where c denotes the velocity of the system relative to some fixed reference energy The energy that a system possesses as a result of its elevation in the gravitational field is called potential energy, denoted as E,, and is expressed as where g is the gravitational acceleration and is the elevation of the center of gravity of a system elative to some arbitrarily selected reference level Both c and are independent of the state of the system. Thus, Ek ande, are irrelevant to 2.1.3 Total Energy and Energy Change of a System In the absence of electric, magnetic, and surface tension effects (i.e, for simple compressible systems) the total energy of a system consists of kinetic, potential, and internal energies and is expressed as E=U+-mc-+mg- (2-1b) On a unit mass basis, the total energy is denoted as e and has the unit J/kg or kJ/kg, that is (2-Ic) The value of a property does not change unless the state of the system changes. Therefore, the energy change of a system is zero if the state of the system does not change during the process. also the change in the total energy of a simple compressible system during a process is the sum of the changes in its internal, kinetic, and potential energies and can be expressed as △E=△U+AEk+AEQ Most systems encountered in practice are stationary, that is, they do not involve any changes in their velocity or elevation during a process. It means the changes in kinetic and potential energies are zero(that is, AEk, AE,=0)for stationary systems. And the total energy and its change reduces to E=U or e=u AE=△Uor△e=△ 2.2 Energy Transfer by Heat, Work or Mass Mass and energy can cross the boundary to fulfill energy transfer and transformation. Generally energy crosses the boundary in the form of heat or work 2.2. 1 Energy Transfer by Heat and by Work (1) Energy transfer by heat
26 where c denotes the velocity of the system relative to some fixed reference. (2) Potential energy The energy that a system possesses as a result of its elevation in the gravitational field is called potential energy, denoted as E p , and is expressed as E = mgz p where g is the gravitational acceleration and z is the elevation of the center of gravity of a system relative to some arbitrarily selected reference level. Both c and z are independent of the state of the system. Thus, Ek and E p are irrelevant to the state of the system. 2.1.3 Total Energy and Energy Change of a System In the absence of electric, magnetic, and surface tension effects (i.e., for simple compressible systems), the total energy of a system consists of kinetic, potential, and internal energies and is expressed as E =U + Ek + Ep (2-1a) or E = U + mc + mgz 2 2 1 (2-1b) On a unit mass basis, the total energy is denoted as e and has the unit J/kg or kJ/kg, that is e = u + c + gz 2 2 1 (2-1c) The value of a property does not change unless the state of the system changes. Therefore, the energy change of a system is zero if the state of the system does not change during the process. Also, the change in the total energy of a simple compressible system during a process is the sum of the changes in its internal, kinetic, and potential energies and can be expressed as E = U + Ek + Ep Most systems encountered in practice are stationary, that is, they do not involve any changes in their velocity or elevation during a process. It means the changes in kinetic and potential energies are zero (that is, k p E ,E = 0) for stationary systems. And the total energy and its change reduces to E =U or e = u E = U or e = u for such systems. 2.2 Energy Transfer by Heat, Work or Mass Mass and energy can cross the boundary to fulfill energy transfer and transformation. Generally, energy crosses the boundary in the form of heat or work. 2.2.1 Energy Transfer by Heat and by Work （1） Energy transfer by heat
Heat is defined as the form of energy that is transferred between two systems(or a system and its surro SURROUNDING HEAT That is, an energy interaction is heat only if it takes place because of a temperature difference. Once the temperature equality is established, energy transfer BAKED POTATO heat stops. It means that there cannot be any heat transfer System between two systems that are at the same Heat is n transition. It contains energy, but this energy is transfer only as it ansfer only as it crosses the passes through the system boundary to reach its boundary surroundings, as shown in Fig 2-1. Once in the surroundings, the transferred heat becomes part of the internal energy of the surroundings. Thus, in thermodynamics, the term heat simply means heat transferred The direction of heat transfer is always from the higher temperature body to the lower temperature one. Conventionally, the transfer of heat into a system is frequently referred to as heat addition and the transfer of heat out of a system as heat rejection. And the heat addition is defined to be positive, heat rejection is negative However, heat is a path function and the amount of heat transferred depends on the path followed It is different from the internal energy, which is a function of state. A path function has inexact differentials and a differential amount of heat is denoted by 8g or &g. As a form of energy, heat has energy units, kJ. The amount of heat transferred during a process between two states(states I and 2)is denoted just by o. Heat transfer per unit mass of a system is denoted asg and is determined from (2) Energy transfer by work Work, like heat, is a kind of energy interaction between a system and its surroundings. An energ interaction that is not caused by a temperature difference between a system and its surrpundings is work. Heat is easy to recognize: Its driving force is a temperature difference between the system and its surroundings. More specifically, work is the energy transfer associated with the force acting through a distance. A rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions. Work has energy unit k. The work done during a process between states land 2 is denoted just by W. Work transfer per unit mass of a system is denoted as w and is determined from w=w/m kJ/kg Boundary work is an indispensable way to complete the energy transformation from thermal energy to mechanical energy. In addition, mechanical work is always transferred by virtual of the rotating of shaft. Therefore, boundary work and shaft work will be introduced in the following 1) work One form of work frequently encountered in practice is associated piston-cylinder device. During this process, part of A the boundary, the inner face of the piston, moves ack and forth as illustrated in Fig. 2-2. Therefore, the expansion and compression work is often called System (gas in cylinder 27 Figure 2-2 Schematic for moving boundary work
27 Figure 2-1 Energy is recognized as heat transfer only as it crosses the system boundary Figure 2-2 Schematic for moving boundary work Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference. That is, an energy interaction is heat only if it takes place because of a temperature difference. Once the temperature equality is established, energy transfer stops. It means that there cannot be any heat transfer between two systems that are at the same temperature. Heat is energy in transition. It is recognized only as it crosses the boundary of a system. The body contains energy, but this energy is transfer only as it passes through the system boundary to reach its surroundings, as shown in Fig. 2–1. Once in the surroundings, the transferred heat becomes part of the internal energy of the surroundings. Thus, in thermodynamics, the term heat simply means heat transferred. The direction of heat transfer is always from the higher temperature body to the lower temperature one. Conventionally, the transfer of heat into a system is frequently referred to as heat addition and the transfer of heat out of a system as heat rejection. And the heat addition is defined to be positive, heat rejection is negative. However, heat is a path function and the amount of heat transferred depends on the path followed. It is different from the internal energy, which is a function of state. A path function has inexact differentials and a differential amount of heat is denoted by δQ or δq . As a form of energy, heat has energy units, kJ. The amount of heat transferred during a process between two states (states 1 and 2) is denoted just by Q. Heat transfer per unit mass of a system is denoted as q and is determined from q = Q/m kJ/kg. （2） Energy transfer by work Work, like heat, is a kind of energy interaction between a system and its surroundings. An energy interaction that is not caused by a temperature difference between a system and its surroundings is work. Heat is easy to recognize: Its driving force is a temperature difference between the system and its surroundings. More specifically, work is the energy transfer associated with the force acting through a distance. A rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions. Work has energy unit kJ. The work done during a process between states 1and 2 is denoted just by W. Work transfer per unit mass of a system is denoted as w and is determined from w = W / m kJ/kg. Boundary work is an indispensable way to complete the energy transformation from thermal energy to mechanical energy. In addition, mechanical work is always transferred by virtual of the rotating of shaft. Therefore, boundary work and shaft work will be introduced in the following. 1) Moving boundary work One form of work frequently encountered in practice is associated with the expansion or compression of a gas in a piston–cylinder device. During this process, part of the boundary, the inner face of the piston, moves back and forth as illustrated in Fig.2-2. Therefore, the expansion and compression work is often called
moving boundary work, or simply boundary work. The volume change is positive during an expansion process and negative during a compression process. Thus, the boundary work is positive during an expansion process and negative during a compression process. There are two requirements for a boundary work interaction between a system and its surroundings to occur: a force acts on the boundary and the boundary must move. Therefore, the presence of forces on the boundary without any displacement of the boundary does not constitute a work interaction. Likewise, the displacement of the boundary without any force to oppose or drive this motion, such as the expansion of a gas into an evacuated space, is not a work interaction since no energy is transferred For open system with a mass flowing in or out, the boundary work of the system is just a portion of technical work output, which can be used technically and transformed into other forms of work. We will introduce the concept of technical work in section 2.4 Work only occurs during a process and it is a path function. As the process finishes, the work Interaction stops. 2)Shaft work Generally shaft work means work done by rotating machinery, which is carried by a shaft(Fig. 2-3(a)). Usually, it is stipulated that the shaft work a system outputs is positive and the shaft work input to a system is negative. As illustrated in Fig 2-3(b), the paddle-wheel work done on an adiabatic closed system through the dissipative effect such as friction. As a result, the internal energy of the system increases. However, shaft work can not be done by a closed system continuously for the heat added to the system can not be changed into mechanical work directly. But, Wse=tNt Adiabatic △E=8kJ TURBINE Wsin=8 k Torque= Fr (a)Definition of shaft work (b) shaft work input into a closed system (c) shaft work done by an open system igure 2-3 Schematic for shaft work for an open system, as mass flows in or out, it may push the shaft to output work(Fig 2-3()). Steam turbines, pumps and compressors are devices usually encountered in practice which transfer work through shaft (3) Moving boundary work and heat transfer in reversible process 1) Moving boundary work in reversible process The energy conversion can be fulfilled by the state change of the working fluid. As shown in Fig. 2-4, there is some working fluid in the cylinder. Suppose the process is a Figure 2-4 The area under the process reversible process, the system is in mechanical equilibrium curve on a p-v diagram represents The force exerted on the system is the pressure of the system, the boundary and the piston sectional area is A, that is F=pA The piston moves a differential amount distance dx in the direction of the force. The work done can be calculated by 8W= Fdx= pAdx= pdl
28 Figure 2-4 The area under the process curve on a p v − diagram represents the boundary work. (a) Definition of shaft work (b) shaft work input into a closed system (c) shaft work done by an open system Figure 2-3 Schematic for shaft work moving boundary work, or simply boundary work. The volume change is positive during an expansion process and negative during a compression process. Thus, the boundary work is positive during an expansion process and negative during a compression process. There are two requirements for a boundary work interaction between a system and its surroundings to occur: a force acts on the boundary and the boundary must move. Therefore, the presence of forces on the boundary without any displacement of the boundary does not constitute a work interaction. Likewise, the displacement of the boundary without any force to oppose or drive this motion, such as the expansion of a gas into an evacuated space, is not a work interaction since no energy is transferred. For open system with a mass flowing in or out, the boundary work of the system is just a portion of technical work output, which can be used technically and transformed into other forms of work. We will introduce the concept of technical work in section 2.4.3. Work only occurs during a process and it is a path function. As the process finishes, the work interaction stops. 2) Shaft work Generally shaft work means work done by rotating machinery, which is carried by a shaft (Fig. 2–3(a)). Usually, it is stipulated that the shaft work a system outputs is positive, and the shaft work input to a system is negative. As illustrated in Fig.2-3(b), the paddle-wheel work done on an adiabatic closed system through the dissipative effect such as friction. As a result, the internal energy of the system increases. However, shaft work can not be done by a closed system continuously for the heat added to the system can not be changed into mechanical work directly. But, for an open system, as mass flows in or out, it may push the shaft to output work (Fig.2-3(c)). Steam turbines, pumps and compressors are devices usually encountered in practice which transfer work through shaft. (3) Moving boundary work and heat transfer in reversible process 1) Moving boundary work in reversible process The energy conversion can be fulfilled by the state change of the working fluid. As shown in Fig. 2-4, there is some working fluid in the cylinder. Suppose the process is a reversible process, the system is in mechanical equilibrium. The force exerted on the system is the pressure of the system, and the piston sectional area is A, that is F pA = . The piston moves a differential amount distance dx in the direction of the force. The work done can be calculated by δW F x pA x p V = = = d d d (2-2a)
In process 1-2, the total work can be obtained by integration The work done per unit mass of the system is denoted by w and is defined as (2-2c) wrwk The integral above is the formula to calculate moving boundary work in a reversible process. It can be evaluated only if we know the function relationship between p and V during the process. That is, p=f()or p=f(v) should be available on a diagram in Fig. 2-4. The differential area da is equal to pdv Figure 2-5 Expansion work in the differential work. The total area A under the process curve 1-2 on a p-vdiagram is the total work. Thus, it reveals that the area different processes under the process curve is equal, in magnitude, to the work done during a quasl-equilibrium expansion or compression process of a closed system. On the p-vdiagram, it represents the boundary work done per unit mass. A gas can follow several different paths as it expands from state I to state 2. In general, each path will have a different area underneath it, and since this area represents the magnitude of the work the work done will be different for each process(Fig 2-5). As we know, work is a path function and is not a property. It depends on the path followed as well as its initial and final states. The systems do not possess work at a state. A differential amount of heat or work is represented by 80or 8W, respectively, instead of door dw The generally accepted formal sign convention for work interactions is as following: work done by a system is positive, work done on a system is negative. In Sl, the unit of work is J or kJ, the unit of specific work is J/kg or kJ/kg 2) Heat transferred in reversible process Heat is defined as the form of energy that is transferred between two systems(or system to its surroundings) at different temperature when they are brought into thermal contact. Thus, heat is a transient quantity that can appear only at the boundaries of sy he amount of heat transferred during the process is denoted by Q, the unit is J or k, and q is used to denote heat transfer per unit mass, the unit is J/kg or kJ/kg Heat is also a path function but not a property. We can not say a body possesses heat. A differential amount of heat transferred is represented by &g or 8o The formal sign convention for heat interactions is as following: heat transfer to a system is positive; heat transfer from a system is negative Since work and heat are both path functions, they must possess some common characteristic Does heat have similar defining fomula? Analogically, we define the state property entropy. When the system undergoes a reversible process, heat transferred per unit mass of a system is defined as (2-3a) s is the entropy per unit mass. The unit is J/(kg.K). Namely: (2-4a) The total entropy of m kg working fluid
29 Figure 2-5 Expansion work in different processes In process 1-2, the total work can be obtained by integration 2 1 d V V W p V = (2-2b) The work done per unit mass of the system is denoted by w and is defined as 2 1 d v v w p v = (2-2c) The integral above is the formula to calculate moving boundary work in a reversible process. It can be evaluated only if we know the function relationship between p and V during the process. That is, p f V = ( ) or p f v = ( ) should be available. The quasi-equilibrium expansion process described is shown on a diagram in Fig. 2-4. The differential area dA is equal to p Vd , the differential work. The total area A under the process curve 1–2 on a p v − diagram is the total work. Thus, it reveals that the area under the process curve is equal, in magnitude, to the work done during a quasi-equilibrium expansion or compression process of a closed system. On the p v − diagram, it represents the boundary work done per unit mass. A gas can follow several different paths as it expands from state 1 to state 2. In general, each path will have a different area underneath it, and since this area represents the magnitude of the work, the work done will be different for each process (Fig.2-5). As we know, work is a path function and is not a property. It depends on the path followed as well as its initial and final states. The systems do not possess work at a state. A differential amount of heat or work is represented by δQ or δW , respectively, instead of dQ or dW . The generally accepted formal sign convention for work interactions is as following: work done by a system is positive; work done on a system is negative. In SI, the unit of work is J or kJ，the unit of specific work is J/kg or kJ/kg. 2）Heat transferred in reversible process Heat is defined as the form of energy that is transferred between two systems (or system to its surroundings) at different temperature when they are brought into thermal contact. Thus, heat is a transient quantity that can appear only at the boundaries of the systems. The amount of heat transferred during the process is denoted by Q, the unit is J or kJ, and q is used to denote heat transfer per unit mass, the unit is J/kg or kJ/kg. Heat is also a path function but not a property. We can not say a body possesses heat. A differential amount of heat transferred is represented by δq or δQ . The formal sign convention for heat interactions is as following: heat transfer to a system is positive; heat transfer from a system is negative. Since work and heat are both path functions, they must possess some common characteristic. Does heat have similar defining formula? Analogically, we define the state property entropy. When the system undergoes a reversible process, heat transferred per unit mass of a system is defined as δq T s = d (2-3a) s is the entropy per unit mass. The unit is J/(kg K) . Namely: δ d q s T = (2-4a) The total entropy of m kg working fluid is：
(2-4b) Notice that s is a state property. The term entropy is generally used to refer to both total and entropy per unit mass since the context usually clarifies which one is meant. The amount of heat transfer is also equal to the area under the process curve on a T-s diagram during a lasi-equilibrium process(Fig2-6) In this chapter, we just give the concept of entropy Further discussion on entropy will be done in chapter 4 Figure 2-6 The area under the process The heat transferred between the system and its curve on a T-s diagram represents surroundings during an irreversible process from l to 2 is the heat transferre q=∫,Q=∫ (2-3b) Based on the change in entropy, it is easy to judge the direction of heat transferred between a system and its surroundings If ds >0, then 9 >0, heat transfer to a system If ds <0, then q <0, heat transfer from a system If ds =0, then q =0, the system is adiabatic. It means a reversible adiabatic process is ar (3) Similarities of energy transfer by heat and by work We can find that both heat and work are energy transfer mechanisms between a sy stem and its surroundings, and there are many similarities between them: Both heat and work are boundary phenomena and recognized at the boundaries of a system as they cross the boundaries; both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state Systems possess energy, but not heat or work; both are path functions, i. e, their magnitudes depend on the path followed during a process as well as the initial and final states. A path function has inexact differentials and a differential amount of heat or work is denoted by using 8. Note that a quantity that is transferred to or from a system during an interaction is not a property since the amount of such a quantity depends on more than just the state of the system. Since they are both directional quantities, the complete description of a heat or work interaction requires the specification of both th magnitude and direction Example 2-1] A kind of gas of a fixed mass in a closed cylinder experiences a reversible expansion During this process, the volume and pressure change according to the following relationship of pl=const. The initial state of the gas is at P,=0.5 MPa and V=0.4 m' and the final volume of linder is,=0.8m. Calculate the expansion work output by the gas (Solution] The gas within the cylinder is chosen as the system. During a reversible process, the work is calculated by As we know p the work output is
30 Figure 2-6 The area under the process curve on a T-s diagram represents the heat transferred δ d Q S T = (2-4b) Notice that s is a state property. The term entropy is generally used to refer to both total and entropy per unit mass since the context usually clarifies which one is meant. The amount of heat transfer is also equal to the area under the process curve on a T-s diagram during a quasi-equilibrium process (Fig.2-6). In this chapter, we just give the concept of entropy. Further discussion on entropy will be done in chapter 4. The heat transferred between the system and its surroundings during an irreversible process from 1 to 2 is 2 1 q T s = d ， 2 1 Q T S = d (2-3b) Based on the change in entropy, it is easy to judge the direction of heat transferred between a system and its surroundings If ds ＞0，then q ＞0，heat transfer to a system; If ds ＜0，then q ＜0，heat transfer from a system; If ds ＝0，then q ＝0，the system is adiabatic. It means a reversible adiabatic process is an isentropic process. (3) Similarities of energy transfer by heat and by work We can find that both heat and work are energy transfer mechanisms between a system and its surroundings, and there are many similarities between them: Both heat and work are boundary phenomena and recognized at the boundaries of a system as they cross the boundaries; both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state. Systems possess energy, but not heat or work; both are path functions, i.e., their magnitudes depend on the path followed during a process as well as the initial and final states. A path function has inexact differentials and a differential amount of heat or work is denoted by using δ . Note that a quantity that is transferred to or from a system during an interaction is not a property since the amount of such a quantity depends on more than just the state of the system. Since they are both directional quantities, the complete description of a heat or work interaction requires the specification of both the magnitude and direction. 【Example 2-1】A kind of gas of a fixed mass in a closed cylinder experiences a reversible expansion process. During this process, the volume and pressure change according to the following relationship of pV = const . The initial state of the gas is at 1 p = 0.5 MPa and 3 1 V = 0.4 m and the final volume of cylinder is 3 2 V = 0.8m . Calculate the expansion work output by the gas. 【Solution】 The gas within the cylinder is chosen as the system. During a reversible process, the work is calculated by 2 1 d V V W p V = As we know 1 1 pV p V = , the work output is