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Thermodynamics 4.1 – key points • No matter can cross the boundary of a closed system. • In an open system, matter can flow into or out of the system across parts of the boundary which are imaginary or permeable. • The matter contained within or flowing through a system can be referred to as the working fluid regardless of whether it is a gas, liquid or vapour. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.1 – key points • A property of a system can be a characteristic defining something particular to the system, such as its volume, or it can be a property of the working fluid. • Pressure is defined as the force exerted per unit area at a boundary. • Usually, absolute pressure values are required for calculations and this is referred to simply as pressure, without the absolute. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.1 – key points • Values of temperature (T) may be presented in more than one unit, either in degrees Celsius or degrees Kelvin, but remember that the SI unit of temperature is the kelvin. • If the values of enough properties of a system can be determined through measurements or calculation to allow the values of all others to be found, the state of the system is defined. • When the state of a system or the working fluid passing through a system changes, it is said to undergo a process. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.1 – key points • During some processes, the states in between will also be states of thermodynamic equilibrium. This type of process is reversible: the changes in the system state can be defined exactly and reversed to restore the initial conditions in the system and the surroundings. • All other processes are irreversible (a common cause of irreversibility is the generation of kinetic energy in fluids and gases). Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.1 – key points • If a closed system undergoes a series of processes such that the initial and final states of the system are the same, the system has undergone a cycle. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.1 Learning summary By the end of this section you will: • • • Unit 4 be familiar with and understand the key terms and definitions given in this section. They are shown in bold. The terminology is used throughout the following sections in the presentation of subjects. be familiar with the properties, nomenclature and units introduced here. Some or all of these properties feature strongly in any thermodynamic analysis. Take care to identify the correct units to use in calculations: if in doubt, use SI units and absolute values of pressures and temperatures. have learned to sketch processes on process or state diagrams to aid understanding, and note given values of properties or other defining information on these. This summarizes information in a concise and useful form. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 – key points • According to the convention adopted, transfers of energy to the system from the surroundings are positive. • When a closed system is taken through a cycle, the sum of the net work transfer and the net heat transfer is zero. V W p dV V1 Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 – key points • When using the following equation, if p is taken to be system pressure, the process must be reversible, because otherwise the pressure cannot be defined. V W p dV V1 Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 – key points • The change in internal energy of a closed system is equal to the sum of the heat transferred and the work done during any change of state. • The internal energy of a closed system remains unchanged if the system is thermally isolated from its surroundings. • Work W and heat transfer Q are not properties, but it is sometimes convenient to consider quantities of work and heat transfer per unit mass of matter in the system. These are described as specific work w and specific heat transfer q and have units of J kg-1. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 – key points • The change in internal energy of a closed system is equal to the sum of the heat transferred and the work done during any change of state. • The internal energy of a closed system remains unchanged if the system is thermally isolated from its surroundings. • Work W and heat transfer Q are not properties, but it is sometimes convenient to consider quantities of work and heat transfer per unit mass of matter in the system. These are described as specific work w and specific heat transfer q and have units of J kg-1. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 Learning summary By the end of this section you will know: • Work and heat transfer are the means by which energy can be transferred across the boundary of a closed system. These are not properties of the system. Our convention is that work or heat transfer to the system will be positive. • The first law of thermodynamics embodies the principle of conservation of energy. When applied to a closed system undergoing a cycle, there is no net transfer of energy into or out of the system over the cycle, nor is there any net change in the energy stored in the system. • When a closed system undergoes a process that changes its state from state 1 to state 2, energy transfer by work or heat transfer will raise or lower the internal energy of the system.Changes in other forms of energy will usually be negligible. (continued...) Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.2 Learning summary By the end of this section you will know: • Two important results from the application of the first law of thermodynamics to a closed system are that, when applied to a closed system undergoing a cycle, Wnet Qnet 0 • and, when applied to a closed system undergoing a process 1–2, W12 Q12 U 2 U1 Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 – key points • No heat engine can produce a net amount of work output while exchanging heat with a single reservoir only. • A heat engine is any device or system designed to convert heat into work output through a cycle of processes; it must have at least one prime mover, one source of heat transfer to the heat engine and one sink of heat transfer from the heat engine. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 – key points • The first Carnot principle is that all reversible heat engines operating on any cycle between the same two reservoirs will have efficiency equal to: carnot 1 T2 T1 where is the Carnot efficiency, and temperatures T1 and T2 are the absolute temperatures, in kelvin, of the heat reservoirs. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 – key points • The second Carnot principle is that the efficiency of a heat engine operating between two reservoirs will be less than the Carnot efficiency if the heat engine is irreversible. • The efficiency of any heat engine, reversible or irreversible, will be less than the Carnot efficiency if it operates between more than two heat reservoirs. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 – key points • The Clausius inequality states that for any reversible heat engine (or closed system undergoing a reversible cycle), the integral around the cycle of dQ/T vwill be zero; for all irreversible heat engines (or closed systems undergoing an irreversible cycle), this integral will be negative. Unit 4 dQ 0 T An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 – key points • Entropy is created during an irreversible process. • It is impossible to construct a system which will operate in a cycle, extract heat from a reservoir, and do an equivalent amount of work on the surroundings. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 Learning summary By the end of this section you will know: • that the second law of thermodynamics distinguishes between work and heat transfer and recognizes that work transfer is the more valuable of these. This does not contradict the first law; energy transferred by one is indistinguishable from energy transferred by the other, and the principle of energy conservation is not violated. There are, however, limits on how efficiently heat can be drawn from a source and converted into work output using a system which operates in a cycle. (continued...) Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 Learning summary By the end of this section you will know: • As a consequence of the second law, a system operating in a cycle and producing work output must be exchanging heat with at least two reservoirs at different temperatures. If a system is operating in a cycle while exchanging heat with only one reservoir, if a net transfer of work occurs it must be to the system. Work can be converted continuously and completely into heat, but heat cannot be converted completely and continuously into work. The efficiency of a heat engine designed to produce a net work output is defined as net work output W heat supplied Q1 (continued...) Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 Learning summary By the end of this section you will know: • • Note that it is the heat supplied that we are trying to convert to work output, not the net heat transfer. Efficiency is the measure of success in achieving this. The highest possible efficiency that can be achieved is the Carnot efficiency: carnot 1 • T2 T1 The existence of entropy is a corollary of the second law. It is important to remember that entropy is a property, like pressure or temperature, but also that it provides a measure of order and irreversibility. It is not conserved, like mass of energy, and the entropy of the Universe is increasing continuously as the result of the myriad irreversible processes taking place: an implication of the Clausius inequality is that entropy is created during an irreversible process; this may result in an increase in entropy of the system and/or of the surroundings. (continued...) Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.3 Learning summary By the end of this section you will know: • Unit 4 Entropy can only be transferred across the boundary of a closed system with heat transfer, not work transfer. If no heat transfer takes place, the entropy within a closed system remains constant during reversible processes and increases during irreversible processes. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.4 – key points • The processes undergone in open systems are flow processes. • For steady flow through an open system which has fixed boundaries, the quantities of matter and energy within the system boundaries are each constant and do not change with time. • Under steady flow conditions, there will be mass flow continuity. • The heat transferred per unit mass (q) is equal to: Q m Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.4 – key points • the work transferred per unit mass (w) is equal to: W m Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.4 Learning summary By the end of this section you will know: • • Open systems have parts of their boundary which matter can cross. The matter passing through an open system undergoes a flow process. Under steady flow conditions, matter enters and leaves the system at the same mass flowrate and the mass of matter in the system remains constant. The analysis of steady flows through open systems is based on the mass flow continuity equation: m m inlets Unit 4 outlets c22 c12 Q W m h2 h1 gz2 gz1 2 2 • and the SFEE • These equations apply to both reversible and irreversible flow processes. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.4 Learning summary By the end of this section you will know: • • Specific enthalpy h is a property defined as the combination of properties (u + pv). This combination appears as a natural grouping in the steady flow equation, and others, including results which apply to closed system problems. Enthalpy and specific enthalpy have the units of energy (J) or specific energy (J kg-1) respectively, but these have no independent physical meaning and enthalpy can be considered to have been invented as a convenience rather than discovered. The specific work done during any, reversible or irreversible, steady flow process can be determined using the SFEE if the remaining terms have known values. In the restricted case of a reversible flow process in which kinetic energy and potential energy changes can be neglected, the specific work can also be determined from: 2 w v dp 1 Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.4 Learning summary By the end of this section you will know: • Students must be careful not to confuse this with the corresponding result for specific work done during a reversible process on a closed system: 2 w p dv 1 Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.5 – key points • R is the universal gas constant (=8.3145 x 103 J kmol-1 K-1). m is the molar mass (kg kmol-1) of the gas; this is numerically equal to the molecular weight of the gas. Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.5 Learning summary By the end of this section you will know: • The working fluids commonly used in thermodynamic systems are gases and condensable vapours which may change phase at conditions of interest. The behaviour of working fluids must be understood as part of the analysis of system behaviour. This requires knowledge of the properties which distinguish one working fluid from another, and models of behaviour which define how the working fluid will respond to changes in state. • The behaviour of air and many other gases used in engineering thermodynamic systems can be modelled as that of a perfect gas. A perfect gas obeys the perfect gas equation pv = mRT • This is the equation of state of the gas. In addition, the specific heats of a perfect gas are constants which do not change as temperature or pressure changes. (Continued...) Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.5 Learning summary By the end of this section you will know: • Unit 4 Water is the example of a condensable vapour covered in this section. The equation of state is more complex than the perfect gas equation and usually evaluated using a computer. Results are presented in tables in (Rogers and Mayhew, 1995). An Introduction to Mechanical Engineering: Part One Thermodynamics 4.6 – key points • A polytropic process is one which obeys the polytropic law , in which n is a constant called the polytropic index. • An adiabatic process is one during which no heat transfer occurs. A reversible adiabatic process will be isentropic: no entropy is created if the process is reversible and none can be transferred to or from the system if no heat transfer occurs. For a perfect gas, reversible adiabatic and isentropic processes will obey the same polytropic law with n Unit 4 An Introduction to Mechanical Engineering: Part One Thermodynamics 4.6 Learning summary By the end of this section you will know: • • the common types of process described in this section and the conditions which apply in each case. The names of the processes are independent of the working fluid: perfect gases and steam can undergo an isothermal process or an isentropic process, etc. For a polytropic process the relationship between pressure and volume changes is fixed by the definition as p1v1n p2 v2n • • Unit 4 In general, however, changes in property values which occur when a working fluid under goes a process depend on the type of process and the characteristics of the working fluid; these are different for a perfect gas and steam. The work done during reversible processes is different for closed and open systems. The results for a perfect gas are summarized in Table 4.8. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.7 Learning summary By the end of this section you will know: • • Unit 4 The modes and processes that control rates of heat transfer have been introduced in this section. The three fundamental modes of heat transfer are conduction, convection and radiation. Heat conduction is the prime mode of heat transfer in solids; convection is usually the dominant mode of heat transport in liquids and gases. Radiation is the only mode which transmits energy through a vacuum and is likely to be the dominant mode of heat transfer from surfaces at high temperatures (>103 K). Heat conduction in a solid is governed by Fourier’s law and the thermal conductivity of the material. Convective heat transfer to or from a surface is governed by Newton’s law of cooling. Heat transfer coefficient is often taken to be a constant for a particular problem although its value may depend on fluid properties, flow conditions and surface geometry. At moderate temperatures and temperature differences between bodies, the effective radiative heat transfer coefficient can be added to the convective heat transfer coefficient. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.7 Learning summary By the end of this section you will know: • Unit 4 Solids and surfaces offer a thermal resistance to heat transfer. Under conditions of steady heat transfer through several layers and surfaces in series, the overall thermal resistance can be determined from the thermal resistances of each layer and surface. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.8 Learning summary By the end of this section you will know: • • • Unit 4 The cycles analysed in this section are ideal, thermodynamic cycles. These provide insights to the types of cycle used to generate mechanical power. No cycle can have a higher efficiency than the Carnot efficiency, but the ideal Stirling and Ericsson cycles achieve an efficiency value equal to this. In these cycles, heat transfer at temperatures between the maximum and minimum available takes place internally, through regeneration. External heat transfer across system boundaries occurs isothermally and only at these maximum and minimum temperatures, meeting conditions for the Carnot efficiency to be achieved. The Rankine cycle with superheat is the basis for a practical cycle for the generation of power output using steam as the working fluid. The cycle is less efficient than the Carnot cycle because heat supply takes place over a range of temperatures rather than the maximum possible. An Introduction to Mechanical Engineering: Part One Thermodynamics 4.8 Learning summary By the end of this section you will know: • • Unit 4 The efficiencies of the Brayton, Otto and Diesel cycles depend on the ratio of specific heats and the pressure ratio (Brayton cycle), compression ratio (Otto cycle) or compression ratio and cut-off ratio (Diesel cycle). There is no need to remember the particular results for these cycles, but students should understand how these are derived. There are similarities between the ideal thermodynamic cycles and real engine and power plant cycles. Plant and engines operating on the Stirling, Ericsson and Rankine cycles have external heat supply and heat rejection and the working fluids do undergo continuous thermodynamic cycles. Differences between the ideal and the real cycles are more marked for internal combustion engines. In these, fuel is burned within the working fluid, changing its composition as well as releasing chemical energy. The working fluid is replaced during successive cycles of the machine, so internal combustion engines such as gas turbines and reciprocating internal combustion engines do not operate on true thermodynamic cycles, but on a machine cycles. An Introduction to Mechanical Engineering: Part One