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 www.egonsthermosite.eu January 12, 2011 / 1
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
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
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
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
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
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
boundary Thermodynamic System V Cylinder, Closed System Mass flow A Mass flow B Heat exchange flow process, Open System heat loss 8
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
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
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
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
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
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
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
State and State Variable VI Molar state variables are defined as ratio of extensive state variable by mol-number (1 mol = 6.0236*10 23 molecules or atoms) (for homogeneous Systems) Molar Volume Molar Internal Energy Molar Entropy 16
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
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
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
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
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
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
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
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
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
Temperature measurement gas thermometer Atmospheric pressure p_out e.g. Fluid e.g. Hg or H2O lhs balance area rhs balance area 26
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
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
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Apple Balance 29
Apple Balance The Apple Balance: 29
Apple Balance The Apple Balance: System: System boundary: Control time: Collection of terms: what is important?: Result: 29
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Forms of Energy Energy Energy supply Energy content Work Heat Energy Internal Kinetic Potential Input Energy Energy Energy 37
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
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 = 273.16 K has been defined. Such natural occurring certain points have been used as fix points for Temperature scales. 39
Temperature Fix Points Definition: Absolute zero Triple point of water Zero Celsius scale = 0 K = 273.16 K = 273.15 K 40
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
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 = 8.314 J/(mol K), R-m applies for all ideal gases. 42
Ideal Gas L= Loschmidt number = 6.022*10 23 1/mol (Avogadro-Number) From now on we will write n instead of just n_mole, n means number of moles. 43
Ideal Gas Thermal state equation of ideal gases in specific form: Ideal Gas equation M=Mol mass 44
Ideal Gas Examples of molecular weight (from the periodic table of elements): 45
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 = 15.999 and M C = 12.01 and not integer numbers? 46
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
Ideal Gas Quantitative plot T 48
pv = mrt! pv = RT! p " = RT! p = RT 1 v 49
Ideal Gas pv = mrt! pv = RT! p " = RT! p = RT 1 v 49
Ideal Gas Density pv = mrt! pv = RT! p " = RT! p = RT 1 v 49
Ideal Gas Density Specific Volume pv = mrt! pv = RT! p " = RT! p = RT 1 v 49
Ideal Gas pv = n R m T! pv m = R m T Molar Volume 50
Ideal Gas Mole volume at STP: STP = Standard Temperature Pressure at T= 0 C = 273.15 K and p = 1 atm = 1.01325 bar V m = 22.4 m3 kmol Mole volume for all Ideal Gases at STP 51
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Nominal definitions (not only for ideal gases) 52
Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: 52
Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: Isobaric = 52
Nominal definitions (not only for ideal gases) In a process or state change from state 1 to state 2 we call: Isobaric = Isothermal = 52
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Ideal Gas: Caloric state equations particularly for non-ideal gases For ideal gases: Which is the exception from the general rule. 66
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
Ideal Gas: Caloric state equations Note: this is wrong: With the caloric state equations, we get only energy differences. 68
Ideal Gas: Caloric state equations Specific Internal Energy difference Absolute Internal Energy difference 69
End of Chapter 2 (www.egonsthermosite.eu) Egon Hassel, 2009, Rome, Italy / 70