PARTO PRELUDE: REVIEW OF UNIFIED ENGINEERING THERMODYNAMICS
PART 0 PRELUDE: REVIEW OF "UNIFIED ENGINEERING THERMODYNAMICS
PARTO- PRELUDE: REVIEW OF UNIFIED ENGINEERING THERMODYNAMICS [AW pp 2-22, 32-41(see IAW for detailed SB&vw references): VN Chapter 1] 0.1 What it's all about The focus of thermodynamics in 16.050 is on the production of work, often in the form of kinetic energy(for example in the exhaust of a jet engine)or shaft power, from different sources of heat. For the most part the heat will be the result of combustion processes, but this is not always the case. The course content can be viewed in terms of a"propulsion chain"as shown below, where we see a progression from an energy source to useful propulsive work(thrust power of a jet engine). In terms of the different blocks, the thermodynamics in Unified Engineering and in this course are mainly about how to progress from the second block to the third, but there is some examination of the pro esented by the other arrows as well. The course content, objectives, and lecture outline are described in detail in handout #1 Energy source Heat Mechanical Useful propulsive chemical (combustion work rk(thrust nuclear. etc process) electric power→·| power) 0.2 Definitions and Fundamental Ideas of Thermodynamics As with all sciences, thermodynamics is concerned with the mathematical modeling of the real world. In order that the mathematical deductions are consistent, we need some precise definitions of the basic concepts A continuum is a smoothed-out model of matter neglecting the fact that real substances are composed of discrete molecules. Classical thermodynamics is concerned only with continua. If statistical mechanics and kinetic theor? we wish to describe the properties of matter at a molecular level, we must use the techniques of a closed system is a fixed quantity of matter around which we can draw a boundary. Everything outside the boundary is the surroundings. Matter cannot cross the boundary of a closed system and hence the principle of the conservation of mass is automatically satisfied whenever we employ a closed system analysis The thermodynamic state of a system is defined by the value of certain properties of that system For fluid systems, typical properties are pressure, volume and temperature. More complex systems batte require the specification of more unusual properties. As an example, the state of an electric battery requires the specification of the amount of electric charge it contains Properties may be extensive or intensive. Extensive properties are additive. Thus, if the system is divided into a number of sub-systems, the value of the property for the whole system is equal to the sum of the values for the parts. Volume is an extensive property. Intensive properties do not depend on the quantity of matter present. Temperature and pressure are intensive properties. Specific properties are extensive properties per unit mass and are denoted by For example specific volume=Wm=ν 0-1
0-1 PART 0 - PRELUDE: REVIEW OF “UNIFIED ENGINEERING THERMODYNAMICS” [IAW pp 2-22, 32-41 (see IAW for detailed SB&VW references); VN Chapter 1] 0.1 What it’s All About The focus of thermodynamics in 16.050 is on the production of work, often in the form of kinetic energy (for example in the exhaust of a jet engine) or shaft power, from different sources of heat. For the most part the heat will be the result of combustion processes, but this is not always the case. The course content can be viewed in terms of a “propulsion chain” as shown below, where we see a progression from an energy source to useful propulsive work (thrust power of a jet engine). In terms of the different blocks, the thermodynamics in Unified Engineering and in this course are mainly about how to progress from the second block to the third, but there is some examination of the processes represented by the other arrows as well. The course content, objectives, and lecture outline are described in detail in Handout #1. 0.2 Definitions and Fundamental Ideas of Thermodynamics As with all sciences, thermodynamics is concerned with the mathematical modeling of the real world. In order that the mathematical deductions are consistent, we need some precise definitions of the basic concepts. A continuum is a smoothed-out model of matter, neglecting the fact that real substances are composed of discrete molecules. Classical thermodynamics is concerned only with continua. If we wish to describe the properties of matter at a molecular level, we must use the techniques of statistical mechanics and kinetic theory. A closed system is a fixed quantity of matter around which we can draw a boundary. Everything outside the boundary is the surroundings. Matter cannot cross the boundary of a closed system and hence the principle of the conservation of mass is automatically satisfied whenever we employ a closed system analysis. The thermodynamic state of a system is defined by the value of certain properties of that system. For fluid systems, typical properties are pressure, volume and temperature. More complex systems may require the specification of more unusual properties. As an example, the state of an electric battery requires the specification of the amount of electric charge it contains. Properties may be extensive or intensive. Extensive properties are additive. Thus, if the system is divided into a number of sub-systems, the value of the property for the whole system is equal to the sum of the values for the parts. Volume is an extensive property. Intensive properties do not depend on the quantity of matter present. Temperature and pressure are intensive properties. Specific properties are extensive properties per unit mass and are denoted by lower case letters. For example: specific volume = V/m = v. Energy source chemical nuclear, etc. Heat (combustion process) Mechanical work, electric power... Useful propulsive work (thrust power)
Specific properties are intensive because they do not depend on the mass of the system a simple system is a system having uniform properties throughout. In general, however, Sub-dividing it(either conceptually or in practice)into a number of simple systems in each of oy properties can vary from point to point in a system. We can usually analyze a general system which the properties are assumed to be uniform If the state of a system changes, then it is undergoing a process. The succession of states through which the system passes defines the path of the process. If, at the end of the process, the properties have returned to their original values, the system has undergone a cyclic process. Note that although the system has returned to its original state, the state of the surroundings may have Muddy points Specific properties(MP o1 What is the difference between extensive and intensive properties?(MP 0. 2) 0.3 Review of Thermodynamic Concepts The following is a brief discussion of some of the concepts introduced in Unified Engineering, which we will need in 16.050. Several of these will be further amplified in the lectures and in other handouts. If you need additional information or examples concerning these topics, they are described clearly and in-depth in the Unified Notes of Professor Waitz, where detailed references to the relevant sections of the text(sB& vw) are given. They are also covered although in a less detailed manner, in Chapters I and 2 of the book by Van Ness 1)Thermodynamics can be regarded as a generalization of an enormous body of empirical evidence. It is extremely general, and there are no hypotheses made concerning the structure and type of matter that we deal with. 2)Thermodynamic system a quantity of matter of fixed identity. Work or heat(see below) can be transferred across the system boundary, but mass cannot. Gas Fluid 3)Thermodynamic properties: For engineering purposes, we want averaged"information, i.e., macroscopic not microscopic(molecular) description.(Knowing the position and velocity of each of 1020+ molecules that we meet in typical engineering applications is generally not useful. 4) The thermodynamic state is defined by specifying values of a(small) set of measured properties which are sufficient to determine all the remaining properties 0-2
0-2 Specific properties are intensive because they do not depend on the mass of the system, A simple system is a system having uniform properties throughout. In general, however, properties can vary from point to point in a system. We can usually analyze a general system by sub-dividing it (either conceptually or in practice) into a number of simple systems in each of which the properties are assumed to be uniform. If the state of a system changes, then it is undergoing a process. The succession of states through which the system passes defines the path of the process. If, at the end of the process, the properties have returned to their original values, the system has undergone a cyclic process. Note that although the system has returned to its original state, the state of the surroundings may have changed. Muddy points Specific properties (MP 0.1) What is the difference between extensive and intensive properties? (MP 0.2) 0.3 Review of Thermodynamic Concepts The following is a brief discussion of some of the concepts introduced in Unified Engineering, which we will need in 16.050. Several of these will be further amplified in the lectures and in other handouts. If you need additional information or examples concerning these topics, they are described clearly and in-depth in the Unified Notes of Professor Waitz, where detailed references to the relevant sections of the text (SB&VW) are given. They are also covered, although in a less detailed manner, in Chapters 1 and 2 of the book by Van Ness. 1) Thermodynamics can be regarded as a generalization of an enormous body of empirical evidence. It is extremely general, and there are no hypotheses made concerning the structure and type of matter that we deal with. 2) Thermodynamic system : A quantity of matter of fixed identity. Work or heat (see below) can be transferred across the system boundary, but mass cannot. Gas, Fluid System Boundary 3) Thermodynamic properties : For engineering purposes, we want "averaged" information, i.e., macroscopic not microscopic (molecular) description. (Knowing the position and velocity of each of 1020+ molecules that we meet in typical engineering applications is generally not useful.) 4) State of a system : The thermodynamic state is defined by specifying values of a (small) set of measured properties which are sufficient to determine all the remaining properties
5) Equilibrium The state of a system in which properties have definite(unchanged) values as lon external conditions are unchanged is called an equilibrium state. Properties(P, pressure T temperature, p, density) describe states only when the system is in equilibrium Mechanical Equilibrium Thermal Equilibrium T1 Gas at Copper Partition Mg +PoA=PA Pressure,P Over time,T1→T 6) Equations of state: the stan for a simple compressible substance(e.g. air, water)we need to know two properties to set P=P(v, T, or v=v(P, T, or T= T(P, v) where v is the volume per unit mass, 1/p that are typically of interest for aerospace applications /s. proximation to real gases at conditong s Any of these is equivalent to an equation f(P, v, T=0 which is known as an equation of state equation of state for an ideal gas, which is a very good RT, where v is the volume per mol of gas and r is the "Universal Gas Constant",8.31 k/kmol-K A form of this equation which is more useful in fluid flow problems is obtained if we divide by the molecular weight, M Py=RT or P= OrT where r is r/M. which has a different value for different gases For air at room conditions.r is 0.287 kJ/kg-K 7) Quasi-equilibrium processes: A system in thermodynamic equilibrium satisfies: a)mechanical equilibrium(no unbalanced forces) b)thermal equilibrium(no temperature differences) c)chemical equilibrium For a finite, unbalanced force, the system can pass through non-equilibrium states. We wish to describe processes using thermodynamic coordinates, so we cannot treat situations in which such imbalances exist. An extremely useful idealization, however, is that only infinitesimal unbalanced forces exist, so that the process can be viewed as taking place in a series of"quas equilibrium"states. (The term quasi can be taken to mean"as if you will see it used in a number of contexts such as quasi-one-dimensional, quasi-steady, etc. For this to be true the process must be slow in relation to the time needed for the system to come to equilibrium internally. For 0-3
0-3 5) Equilibrium : The state of a system in which properties have definite (unchanged) values as long as external conditions are unchanged is called an equilibrium state. Properties (P, pressure, T, temperature, ρ, density) describe states only when the system is in equilibrium. Mg + P oA = PA Gas at Pressure, P Mass Mechanical Equilibrium Po Insulation Copper Partition Thermal Equilibrium Gas T1 Over time, T1 → T2 Gas T2 6) Equations of state: For a simple compressible substance (e.g., air, water) we need to know two properties to set the state. Thus: P = P(v,T), or v = v(P, T), or T = T(P,v) where v is the volume per unit mass, 1/ρ. Any of these is equivalent to an equation f(P,v,T) = 0 which is known as an equation of state. The equation of state for an ideal gas, which is a very good approximation to real gases at conditions that are typically of interest for aerospace applications is: Pv– = RT, where v – is the volume per mol of gas and R is the "Universal Gas Constant", 8.31 kJ/kmol-K. A form of this equation which is more useful in fluid flow problems is obtained if we divide by the molecular weight, M: Pv = RT, or P = ρRT where R is R/M, which has a different value for different gases. For air at room conditions, R is 0.287 kJ/kg-K. 7) Quasi-equilibrium processes: A system in thermodynamic equilibrium satisfies: a) mechanical equilibrium (no unbalanced forces) b) thermal equilibrium (no temperature differences) c) chemical equilibrium. For a finite, unbalanced force, the system can pass through non-equilibrium states. We wish to describe processes using thermodynamic coordinates, so we cannot treat situations in which such imbalances exist. An extremely useful idealization, however, is that only "infinitesimal" unbalanced forces exist, so that the process can be viewed as taking place in a series of "quasiequilibrium" states. (The term quasi can be taken to mean "as if"; you will see it used in a number of contexts such as quasi-one-dimensional, quasi-steady, etc.) For this to be true the process must be slow in relation to the time needed for the system to come to equilibrium internally. For a gas
at conditions of interest to us, a given molecule can undergo roughly 10 molecular collisions per second, so that, if ten collisions are needed to come to equilibrium, the equilibration time is on the order of 10-9 seconds. This is generally much shorter than the time scales associated with the bulk properties of the flow(say the time needed for a fluid particle to move some significant fraction of the lighten of the device of interest). Over a large range of parameters, therefore, it is a very good approximation to view the thermodynamic processes as consisting of such a succession of equilibrium states 8)Reversible process For a simple compressible substance Work If we look at a simple system, for example a cylinder of gas and a piston, we see that there can be two pressures, Ps, the system pressure and Px, the external pressure The work done by the system on the environment is Work=Pdv This can only be related to the system properties if Px=Ps. For this to occur, there cannot be any friction, and the process must also be slow enough so that pressure differences due to accelerations are not significant P with friction ∫PxdV≠0 but jPs dV=0 Work during an irreversible Under these conditions, we say that the process is reversible. The conditions for reversibility are a) If the process is reversed, the system and the surroundings will be returned to the b) To reverse the process we need to apply only an infinitesimal dP. a reversible process can be altered in direction by infinitesimal changes in the external conditions (see Van Ness, Chapter 2) 9)Work For simple compressible substances in reversible processes, the work done by the system on the environment is PdV. This can be represented as the area under a curve in a Pressure volume diagram 0-4
0-4 at conditions of interest to us, a given molecule can undergo roughly 1010 molecular collisions per second, so that, if ten collisions are needed to come to equilibrium, the equilibration time is on the order of 10-9 seconds. This is generally much shorter than the time scales associated with the bulk properties of the flow (say the time needed for a fluid particle to move some significant fraction of the lighten of the device of interest). Over a large range of parameters, therefore, it is a very good approximation to view the thermodynamic processes as consisting of such a succession of equilibrium states. 8) Reversible process For a simple compressible substance, Work = ∫PdV. If we look at a simple system, for example a cylinder of gas and a piston, we see that there can be two pressures, Ps, the system pressure and Px, the external pressure. Ps Px The work done by the system on the environment is Work = ∫PxdV. This can only be related to the system properties if Px ≈ Ps. For this to occur, there cannot be any friction, and the process must also be slow enough so that pressure differences due to accelerations are not significant. Work during an irreversible process ≠ ∫Ps dV ∫PxdV ≠ 0 but ∫Ps dV = 0 Ps (V) Px with friction P Vs ➀ ➀ ➀ ➁ ➁ Under these conditions, we say that the process is reversible. The conditions for reversibility are that: a) If the process is reversed, the system and the surroundings will be returned to the original states. b) To reverse the process we need to apply only an infinitesimal dP. A reversible process can be altered in direction by infinitesimal changes in the external conditions (see Van Ness, Chapter 2). 9) Work: For simple compressible substances in reversible processes , the work done by the system on the environment is ∫PdV. This can be represented as the area under a curve in a Pressurevolume diagram: