an be measured directly or indirectly, such The derived properties can be calculated in terms of the basic state properties, such as internal energy u, enthalpy h, entropy s and so on 1. 2. 2 Basic State Prope (1)Temperature Based on our physiological sensations, we say the temperature is very high in summer, and it is low in winter. But we cannot assign numerical values to temperatures based on our sensations alone. It is not easy to give an exact definition for it. In an isolated system, when a body is brought into contact with another one that is at a different temperature, heat is transferred from the body at higher temperature to the other at lower temperature until both bodies attain the same temperature. At that point, the heat transfer stops, and the two bodies are said to have reached thermal equilibrium. Therefore, temperature Is the property The Zeroth Law of Thermodynamics states that if two bodies are in thermal equilibrium with a third body they are also in thermal equilibrium with each other as well. It serves as the basis for the validity of temperature measurement. When the test system and the thermometer which has been numerical calibrated are in thermal equilibrium, temperature reading of the themometer is equivalent to the test system. Temperature is the property describing the characteristic of the heat balance Temperature scales are used to record temperature readings. To establish a temperature scale, it needs to take advantage of a certain physical properties of a substance and to choose reference points and sub-degree methods. All temperature scales are based on some easily reproducible states such as the freezing and boiling points of water, which are also called the ice point and the steam point, vely. Temperature scale in the SI is the Kelvin scale, also called thermodyna mic temperature scale. It is independent of the properties of the substances that are used to measure temperature. The unit of thermodynamic temperature T is defined as 1/273. 16 of the thermodynamic temperature of the triple point of water (the state at which all three phases of water coexist in equilibrium), which is assigned the value 273. 16 K. And the temperatures on this scale are called absolute temperatures. Its unit is the Kelvin, designated by K The temperature scale used synchronously in the SI today is the Celsius scale and its unit is the Celsius, designated by C. The temperature on this scale is denoted by t. It is related to the Kelvin scale temperature T by -273.15 2)Pressure 1)Pressure and units Pressure p is defined as the force exerted by a fluid on per unit area. That where F stands for the force perpendicular to the surface, N; A stands for the area of a surface,m There is a certain amount of gas within the system, a large number of gas molecules randomly move and continuously hit the wall. For a particular molecule, this collision is intermittent, but for the whole system with a large number of molecules, the collision is simultaneous and continuous, pressure behaves a constant at macro-scale. Pressure at any point in a fluid is the same in all directions
16 1 1 = = x x → d 0 State properties are divided into basic state properties and derived properties. The basic state properties can be measured directly or indirectly, such as pressure p , temperature T and volume V . The derived properties can be calculated in terms of the basic state properties, such as internal energy u, enthalpy h, entropy s and so on. 1.2.2 Basic State Properties (1) Temperature Based on our physiological sensations, we say the temperature is very high in summer, and it is low in winter. But we cannot assign numerical values to temperatures based on our sensations alone. It is not easy to give an exact definition for it. In an isolated system, when a body is brought into contact with another one that is at a different temperature, heat is transferred from the body at higher temperature to the other at lower temperature until both bodies attain the same temperature. At that point, the heat transfer stops, and the two bodies are said to have reached thermal equilibrium. Therefore, temperature is the property. The Zeroth Law of Thermodynamics states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other as well. It serves as the basis for the validity of temperature measurement. When the test system and the thermometer which has been numerical calibrated are in thermal equilibrium, temperature reading of the thermometer is equivalent to the test system. Temperature is the property describing the characteristic of the heat balance. Temperature scales are used to record temperature readings. To establish a temperature scale, it needs to take advantage of a certain physical properties of a substance and to choose reference points and sub-degree methods. All temperature scales are based on some easily reproducible states such as the freezing and boiling points of water, which are also called the ice point and the steam point, respectively. Temperature scale in the SI is the Kelvin scale, also called thermodynamic temperature scale. It is independent of the properties of the substances that are used to measure temperature. The unit of thermodynamic temperature T is defined as 1/273.16 of the thermodynamic temperature of the triple point of water (the state at which all three phases of water coexist in equilibrium), which is assigned the value 273.16 K. And the temperatures on this scale are called absolute temperatures. Its unit is the Kelvin, designated by K. The temperature scale used synchronously in the SI today is the Celsius scale and its unit is the Celsius, designated by ℃. The temperature on this scale is denoted by t . It is related to the Kelvin scale temperature T by t T = − 273.15 (1-3) (2) Pressure 1) Pressure and units Pressure p is defined as the force exerted by a fluid on per unit area. That is F p A = (1-4 ) where F stands for the force perpendicular to the surface, N; A stands for the area of a surface, 2 m . There is a certain amount of gas within the system, a large number of gas molecules randomly move and continuously hit the wall. For a particular molecule, this collision is intermittent, but for the whole system with a large number of molecules, the collision is simultaneous and continuous, pressure behaves a constant at macro-scale. Pressure at any point in a fluid is the same in all directions
The pressure unit is Newton per square meter(N/m ), which is called Pascal(Pa). I Pa=l N/ ut the Pascal is too small for pressure encountered in engineering practice. Therefore, its multiple kilopascal( kPa )and Mega-Pascal( MPa ) are commonly used And kPa10' Pa, I MPa=10Pa Moreover, the other four pressure units commonly used in practice are bar, standard atmosphere (atm), engineering atmosphere(at), mmH,O, and mmHg. The conversion of the different pressure units refers to as following 1 Pa=l N/m2 1 bar=105 Pa 1at=1 kgf/cm2=9.807×104Pa=10mH2O latm=101325×105Pa=760mmH 2)Absolute pressure and gage pressure Pressure is measured with pressure gages(gauge) There are two types of pressure gage used commonly( Fig 1-4). They are the bourdon-tube pressur gage and the U-tube manometer. However, they are calibrated to read zero in the atmosphere, and so they indicate the difference between the absolute pressure and the local atmospheric pressure. The actual pressure at a given position is called the absolute pressure, and their difference is called the gage pressure. Pressure below atmospheric pressure is called vacuum pressure and is measured by vacuum gage that indicate the difference between the atmospheric pressure and the absolute pressure Absolute, gage, and vacuum pressures are all positive quantities and are related to each other by eq(1-5)and eq (1-6), as illustrated in Fig. 1-5 (a) The U-tube manometer (b)C-Type Bourdon Tube Fig 1-4 Some basic pressure gages If p>P, then p=P.+pe for pressure higher than the local atmospheric pres If p<p, then p=P-P, for pressure lower than the local atmospheric pressure where P, P, and P, are the local atmospheric pressure, the gage pressure and the vacuum pressure respectively The atmospheric pressure changes not only with elevation but also with weather ospheric pressure different conditions, the gage pressure is P different even though the absolute pressure of the system is consistent. Therefore, the gage pressure is not a state property. Only Fig 1-5 Absolute, gage, and vacuum pressures absolute pressure is a state property
17 Fig.1-5 Absolute, gage, and vacuum pressures The pressure unit is Newton per square meter (N/m2 ), which is called Pascal (Pa). 2 1 Pa=1 N/m . But the Pascal is too small for pressure encountered in engineering practice. Therefore, its multiples kilopascal ( kPa ) and Mega-Pascal ( MPa ) are commonly used. And 3 1 kPa=10 Pa , 6 1 MPa=10 Pa Moreover, the other four pressure units commonly used in practice are bar, standard atmosphere (atm), engineering atmosphere (at), mmH O2 , and mmHg . The conversion of the different pressure units refersto as following, 1 Pa=1 N/m2 1 bar=105 Pa 1 at=1 kgf/cm2 = 9.807×104 Pa=10 mH2O 1 atm=1.01325×105 Pa=760 mm Hg 2) Absolute pressure and gage pressure Pressure is measured with pressure gages (gauge). There are two types of pressure gage used commonly ( Fig.1-4). They are the bourdon-tube pressure gage and the U-tube manometer. However, they are calibrated to read zero in the atmosphere, and so they indicate the difference between the absolute pressure and the local atmospheric pressure. The actual pressure at a given position is called the absolute pressure, and their difference is called the gage pressure. Pressure below atmospheric pressure is called vacuum pressure and is measured by vacuum gage that indicate the difference between the atmospheric pressure and the absolute pressure. Absolute, gage, and vacuum pressures are all positive quantities and are related to each other by eq.(1-5) and eq.(1-6), as illustrated in Fig.1-5 If b p p , then b g p p p = + for pressure higher than the local atmospheric pressure. . If b p p , then b v p p p = − for pressure lower than the local atmospheric pressure. where b p , g p and v p are the local atmospheric pressure, the gage pressure and the vacuum pressure respectively. The atmospheric pressure changes not only with elevation but also with weather conditions. If atmospheric pressure is in different conditions, the gage pressure is different even though the absolute pressure of the system is consistent. Therefore, the gage pressure is not a state property. Only absolute pressure is a state property. (a) The U-tube manometer (b) C-Type Bourdon Tube Fig.1-4 Some basic pressure gages
(3)Specific volume and density Specific volume is defined as the volume per unit mass. It has the unit of m /kg Density is the reciprocal of specific volume and is defined as the mass per unit volume, kg/m In general, the density of a substance depends on its pressure and temperature. The density of most gases is proportional to the pressure and inversely proportional to the temperature. The densities of liquids are essentially constant and are often approximated to be incompressible (4)Intensive properties and extensive properties In accordance with the mass of a system, properties are considered to be either intensive or extensive Intensive properties are those independent of the mass of a system, such as temperature, pressure, and density. Extensive properties are those whose values depend on the size or extent of T the system, such as total volume, internal energy, enthalpy, and entropy. Extensive properties can be added. For example, the system is divided into two equal parts with an imaginary partition as shown in Fig. 1-6. Each part have the same value of intensive properties as the original system, but half the value of the extensive Intensive properties In general, uppercase letters are used to denote extensive properties( with mass m being exception). Extensive properties per Fig. 1-6 Extensive and intensive unit mass are called specific properties, such as specific volume(v), properties the specific internal energy, specific enthalpy and specific entropy, And lowercase letters are used to denote specific properties Example 1-1) There are two containers A and B, the gage pressure measured for container A is 3.5 bar, the vacuum pressure for B is 0.85 bar.(1) The local atmospheric pressure is 735 mmHg Determine the absolute pressures inside A and B;(2) The local atmospheric pressure is 1 bar approximately. Determine the absolute pressures inside a and B, and the error between(1)and(2); (3) When the local atmospheric pressure changes to be 755 mmHg, determine the gage pressure and the vacuum pressure (Solution](1) Firstly, make the unit of pressure identical. All units of pressure are converted to bar. B=735×133.3×103=09798ba The absolute pressures of side a PA=B+P2=0.9798+35=44798bar The absolute pressures of side B pB=B-H=09798-0.85=0.1298bar (2) If the local atmospheric pressure is I bar approximately B’=1bar
18 Fig.1-6 Extensive and intensive properties (3) Specific volume and density Specific volume is defined as the volume per unit mass. It has the unit of 3 m /kg . V v m = (1-7) Density is the reciprocal of specific volume and is defined as the mass per unit volume, 3 kg/m . m V = (1-8) In general, the density of a substance depends on its pressure and temperature. The density of most gases is proportional to the pressure and inversely proportional to the temperature. The densities of liquids are essentially constant and are often approximated to be incompressible. (4) Intensive properties and extensive properties In accordance with the mass of a system, properties are considered to be either intensive or extensive. Intensive properties are those independent of the mass of a system, such as temperature, pressure, and density. Extensive properties are those whose values depend on the size or extent of the system, such as total volume, internal energy, enthalpy, and entropy. Extensive properties can be added. For example, the system is divided into two equal parts with an imaginary partition, as shown in Fig.1-6. Each part have the same value of intensive properties as the original system, but half the value of the extensive properties. In general, uppercase letters are used to denote extensive properties (with mass m being exception). Extensive properties per unit mass are called specific properties, such as specific volume (v), the specific internal energy, specific enthalpy and specific entropy. And lowercase letters are used to denote specific properties. 【Example 1-1】There are two containers A and B, the gage pressure measured for container A is 3.5 bar，the vacuum pressure for B is 0.85 bar. (1) The local atmospheric pressure is 735 mmHg. Determine the absolute pressures inside A and B; (2) The local atmospheric pressure is 1 bar approximately. Determine the absolute pressures inside A and B, and the error between (1) and (2); (3) When the local atmospheric pressure changes to be 755 mmHg, determine the gage pressure and the vacuum pressure. 【Solution】(1) Firstly, make the unit of pressure identical. All units of pressure are converted to bar. 5 B 735 133.3 10 0.979 8 bar − = = The absolute pressures of side A A g p B p = + = + = 0.979 8 3.5 4.479 8 bar The absolute pressures of side B B p B H = − = − = 0.979 8 0.85 0.129 8 bar (2) If the local atmospheric pressure is 1 bar approximately B = 1 bar
PA=B+P=10+3:5=4.5bar p=B-H=1.0-0.85=0.15bar Comparing with(1), the errors are PA-P44.5-44798 P 44798×100%=0.45% B:P=Pn=015-01298×100=156%6 pB 0.1298 (3) If the atmospheric pressure is B"=755x133 3x10=1.006 bar, and the absolute pressures inside two containers remain unchanged, then the readings of the two pressure gages will change to be the P=PA-B=44798-1.006=34738bar H"=B"-p3=1.006-0.1298=08762bar Discussions: (1) The absolute pressure is a state property. The gage pressure may change with the local atmospheric (2)When the absolute pressure of a container is greater than atmospheric pressure, the atmospheric pressure can be approximated by b=l bar ()When the absolute pressure of the container is approximate or below the atmospheric pressure, th atmospheric pressure cannot be approximated by using B=l bar; otherwise there is an obvious error for the results of absolute pressure (4) Attentions to the pressure unit conversio 1.3 Equilibrium State, State Equation and state Diagram 1.3. 1 Equilibrium State Thermodynamics deals with equilibrium states. Equilibrium state is an important concept. It implies a state of balance. In an equilibrium state there are no unbalanced potentials or driving forces within the system. For example, if the temperature is not the same throughout the entire system, the system is not in thermal equilibrium, then heat will flow from the high temperature part to other low temperature parts until the temperature turns to be the same throughout the entire system. Then the system is in thermal equilibrium. There are many types of equilibrium, and a system is not in thermodynamic equilibrium unless all the relevant types of equilibrium are satisfied. Besides the thermal equilibrium, mechanical equilibrium is related to pressure. And a system is in mechanical equilibrium if there is no change in pressure at any point of the system with time. A system involving two phases is in phase equilibrium en the mass of each phase reaches equilibrium level and keeps the level there. Chemical equilibrium means the chemical composition of a system does not change with time, that is,no chemical reaction occurs. A system will not be in equilibrium unless all the relevant equilibriums are satisfied When the system is in equilibrium, the state properties are the same throughout the entire system including the pressure, temperature, etc. The state can be described by its properties 1.3. 2 The State Postulate When a system is in equilibrium, the state can be described by its properties. Do we need to specify all the properties in order to fix a state? Actually, the properties are not isolated. Once a sufficient number of properties are specified, the rest of the properties are certain automatically. That is, specifying a
19 then p B p A g = + = + = 1.0 3.5 4.5 bar B p B H = − = − = 1.0 0.85 0.15 bar Comparing with (1), the errors are A： A A A 4.5 4.479 8 100%=0.45% 4.479 8 p p p − − = B： B B B 0.15 0.129 8 100%=15.6% 0.129 8 p p p − − = (3) If the atmospheric pressure is 5 B 755 133.3 10 1.006 bar − = = , and the absolute pressures inside two containers remain unchanged, then the readings of the two pressure gages will change to be the following, p p B g A = − = − = 4.4798 1.006 3.4738 bar H B p = − = − = B 1.006 0.1298 0.8762 bar Discussions: (1) The absolute pressure is a state property. The gage pressure may change with the local atmospheric pressure. (2) When the absolute pressure of a container is greater than atmospheric pressure，the atmospheric pressure can be approximated by B =1 bar ； (3) When the absolute pressure of the container is approximate or below the atmospheric pressure, the atmospheric pressure cannot be approximated by using B =1 bar ; otherwise there is an obvious error for the results of absolute pressure. (4) Attentions to the pressure unit conversion and consistency. 1.3 Equilibrium State, State Equation and State Diagram 1.3.1 Equilibrium State Thermodynamics deals with equilibrium states. Equilibrium state is an important concept. It implies a state of balance. In an equilibrium state there are no unbalanced potentials or driving forces within the system. For example, if the temperature is not the same throughout the entire system, the system is not in thermal equilibrium, then heat will flow from the high temperature part to other low temperature parts until the temperature turns to be the same throughout the entire system. Then the system is in thermal equilibrium. There are many types of equilibrium, and a system is not in thermodynamic equilibrium unless all the relevant types of equilibrium are satisfied. Besides the thermal equilibrium, mechanical equilibrium is related to pressure. And a system is in mechanical equilibrium if there is no change in pressure at any point of the system with time. A system involving two phases is in phase equilibrium when the mass of each phase reaches equilibrium level and keeps the level there. Chemical equilibrium means the chemical composition of a system does not change with time, that is, no chemical reaction occurs. A system will not be in equilibrium unless all the relevant equilibriums are satisfied. When the system is in equilibrium, the state properties are the same throughout the entire system, including the pressure, temperature, etc. The state can be described by its properties. 1.3.2 The State Postulate When a system is in equilibrium, the state can be described by its properties. Do we need to specify all the properties in order to fix a state? Actually, the properties are not isolated. Once a sufficient number of properties are specified, the rest of the properties are certain automatically. That is, specifying a
certain number of properties is sufficient to fix a state The state postulate indicates the state of a simple compressible system is completely specified two independent intensive properties A system is called a simple compressible system, when all other forms of work can be ignored esides interactions of heat exchange and expansion work. That is, there are no electrical, magnetic gravitational, motion and surface tension effects involved Two properties are independent if one property can be varied while the other one is held constant 1.3.3 Equation of State The state postulate indicates that in a simple compressible sy stem the state can be described by only pecifying two independent properties. Temperature and pressure, for example, are al ways independen properties for a single phase system, and together they can fix the state of a system and other f(p, T) l=f2(P,7) It can also be expressed in the following form F(P,T,v)=0 (1-9c) As the equilibrium state of a system ca coordinates to constitute a Cartesian coordinate system which called the state diagram. Some T-s diagram, as shown in Fig. 1-7 Only an equilibrium state can be denoted by a Fig 1-7 p-v diagram and T-s diagram point on the diagram 1.4 Quasi-equilibrium Process and Reversible Process When the state of a sy stem changes from one equilibrium state to another, it undergoes a process. The series of states through which a system passes during a process is called the path of the process If there are unbalanced potentials occurring in an equilibrium state, the equilibrium is destroyed The state of the system will change until it reaches another equilibrium state. There are a series of unbalanced states between two equilibrium states. Because unbalanced state can not be described by certain state properties, thus some ideal processes will be defined 1.4.1 Quasi-equilibrium Process When a process proceeds in such a manner that the system remains infinitesimally close to equilibrium state at all times, it is called a quasi-equilibrium, or quasi-static process. It can be illustrated by a solid line on a state diagram As illustrated in Fig. 1-8, a certain amount of gas is enclosed in a piston-cylinder device and a heavy weight is put on the piston to compress the gas. Initially, the gas is in equilibrium. If the weight is removed suddenly, the mechanical equilibrium of the system is damaged. The state will change until it reaches a new equilibrium. during this process, the states are in non-equilibrium besides the initial and final states (statel and state 2). The entire process is a non-quasi-equilibrium process and is denoted by a dashed line between the initial and final states
20 Fig.1-7 p v − diagram and T s − diagram certain number of properties is sufficient to fix a state. The state postulate indicates the state of a simple compressible system is completely specified by two independent intensive properties. A system is called a simple compressible system，when all other forms of work can be ignored besides interactions of heat exchange and expansion work. That is, there are no electrical, magnetic, gravitational, motion and surface tension effects involved. Two properties are independent if one property can be varied while the other one is held constant. 1.3.3 Equation of State The state postulate indicates that in a simple compressible system the state can be described by only specifying two independent properties. Temperature and pressure, for example, are always independent properties for a single phase system, and together they can fix the state of a system and other properties. 1 v f p T = ( , ) (1-9a) 2 u f p T = ( , ) (1-9b) It can also be expressed in the following form： 1 F p T v ( , , ) 0 = (1-9c) These relations are called the equations of state. As the equilibrium state of a system can be specified by any two independent properties, we may choose two independent properties as two coordinates to constitute a Cartesian coordinates system which called the state diagram. Some familiar diagrams include p v − diagram and T s − diagram, as shown in Fig. 1-7. Only an equilibrium state can be denoted by a point on the diagram. 1.4 Quasi-equilibrium Process and Reversible Process When the state of a system changes from one equilibrium state to another, it undergoes a process. The series of states through which a system passes during a process is called the path of the process. If there are unbalanced potentials occurring in an equilibrium state, the equilibrium is destroyed. The state of the system will change until it reaches another equilibrium state. There are a series of unbalanced states between two equilibrium states. Because unbalanced state can not be described by certain state properties, thus some ideal processes will be defined. 1.4.1 Quasi-equilibrium Process When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a quasi-equilibrium, or quasi-static process. It can be illustrated by a solid line on a state diagram. As illustrated in Fig. 1-8, a certain amount of gas is enclosed in a piston-cylinder device and a heavy weight is put on the piston to compress the gas. Initially, the gas is in equilibrium. If the weight is removed suddenly, the mechanical equilibrium of the system is damaged. The state will change until it reaches a new equilibrium. During this process, the states are in non-equilibrium besides the initial and final states (state1 and state 2). The entire process is a non-quasi-equilibrium process and is denoted by a dashed line between the initial and final states