = n R m T! pv m = R m T Molar Volume 50

64 Ideal Gas Mole volume at STP: STP = Standard Temperature Pressure at T= 0 C = K and p = 1 atm = bar V m = 22.4 m3 kmol Mole volume for all Ideal Gases at STP 51

65 52

66 Nominal definitions (not only for ideal gases) 52

67 Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: 52

68 Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: Isobaric = 52

69 Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: Isobaric = Isothermal = 52

70 Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: Isobaric = Isothermal = Isochoric = 52

71 1 2 heat bath T=const some gas Example for an isothermal process. The yellow gas expand and delivers work δw whereas its temperature is kept constant by a heat bath from which it gets heat δq. The process should be carried out very very slow aka quasi static. 53

72 Nominal definitions (not only for ideal gases) e.g. an isothermal process: 1 2 heat bath T=const some gas Example for an isothermal process. The yellow gas expand and delivers work δw whereas its temperature is kept constant by a heat bath from which it gets heat δq. The process should be carried out very very slow aka quasi static. 53

73 Ideal Gas: Caloric state equations The state of an ideal gas and other simple thermodynamic systems can be described exactly by only two intensive state variables e.g. (p,v), (p,t), (v,t), or (h,s) All other measurable quantities are dependent on these two quantities, like u(p,t), h(p,v), s(p,t). 54

74 Mathematics: The complete differential of a function of two variables : Let be: Ideal Gas: Caloric state equations " dz =!z # \$!x % & ' y " dx +!z % # \$!y& ' x dy Complete mathematical differential Notice: for total differential and for partial differential 55

75 Ideal Gas: Caloric state equations The internal energy U is a state variable. The eqn u = u(t,v) is called Caloric State Equations of ideal gases. In general it must be determined experimentally " du =!u # \$!T % & ' v " dt +!u # \$!v % & ' T dv Also applies for non-ideal gases Abbreviation: " c v =!u # \$!T % & ' v = specific heat capacity at constant volume 56

76 Four different heat capacities " C V =!U # \$!T % & ' V " c v =!u # \$!T % & ' v " C p =!H # \$!T % & ' p " c p =!h # \$!T % & ' p 57

77 Four different heat capacities " C V =!U # \$!T % & ' V = f (V,T ) ( ) * kj K +, - Absolute heat capacity C V with constant volume V [m 3 ] as partial derivation of the absolute internal energy U [kj] with respect to the temperature T. The result is a function of V and T. The dimension is kj/ K. 58

78 Four different heat capacities " c v =!u # \$!T % & ' v = f (v,t ) ( * ) kj kg * K + -, Specific heat capacity c v with constant volume as partial derivation of the specific internal energy u=u/m [kj/kg] (m = mass) with respect to the temperature T. The result is a function of v and T. The dimension is kj/(kg*k). v=v/m [m 3 /kg]. 59

79 Four different heat capacities " C p =!H # \$!T % & ' p = f (p,t ) ( ) * kj K +, - Absolute heat capacity C p with constant pressure p as partial derivation of the absolute enthalpy H [kj] with respect to the temperature T. The result is a function of p and T. The dimension is kj/k. The enthalpy is defined as H = U + pv or h = u + pv and will be explained in detail in connection to the first law with open systems. 60

80 Four different heat capacities " c p =!h # \$!T % & ' p = f (p,t ) ( * ) kj kg * K + -, Specific heat capacity c p with constant pressure p as partial derivation of the specific enthalpy h=h/m [kj/kg] (m = mass) with respect to the temperature T. The result is a function of p and T. The dimension is kj/(kg*k). 61

81 Meaning of c v : Ideal Gas: Caloric state equations " c v =!u # \$!T % & ' v = specific heat capacity at constant volume To see this better we invert the eqn to: 1 " =!T c v # \$!u % & ' v That means: 1/c v shows how much T is changing if we add a certain amount of specific energy u (kj/kg) to the system and keep the volume of the system constant. And from experience we know, if we add energy to wood it can not store energy as good as a metal like copper, and thus dt with wood would be larger than with copper. Thats the meaning of the heat capacity. 62

82 Ideal Gas: Caloric state equations Meaning of c v : " c v =!u # \$!T % & ' v = specific heat capacity at constant volume Warning: One might wrongly assume, that cv can be applied only to processes where v is constant. This is wrong, but erroneously written in some books. cv is a function of T and v and can be applied to all processes. It is only an abbreviation for the differential in oder to save writing work. 63

83 u Ideal Gas: Caloric state equations v 3 v 2 " c v =!u % # \$!T & ' v = c v (T 2,v 2 ) u 2 v 1 c v depends on T and v. T T 2 c v is a function of T and v, it changes it s value if we change the value of T or v. 64

84 Ideal Gas: Caloric state equations Note: is a material property and has no connection with a process that is being carried out. particularly for non-ideal gases 65

85 Ideal Gas: Caloric state equations particularly for non-ideal gases For ideal gases: Which is the exception from the general rule. 66

86 Ideal Gas: Caloric state equations #! du = c v dt + "u \$ % "v & ' ( T dv According to Gay-Lussac experiment, (GL experiment comes later) Caloric state equations of ideal gases In general for Ideal gas 67

87 Ideal Gas: Caloric state equations Note: this is wrong: With the caloric state equations, we get only energy differences. 68

88 Ideal Gas: Caloric state equations Specific Internal Energy difference Absolute Internal Energy difference 69

89 End of Chapter 2 ( Egon Hassel, 2009, Rome, Italy / 70

### Chapter 10 Temperature and Heat

Chapter 10 Temperature and Heat What are temperature and heat? Are they the same? What causes heat? What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its

### HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases

UNIT HEAT. KINETIC THEORY OF GASES.. Introduction Molecules have a diameter of the order of Å and the distance between them in a gas is 0 Å while the interaction distance in solids is very small. R. Clausius

### Gas Laws. The kinetic theory of matter states that particles which make up all types of matter are in constant motion.

Name Period Gas Laws Kinetic energy is the energy of motion of molecules. Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule is very far from other atoms or molecules.

### Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004

Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein

### The First Law of Thermodynamics

Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat Pumps The Carnot

### Exergy: the quality of energy N. Woudstra

Exergy: the quality of energy N. Woudstra Introduction Characteristic for our society is a massive consumption of goods and energy. Continuation of this way of life in the long term is only possible if

### THE KINETIC THEORY OF GASES

Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure

### Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

### CHAPTER 12. Gases and the Kinetic-Molecular Theory

CHAPTER 12 Gases and the Kinetic-Molecular Theory 1 Gases vs. Liquids & Solids Gases Weak interactions between molecules Molecules move rapidly Fast diffusion rates Low densities Easy to compress Liquids

### Problem Set 1 3.20 MIT Professor Gerbrand Ceder Fall 2003

LEVEL 1 PROBLEMS Problem Set 1 3.0 MIT Professor Gerbrand Ceder Fall 003 Problem 1.1 The internal energy per kg for a certain gas is given by U = 0. 17 T + C where U is in kj/kg, T is in Kelvin, and C

### Chapter 8 Maxwell relations and measurable properties

Chapter 8 Maxwell relations and measurable properties 8.1 Maxwell relations Other thermodynamic potentials emerging from Legendre transforms allow us to switch independent variables and give rise to alternate

### AS1 MOLES. oxygen molecules have the formula O 2 the relative mass will be 2 x 16 = 32 so the molar mass will be 32g mol -1

Moles 1 MOLES The mole the standard unit of amount of a substance the number of particles in a mole is known as Avogadro s constant (L) Avogadro s constant has a value of 6.023 x 10 23 mol -1. Example

### CLASSICAL CONCEPT REVIEW 8

CLASSICAL CONCEPT REVIEW 8 Kinetic Theory Information concerning the initial motions of each of the atoms of macroscopic systems is not accessible, nor do we have the computational capability even with

### Thermodynamics of Mixing

Thermodynamics of Mixing Dependence of Gibbs energy on mixture composition is G = n A µ A + n B µ B and at constant T and p, systems tend towards a lower Gibbs energy The simplest example of mixing: What

### FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

### Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.

.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations

### Thermodynamics AP Physics B. Multiple Choice Questions

Thermodynamics AP Physics B Name Multiple Choice Questions 1. What is the name of the following statement: When two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium

### F321 MOLES. Example If 1 atom has a mass of 1.241 x 10-23 g 1 mole of atoms will have a mass of 1.241 x 10-23 g x 6.02 x 10 23 = 7.

Moles 1 MOLES The mole the standard unit of amount of a substance (mol) the number of particles in a mole is known as Avogadro s constant (N A ) Avogadro s constant has a value of 6.02 x 10 23 mol -1.

### The final numerical answer given is correct but the math shown does not give that answer.

Note added to Homework set 7: The solution to Problem 16 has an error in it. The specific heat of water is listed as c 1 J/g K but should be c 4.186 J/g K The final numerical answer given is correct but

### 7. 1.00 atm = 760 torr = 760 mm Hg = 101.325 kpa = 14.70 psi. = 0.446 atm. = 0.993 atm. = 107 kpa 760 torr 1 atm 760 mm Hg = 790.

CHATER 3. The atmosphere is a homogeneous mixture (a solution) of gases.. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. have volumes that depend on their conditions,

### a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L

hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal

### = 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm

Chapter 13 Gases 1. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. Gases have volumes that depend on their conditions, and can be compressed or expanded by

### Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

### Problem Set 3 Solutions

Chemistry 360 Dr Jean M Standard Problem Set 3 Solutions 1 (a) One mole of an ideal gas at 98 K is expanded reversibly and isothermally from 10 L to 10 L Determine the amount of work in Joules We start

### Physics 5D - Nov 18, 2013

Physics 5D - Nov 18, 2013 30 Midterm Scores B } Number of Scores 25 20 15 10 5 F D C } A- A A + 0 0-59.9 60-64.9 65-69.9 70-74.9 75-79.9 80-84.9 Percent Range (%) The two problems with the fewest correct

### Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity

### We will try to get familiar with a heat pump, and try to determine its performance coefficient under different circumstances.

C4. Heat Pump I. OBJECTIVE OF THE EXPERIMENT We will try to get familiar with a heat pump, and try to determine its performance coefficient under different circumstances. II. INTRODUCTION II.1. Thermodynamic

### ES-7A Thermodynamics HW 1: 2-30, 32, 52, 75, 121, 125; 3-18, 24, 29, 88 Spring 2003 Page 1 of 6

Spring 2003 Page 1 of 6 2-30 Steam Tables Given: Property table for H 2 O Find: Complete the table. T ( C) P (kpa) h (kj/kg) x phase description a) 120.23 200 2046.03 0.7 saturated mixture b) 140 361.3

### Problem Set 4 Solutions

Chemistry 360 Dr Jean M Standard Problem Set 4 Solutions 1 Two moles of an ideal gas are compressed isothermally and reversibly at 98 K from 1 atm to 00 atm Calculate q, w, ΔU, and ΔH For an isothermal

### 1.4.6-1.4.8 Gas Laws. Heat and Temperature

1.4.6-1.4.8 Gas Laws Heat and Temperature Often the concepts of heat and temperature are thought to be the same, but they are not. Perhaps the reason the two are incorrectly thought to be the same is because

### Science Standard Articulated by Grade Level Strand 5: Physical Science

Concept 1: Properties of Objects and Materials Classify objects and materials by their observable properties. Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 PO 1. Identify the following observable properties

### Introduction to the Ideal Gas Law

Course PHYSICS260 Assignment 5 Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room temperature. It undergoes an isobaric expansion resulting in a quadrupling of its volume.

### Thermodynamics - Example Problems Problems and Solutions

Thermodynamics - Example Problems Problems and Solutions 1 Examining a Power Plant Consider a power plant. At point 1 the working gas has a temperature of T = 25 C. The pressure is 1bar and the mass flow

### Chapter 6 The first law and reversibility

Chapter 6 The first law and reversibility 6.1 The first law for processes in closed systems We have discussed the properties of equilibrium states and the relationship between the thermodynamic parameters

### Physics 176 Topics to Review For the Final Exam

Physics 176 Topics to Review For the Final Exam Professor Henry Greenside May, 011 Thermodynamic Concepts and Facts 1. Practical criteria for identifying when a macroscopic system is in thermodynamic equilibrium:

### Name Class Date. In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question.

Assessment Chapter Test A Chapter: States of Matter In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. The kinetic-molecular

### = 800 kg/m 3 (note that old units cancel out) 4.184 J 1000 g = 4184 J/kg o C

Units and Dimensions Basic properties such as length, mass, time and temperature that can be measured are called dimensions. Any quantity that can be measured has a value and a unit associated with it.

### Define the notations you are using properly. Present your arguments in details. Good luck!

Umeå Universitet, Fysik Vitaly Bychkov Prov i fysik, Thermodynamics, 0-0-4, kl 9.00-5.00 jälpmedel: Students may use any book(s) including the textbook Thermal physics. Minor notes in the books are also

### Thermochemistry. r2 d:\files\courses\1110-20\99heat&thermorans.doc. Ron Robertson

Thermochemistry r2 d:\files\courses\1110-20\99heat&thermorans.doc Ron Robertson I. What is Energy? A. Energy is a property of matter that allows work to be done B. Potential and Kinetic Potential energy

### Gases. States of Matter. Molecular Arrangement Solid Small Small Ordered Liquid Unity Unity Local Order Gas High Large Chaotic (random)

Gases States of Matter States of Matter Kinetic E (motion) Potential E(interaction) Distance Between (size) Molecular Arrangement Solid Small Small Ordered Liquid Unity Unity Local Order Gas High Large

### Kinetic Theory of Gases

Kinetic Theory of Gases Physics 1425 Lecture 31 Michael Fowler, UVa Bernoulli s Picture Daniel Bernoulli, in 1738, was the first to understand air pressure in terms of molecules he visualized them shooting

### Engineering Problem Solving as Model Building

Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving When we solve a problem

### The first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work.

The first law: transformation of energy into heat and work Chemical reactions can be used to provide heat and for doing work. Compare fuel value of different compounds. What drives these reactions to proceed

### Gases. Macroscopic Properties. Petrucci, Harwood and Herring: Chapter 6

Gases Petrucci, Harwood and Herring: Chapter 6 CHEM 1000A 3.0 Gases 1 We will be looking at Macroscopic and Microscopic properties: Macroscopic Properties of bulk gases Observable Pressure, volume, mass,

### High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

### CHEMISTRY GAS LAW S WORKSHEET

Boyle s Law Charles Law Guy-Lassac's Law Combined Gas Law For a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure PV = k The volume of a fixed mass of gas is

### Phys222 W11 Quiz 1: Chapters 19-21 Keys. Name:

Name:. In order for two objects to have the same temperature, they must a. be in thermal equilibrium.

### 39th International Physics Olympiad - Hanoi - Vietnam - 2008. Theoretical Problem No. 3

CHANGE OF AIR TEMPERATURE WITH ALTITUDE, ATMOSPHERIC STABILITY AND AIR POLLUTION Vertical motion of air governs many atmospheric processes, such as the formation of clouds and precipitation and the dispersal

### vap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K

Thermodynamics: Examples for chapter 6. 1. The boiling point of hexane at 1 atm is 68.7 C. What is the boiling point at 1 bar? The vapor pressure of hexane at 49.6 C is 53.32 kpa. Assume that the vapor

### There is no such thing as heat energy

There is no such thing as heat energy We have used heat only for the energy transferred between the objects at different temperatures, and thermal energy to describe the energy content of the objects.

### Chapter 6 Thermodynamics: The First Law

Key Concepts 6.1 Systems Chapter 6 Thermodynamics: The First Law Systems, States, and Energy (Sections 6.1 6.8) thermodynamics, statistical thermodynamics, system, surroundings, open system, closed system,

### Thermodynamics. Thermodynamics 1

Thermodynamics 1 Thermodynamics Some Important Topics First Law of Thermodynamics Internal Energy U ( or E) Enthalpy H Second Law of Thermodynamics Entropy S Third law of Thermodynamics Absolute Entropy

### CHEM 120 Online Chapter 7

CHEM 120 Online Chapter 7 Date: 1. Which of the following statements is not a part of kinetic molecular theory? A) Matter is composed of particles that are in constant motion. B) Particle velocity increases

### Lecture Notes: Gas Laws and Kinetic Molecular Theory (KMT).

CHEM110 Week 9 Notes (Gas Laws) Page 1 of 7 Lecture Notes: Gas Laws and Kinetic Molecular Theory (KMT). Gases Are mostly empty space Occupy containers uniformly and completely Expand infinitely Diffuse

### Final Exam CHM 3410, Dr. Mebel, Fall 2005

Final Exam CHM 3410, Dr. Mebel, Fall 2005 1. At -31.2 C, pure propane and n-butane have vapor pressures of 1200 and 200 Torr, respectively. (a) Calculate the mole fraction of propane in the liquid mixture

### The Mole. Chapter 10. Dimensional Analysis. The Mole. How much mass is in one atom of carbon-12? Molar Mass of Atoms 3/1/2015

The Mole Chapter 10 1 Objectives Use the mole and molar mass to make conversions among moles, mass, and number of particles Determine the percent composition of the components of a compound Calculate empirical

### Chemistry 13: States of Matter

Chemistry 13: States of Matter Name: Period: Date: Chemistry Content Standard: Gases and Their Properties The kinetic molecular theory describes the motion of atoms and molecules and explains the properties

### Chapter 10: Temperature and Heat

Chapter 10: Temperature and Heat 1. The temperature of a substance is A. proportional to the average kinetic energy of the molecules in a substance. B. equal to the kinetic energy of the fastest moving

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

### Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows

Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3.- 1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical

### CHAPTER 14 THE CLAUSIUS-CLAPEYRON EQUATION

CHAPTER 4 THE CAUIU-CAPEYRON EQUATION Before starting this chapter, it would probably be a good idea to re-read ections 9. and 9.3 of Chapter 9. The Clausius-Clapeyron equation relates the latent heat

### momentum change per impact The average rate of change of momentum = Time interval between successive impacts 2m x 2l / x m x m x 2 / l P = l 2 P = l 3

Kinetic Molecular Theory This explains the Ideal Gas Pressure olume and Temperature behavior It s based on following ideas:. Any ordinary sized or macroscopic sample of gas contains large number of molecules.

### Kinetic Theory & Ideal Gas

1 of 6 Thermodynamics Summer 2006 Kinetic Theory & Ideal Gas The study of thermodynamics usually starts with the concepts of temperature and heat, and most people feel that the temperature of an object

### Heterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi

Heterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi Module - 03 Lecture 10 Good morning. In my last lecture, I was

### THE IDEAL GAS LAW AND KINETIC THEORY

Chapter 14 he Ideal Gas Law and Kinetic heory Chapter 14 HE IDEAL GAS LAW AND KINEIC HEORY REIEW Kinetic molecular theory involves the study of matter, particularly gases, as very small particles in constant

### Chapter 7 Energy and Energy Balances

CBE14, Levicky Chapter 7 Energy and Energy Balances The concept of energy conservation as expressed by an energy balance equation is central to chemical engineering calculations. Similar to mass balances

### 5. Which temperature is equal to +20 K? 1) 253ºC 2) 293ºC 3) 253 C 4) 293 C

1. The average kinetic energy of water molecules increases when 1) H 2 O(s) changes to H 2 O( ) at 0ºC 3) H 2 O( ) at 10ºC changes to H 2 O( ) at 20ºC 2) H 2 O( ) changes to H 2 O(s) at 0ºC 4) H 2 O( )

### 18 Q0 a speed of 45.0 m/s away from a moving car. If the car is 8 Q0 moving towards the ambulance with a speed of 15.0 m/s, what Q0 frequency does a

First Major T-042 1 A transverse sinusoidal wave is traveling on a string with a 17 speed of 300 m/s. If the wave has a frequency of 100 Hz, what 9 is the phase difference between two particles on the

### Topic 3b: Kinetic Theory

Topic 3b: Kinetic Theory What is temperature? We have developed some statistical language to simplify describing measurements on physical systems. When we measure the temperature of a system, what underlying

### Temperature. Temperature

Chapter 8 Temperature Temperature a number that corresponds to the warmth or coldness of an object measured by a thermometer is a per-particle property no upper limit definite limit on lower end Temperature

### EXPERIMENT 15: Ideal Gas Law: Molecular Weight of a Vapor

EXPERIMENT 15: Ideal Gas Law: Molecular Weight of a Vapor Purpose: In this experiment you will use the ideal gas law to calculate the molecular weight of a volatile liquid compound by measuring the mass,

### Chemistry. The student will be able to identify and apply basic safety procedures and identify basic equipment.

Chemistry UNIT I: Introduction to Chemistry The student will be able to describe what chemistry is and its scope. a. Define chemistry. b. Explain that chemistry overlaps many other areas of science. The

### Diesel Cycle Analysis

Engineering Software P.O. Box 1180, Germantown, MD 20875 Phone: (301) 540-3605 FAX: (301) 540-3605 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Diesel Cycle Analysis Diesel Cycle

### Chapter 1 Classical Thermodynamics: The First Law. 1.2 The first law of thermodynamics. 1.3 Real and ideal gases: a review

Chapter 1 Classical Thermodynamics: The First Law 1.1 Introduction 1.2 The first law of thermodynamics 1.3 Real and ideal gases: a review 1.4 First law for cycles 1.5 Reversible processes 1.6 Work 1.7

### Module 5: Combustion Technology. Lecture 34: Calculation of calorific value of fuels

1 P age Module 5: Combustion Technology Lecture 34: Calculation of calorific value of fuels 2 P age Keywords : Gross calorific value, Net calorific value, enthalpy change, bomb calorimeter 5.3 Calculation

### DET: Mechanical Engineering Thermofluids (Higher)

DET: Mechanical Engineering Thermofluids (Higher) 6485 Spring 000 HIGHER STILL DET: Mechanical Engineering Thermofluids Higher Support Materials *+,-./ CONTENTS Section : Thermofluids (Higher) Student

### (1) The size of a gas particle is negligible as compared to the volume of the container in which the gas is placed.

Gas Laws and Kinetic Molecular Theory The Gas Laws are based on experiments, and they describe how a gas behaves under certain conditions. However, Gas Laws do not attempt to explain the behavior of gases.

### ME 201 Thermodynamics

ME 0 Thermodynamics Second Law Practice Problems. Ideally, which fluid can do more work: air at 600 psia and 600 F or steam at 600 psia and 600 F The maximum work a substance can do is given by its availablity.

### Thermodynamics. Chapter 13 Phase Diagrams. NC State University

Thermodynamics Chapter 13 Phase Diagrams NC State University Pressure (atm) Definition of a phase diagram A phase diagram is a representation of the states of matter, solid, liquid, or gas as a function

### 9460218_CH06_p069-080.qxd 1/20/10 9:44 PM Page 69 GAS PROPERTIES PURPOSE

9460218_CH06_p069-080.qxd 1/20/10 9:44 PM Page 69 6 GAS PROPERTIES PURPOSE The purpose of this lab is to investigate how properties of gases pressure, temperature, and volume are related. Also, you will

### Thermodynamics and Equilibrium

Chapter 19 Thermodynamics and Equilibrium Concept Check 19.1 You have a sample of 1.0 mg of solid iodine at room temperature. Later, you notice that the iodine has sublimed (passed into the vapor state).

### Gas Laws. vacuum. 760 mm. air pressure. mercury

Gas Laws Some chemical reactions take place in the gas phase and others produce products that are gases. We need a way to measure the quantity of compounds in a given volume of gas and relate that to moles.

### 1. The Kinetic Theory of Matter states that all matter is composed of atoms and molecules that are in a constant state of constant random motion

Physical Science Period: Name: ANSWER KEY Date: Practice Test for Unit 3: Ch. 3, and some of 15 and 16: Kinetic Theory of Matter, States of matter, and and thermodynamics, and gas laws. 1. The Kinetic

### A. Kinetic Molecular Theory (KMT) = the idea that particles of matter are always in motion and that this motion has consequences.

I. MOLECULES IN MOTION: A. Kinetic Molecular Theory (KMT) = the idea that particles of matter are always in motion and that this motion has consequences. 1) theory developed in the late 19 th century to

### Give all answers in MKS units: energy in Joules, pressure in Pascals, volume in m 3, etc. Only work the number of problems required. Chose wisely.

Chemistry 45/456 0 July, 007 Midterm Examination Professor G. Drobny Universal gas constant=r=8.3j/mole-k=0.08l-atm/mole-k Joule=J= Nt-m=kg-m /s 0J= L-atm. Pa=J/m 3 =N/m. atm=.0x0 5 Pa=.0 bar L=0-3 m 3.

### 6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated

Chapter 6 Concept Tests 6-1. In a gas of hydrogen atoms at room temperature, what is the ratio of atoms in the 1 st excited energy state (n=2) to atoms in the ground state(n=1). (Actually H forms H 2 molecules,

### Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

### Introduction to Chemistry. Course Description

CHM 1025 & CHM 1025L Introduction to Chemistry Course Description CHM 1025 Introduction to Chemistry (3) P CHM 1025L Introduction to Chemistry Laboratory (1) P This introductory course is intended to introduce

### The Second Law of Thermodynamics

Objectives MAE 320 - Chapter 6 The Second Law of Thermodynamics The content and the pictures are from the text book: Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill,

### Sound. References: L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol. 2, Gas Dynamics, Chapter 8

References: Sound L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol., Gas Dynamics, Chapter 8 1 Speed of sound The phenomenon of sound waves is one that

### DETERMINATION OF THE HEAT STORAGE CAPACITY OF PCM AND PCM-OBJECTS AS A FUNCTION OF TEMPERATURE. E. Günther, S. Hiebler, H. Mehling

DETERMINATION OF THE HEAT STORAGE CAPACITY OF PCM AND PCM-OBJECTS AS A FUNCTION OF TEMPERATURE E. Günther, S. Hiebler, H. Mehling Bavarian Center for Applied Energy Research (ZAE Bayern) Walther-Meißner-Str.

### ESSAY. Write your answer in the space provided or on a separate sheet of paper.

Test 1 General Chemistry CH116 Summer, 2012 University of Massachusetts, Boston Name ESSAY. Write your answer in the space provided or on a separate sheet of paper. 1) Sodium hydride reacts with excess

### STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE CHEM 150 - COLLEGE CHEMISTRY I

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE CHEM 150 - COLLEGE CHEMISTRY I PREPARED BY: NICOLE HELDT SCHOOL OF SCIENCE, HEALTH, AND PROFESSIONAL STUDIES SCIENCE DEPARTMENT

### Chapter 2 Classical Thermodynamics: The Second Law

Chapter 2 Classical hermodynamics: he Second Law 2.1 Heat engines and refrigerators 2.2 he second law of thermodynamics 2.3 Carnot cycles and Carnot engines 2.4* he thermodynamic temperature scale 2.5

### Chapter 7 : Simple Mixtures

Chapter 7 : Simple Mixtures Using the concept of chemical potential to describe the physical properties of a mixture. Outline 1)Partial Molar Quantities 2)Thermodynamics of Mixing 3)Chemical Potentials

### 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics

Chem 105 Fri 10-23-09 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics 10/23/2009 1 Please PICK UP your graded EXAM in front.

### Boyle s law - For calculating changes in pressure or volume: P 1 V 1 = P 2 V 2. Charles law - For calculating temperature or volume changes: V 1 T 1

Common Equations Used in Chemistry Equation for density: d= m v Converting F to C: C = ( F - 32) x 5 9 Converting C to F: F = C x 9 5 + 32 Converting C to K: K = ( C + 273.15) n x molar mass of element

### Chapter Test B. Chapter: Measurements and Calculations

Assessment Chapter Test B Chapter: Measurements and Calculations PART I In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1.