1.6 Pressure 15 HORIZONS Big Hopes for Nanotechnology Nanoscience is the study of molecules and tinuum model may no longer apply owing to the interactions molecular structures,called nanostructures,hav- among the atoms under consideration.Also at these scales, ing one or more dimensions less than about 100 the nature of physical phenomena such as current flow may nanometers.One nanometer is one-billionth of a meter: depend explicitly on the physical size of devices.After many 1 nm=10-9m.To grasp this level of smallness,a stack of years of fruitful research,nanotechnology is now poised to 10 hydrogen atoms would have a height of 1 nm,while a provide new products with a broad range of uses,including human hair has a diameter of about 50,000 nm.Nanotech- implantable chemotherapy devices,biosensors for glucose nology is the engineering of nanostructures into useful detection in diabetics,novel electronic devices,new energy products.At the nanotechnology scale,behavior may differ conversion technologies,and smart materials as,for example, from our macroscopic expectations.For example,the aver- fabrics that allow water vapor to escape while keeping aging used to assign property values at a point in the con- liquid water out. If the area A'was given new orientations by rotating it around the given point, and the pressure determined for each new orientation,it would be found that the pressure at the point is the same in all directions as long as the fluid is at rest.This is a consequence of the equilibrium of forces acting on an element of volume sur- rounding the point.However,the pressure can vary from point to point within a fluid at rest;examples are the variation of atmospheric pressure with elevation and the pressure variation with depth in oceans,lakes,and other bodies of water. Consider next a fluid in motion.In this case the force exerted on an area passing through a point in the fluid may be resolved into three mutually perpendicular com- ponents:one normal to the area and two in the plane of the area.When expressed on absolute pressure a unit area basis,the component normal to the area is called the normal stress,and the two components in the plane of the area are termed shear stresses.The magnitudes Gas at of the stresses generally vary with the orientation of the area.The state of stress in a pressure p fluid in motion is a topic that is normally treated thoroughly in fluid mechanics.The deviation of a normal stress from the pressure,the normal stress that would exist were the fluid at rest,is typically very small.In this book we assume that the normal stress at a point is equal to the pressure at that point.This assumption yields results of acceptable accuracy for the applications considered.Also,the term pressure,unless Tank stated otherwise,refers to absolute pressure:pressure with respect to the zero pressure of a complete vacuum.The lowest possible value of absolute pressure is zero. Manometer liquid 1.6.1 Pressure Measurement Fig.1.7 Manometer. Manometers and barometers measure pressure in terms of the length of a column of liquid such as mercury,water,or oil.The manometer shown in Fig.1.7 has one end Mercury vapor,Pvapor open to the atmosphere and the other attached to a tank containing a gas at a uniform pressure.Since pressures at equal elevations in a continuous mass of a liquid or gas at rest are equal,the pressures at points a and b of Fig.1.7 are equal.Applying an elementary force balance,the gas pressure is p=Patm pgL (1.11) where patm is the local atmospheric pressure,p is the density of the manometer liquid, g is the acceleration of gravity,and L is the difference in the liquid levels. The barometer shown in Fig.1.8 is formed by a closed tube filled with liquid mer- Mercury,Pm cury and a small amount of mercury vapor inverted in an open container of liquid mercury.Since the pressures at points a and b are equal,a force balance gives the Fig.1.8 Barometer
1.6 Pressure 15 If the area A9 was given new orientations by rotating it around the given point, and the pressure determined for each new orientation, it would be found that the pressure at the point is the same in all directions as long as the fluid is at rest. This is a consequence of the equilibrium of forces acting on an element of volume surrounding the point. However, the pressure can vary from point to point within a fluid at rest; examples are the variation of atmospheric pressure with elevation and the pressure variation with depth in oceans, lakes, and other bodies of water. Consider next a fluid in motion. In this case the force exerted on an area passing through a point in the fluid may be resolved into three mutually perpendicular components: one normal to the area and two in the plane of the area. When expressed on a unit area basis, the component normal to the area is called the normal stress, and the two components in the plane of the area are termed shear stresses. The magnitudes of the stresses generally vary with the orientation of the area. The state of stress in a fluid in motion is a topic that is normally treated thoroughly in fluid mechanics. The deviation of a normal stress from the pressure, the normal stress that would exist were the fluid at rest, is typically very small. In this book we assume that the normal stress at a point is equal to the pressure at that point. This assumption yields results of acceptable accuracy for the applications considered. Also, the term pressure, unless stated otherwise, refers to absolute pressure: pressure with respect to the zero pressure of a complete vacuum. The lowest possible value of absolute pressure is zero. 1.6.1 Pressure Measurement Manometers and barometers measure pressure in terms of the length of a column of liquid such as mercury, water, or oil. The manometer shown in Fig. 1.7 has one end open to the atmosphere and the other attached to a tank containing a gas at a uniform pressure. Since pressures at equal elevations in a continuous mass of a liquid or gas at rest are equal, the pressures at points a and b of Fig. 1.7 are equal. Applying an elementary force balance, the gas pressure is p patm rgL (1.11) where patm is the local atmospheric pressure, is the density of the manometer liquid, g is the acceleration of gravity, and L is the difference in the liquid levels. The barometer shown in Fig. 1.8 is formed by a closed tube filled with liquid mercury and a small amount of mercury vapor inverted in an open container of liquid mercury. Since the pressures at points a and b are equal, a force balance gives the absolute pressure Nanoscience is the study of molecules and molecular structures, called nanostructures, having one or more dimensions less than about 100 nanometers. One nanometer is one-billionth of a meter: 1 nm 5 1029 m. To grasp this level of smallness, a stack of 10 hydrogen atoms would have a height of 1 nm, while a human hair has a diameter of about 50,000 nm. Nanotechnology is the engineering of nanostructures into useful products. At the nanotechnology scale, behavior may differ from our macroscopic expectations. For example, the averaging used to assign property values at a point in the continuum model may no longer apply owing to the interactions among the atoms under consideration. Also at these scales, the nature of physical phenomena such as current flow may depend explicitly on the physical size of devices. After many years of fruitful research, nanotechnology is now poised to provide new products with a broad range of uses, including implantable chemotherapy devices, biosensors for glucose detection in diabetics, novel electronic devices, new energy conversion technologies, and smart materials as, for example, fabrics that allow water vapor to escape while keeping liquid water out. Big Hopes for Nanotechnology HORIZONS Fig. 1.8 Barometer. Fig. 1.7 Manometer. Tank L a b patm Manometer liquid Gas at pressure p a patm L Mercury vapor, pvapor b Mercury, ρm
16 Chapter 1 Getting Started Elliptical metal Pointer atmospheric pressure as Bourdon tube Patm =Pvapor pmgL (1.12） where pm is the density of liquid mercury.Because the pressure of the mercury vapor is much less than that of the atmosphere,Eq.1.12 can Pinion be approximated closely as Patm =pmgL.For short columns of liquid, gear p and g in Eqs.1.11 and 112 may be taken as constant. Support Pressures measured with manometers and barometers are frequently Linkage expressed in terms of the length L in millimeters of mercury(mmHg), inches of mercury (inHg),inches of water (inH2O),and so on. FOR EXAMPLE a barometer reads 750 mmHg.If pm=13.59 g/cm and g 9.81 m/s2,the atmospheric pressure,in N/m2,is calculated as Gas at pressure p follows: Fig.1.9 Pressure measurement by a Bourdon tube gage. Patm =PmgL 9.81 750mmHg） 1m 103mm kg·m/s2 =105N/m244444 A Bourdon tube gage is shown in Fig.1.9.The figure shows a curved tube having an elliptical cross section with one end attached to the pressure to be measured and the other end connected to a pointer by a mechanism.When fluid under pressure fills the tube,the elliptical section tends to become circular,and the tube straightens. This motion is transmitted by the mechanism to the pointer.By calibrating the deflection of the pointer for known pressures,a graduated scale can be determined from which any applied pressure can be read in suitable units.Because of its con- struction,the Bourdon tube measures the pressure relative to the pressure of the surroundings existing at the instrument.Accordingly,the dial reads zero when the inside and outside of the tube are at the same pressure. Pressure can be measured by other means as well.An impor- tant class of sensors utilizes the piezoelectric effect:A charge is generated within certain solid materials when they are deformed. This mechanical input/electrical output provides the basis for pres- sure measurement as well as displacement and force measure- ments.Another important type of sensor employs a diaphragm that deflects when a force is applied,altering an inductance,resis- Fig.1.10 Pressure sensor with automatic data tance,or capacitance.Figure 1.10 shows a piezoelectric pressure acquisition. sensor together with an automatic data acquisition system. 1.6.2 Buoyancy When a body is completely or partially submerged in a liquid,the resultant pressure buoyant force force acting on the body is called the buoyant force.Since pressure increases with depth from the liquid surface,pressure forces acting from below are greater than pressure forces acting from above;thus,the buoyant force acts vertically upward.The buoyant force has a magnitude equal to the weight of the displaced liquid (Archimedes' principle). RXAMPLapplying Eq.111 to the submerged rectangular block shown in Fig.1.11,the magnitude of the net force of pressure acting upward,the buoyant
16 Chapter 1 Getting Started A Bourdon tube gage is shown in Fig. 1.9. The figure shows a curved tube having an elliptical cross section with one end attached to the pressure to be measured and the other end connected to a pointer by a mechanism. When fluid under pressure fills the tube, the elliptical section tends to become circular, and the tube straightens. This motion is transmitted by the mechanism to the pointer. By calibrating the deflection of the pointer for known pressures, a graduated scale can be determined from which any applied pressure can be read in suitable units. Because of its construction, the Bourdon tube measures the pressure relative to the pressure of the surroundings existing at the instrument. Accordingly, the dial reads zero when the inside and outside of the tube are at the same pressure. Pressure can be measured by other means as well. An important class of sensors utilizes the piezoelectric effect: A charge is generated within certain solid materials when they are deformed. This mechanical input/electrical output provides the basis for pressure measurement as well as displacement and force measurements. Another important type of sensor employs a diaphragm that deflects when a force is applied, altering an inductance, resistance, or capacitance. Figure 1.10 shows a piezoelectric pressure sensor together with an automatic data acquisition system. atmospheric pressure as patm pvapor rmgL (1.12) where m is the density of liquid mercury. Because the pressure of the mercury vapor is much less than that of the atmosphere, Eq. 1.12 can be approximated closely as patm 5 mgL. For short columns of liquid, and g in Eqs. 1.11 and 1.12 may be taken as constant. Pressures measured with manometers and barometers are frequently expressed in terms of the length L in millimeters of mercury (mmHg), inches of mercury (inHg), inches of water (inH2O), and so on. a barometer reads 750 mmHg. If m 5 13.59 g/cm3 and g 5 9.81 m/s2 , the atmospheric pressure, in N/m2 , is calculated as follows: Support Linkage Pinion gear Elliptical metal Pointer Bourdon tube Gas at pressure p Fig. 1.9 Pressure measurement by a Bourdon tube gage. patm rmgL c a13.59 g cm3 b ` 1 kg 103 g ` ` 102 cm 1 m ` 3 d c9.81m s 2 d c1750 mmHg2 ` 1 m 103 mm `d ` 1 N 1 kg m/s 2 ` 105 N/m2 b b b b b Fig. 1.10 Pressure sensor with automatic data acquisition. 1.6.2 Buoyancy When a body is completely or partially submerged in a liquid, the resultant pressure force acting on the body is called the buoyant force. Since pressure increases with depth from the liquid surface, pressure forces acting from below are greater than pressure forces acting from above; thus, the buoyant force acts vertically upward. The buoyant force has a magnitude equal to the weight of the displaced liquid (Archimedes’ principle). applying Eq. 1.11 to the submerged rectangular block shown in Fig. 1.11, the magnitude of the net force of pressure acting upward, the buoyant buoyant force
1.6 Pressure 17 force,is Patm F=A(p2-p1)=A(patm +pgL2)-A(Patm pgL1) P8A(L2-L1) pgV Liquid with density p where V is the volume of the block and p is the density of the surrounding liquid.Thus,the magnitude of the buoyant force acting on the block is equal to the weight of the displaced liquid. Block 1.6.3 Pressure Units Area=A The SI unit of pressure and stress is the pascal: 1 pascal 1 N/m2 Fig.1.11 Evaluation of buoyant force for a Multiples of the pascal,the kPa,the bar,and the MPa,are frequently submerged body. used. 1 kPa 10 N/m2 1 bar 105 N/m2 1 MPa 106 N/m2 Commonly used English units for pressure and stress are pounds force per square foot,Ibf/ft2,and pounds force per square inch,Ibf/in.2 Although atmospheric pressure varies with location on the earth,a standard refer- ence value can be defined and used to express other pressures. 1.01325×105N/m2 1 standard atmosphere (atm) 14.6961bfin.2 (1.13) 760 mmHg 29.92 inHg Since 1 bar (105 N/m2)closely equals one standard atmosphere,it is a convenient pressure unit despite not being a standard SI unit.When working in SI,the bar,MPa, and kPa are all used in this text. Although absolute pressures must be used in thermodynamic relations,pressure- measuring devices often indicate the difference between the absolute pressure of a system and the absolute pressure of the atmosphere existing outside the measuring device.The magnitude of the difference is called a gage pressure or a vacuum pressure. gage pressure The term gage pressure is applied when the pressure of the system is greater than the vacuum pressure local atmospheric pressure,Patm. p(gage)=p(absolute)-patm(absolute) (1.14) When the local atmospheric pressure is greater than the pressure of the system,the term vacuum pressure is used. TAKE NOTE... In this book,the term pres- p(vacuum)=Patm(absolute)-p(absolute) (1.15) sure refers to absolute pressure unless indicated Engineers in the United States frequently use the letters a and g to distinguish between otherwise. absolute and gage pressures.For example,the absolute and gage pressures in pounds force per square inch are written as psia and psig,respectively.The relationship among the various ways of expressing pressure measurements is shown in Fig.1.12
1.6 Pressure 17 force, is F A1p2 p12 A1patm rgL22 A1patm rgL12 rgA1L2 L12 rgV where V is the volume of the block and is the density of the surrounding liquid. Thus, the magnitude of the buoyant force acting on the block is equal to the weight of the displaced liquid. b b b b b 1.6.3 Pressure Units The SI unit of pressure and stress is the pascal: 1 pascal 1 N/m2 Multiples of the pascal, the kPa, the bar, and the MPa, are frequently used. 1 kPa 103 N/m2 1 bar 105 N/m2 1 MPa 106 N/m2 Commonly used English units for pressure and stress are pounds force per square foot, lbf/ft2 , and pounds force per square inch, lbf/in.2 Although atmospheric pressure varies with location on the earth, a standard reference value can be defined and used to express other pressures. 1 standard atmosphere 1atm2 • 1.01325 105 N/m2 14.696 lbf/in.2 760 mmHg 29.92 inHg (1.13) Since 1 bar (105 N/m2 ) closely equals one standard atmosphere, it is a convenient pressure unit despite not being a standard SI unit. When working in SI, the bar, MPa, and kPa are all used in this text. Although absolute pressures must be used in thermodynamic relations, pressuremeasuring devices often indicate the difference between the absolute pressure of a system and the absolute pressure of the atmosphere existing outside the measuring device. The magnitude of the difference is called a gage pressure or a vacuum pressure. The term gage pressure is applied when the pressure of the system is greater than the local atmospheric pressure, patm. p1gage2 p1absolute2 patm1absolute2 (1.14) When the local atmospheric pressure is greater than the pressure of the system, the term vacuum pressure is used. p1vacuum2 patm1absolute2 p1absolute2 (1.15) Engineers in the United States frequently use the letters a and g to distinguish between absolute and gage pressures. For example, the absolute and gage pressures in pounds force per square inch are written as psia and psig, respectively. The relationship among the various ways of expressing pressure measurements is shown in Fig. 1.12. gage pressure vacuum pressure L2 L1 patm p2A p1A Area = A Liquid with density ρ Block Fig. 1.11 Evaluation of buoyant force for a submerged body. TAKE NOTE... In this book, the term pressure refers to absolute pressure unless indicated otherwise.
18 Chapter 1 Getting Started p(gage) Absolute pressure that is Atmospheric greater than the local pressure atmospheric pressure p(absolute) p(vacuum) Absolute pressure that is (absolute) less than the local atmospheric pressure p (absolute) Zero pressure Zero pressure Fig.1.12 Relationships among the absolute,atmospheric,gage,and vacuum pressures. BIOCONNECTIONS One in three Americans is said to have high blood pressure.Since this can lead to heart disease,strokes,and other serious medical complications,medical practitioners recommend regular blood pres- sure checks for everyone.Blood pressure measurement aims to determine the maximum pressure (systolic pressure)in an artery when the heart is pumping blood and the minimum pressure(diastolic pressure)when the heart is resting,each pres- sure expressed in millimeters of mercury,mmHg.The systolic and diastolic pressures of healthy persons should be less than about 120 mmHg and 80 mmHg,respectively. The standard blood pressure measurement apparatus in use for decades involving an inflatable cuff,mercury manometer,and stethoscope is gradually being replaced because of concerns over mercury toxicity and in response to special requirements,including monitor- ing during clinical exercise and during anesthesia.Also,for home use and self-monitoring, many patients prefer easy-to-use automated devices that provide digital displays of blood pressure data.This has prompted biomedical engineers to rethink blood pressure measure- ment and develop new mercury-free and stethoscope-free approaches.One of these uses a highly sensitive pressure transducer to detect pressure oscillations within an inflated cuff placed around the patient's arm.The monitor's software uses these data to calculate the systolic and diastolic pressures,which are displayed digitally. 1.7 Temperature In this section the intensive property temperature is considered along with means for measuring it.A concept of temperature,like our concept of force,originates with our sense perceptions.Temperature is rooted in the notion of the"hotness"or"coldness" of objects.We use our sense of touch to distinguish hot objects from cold objects and to arrange objects in their order of"hotness,"deciding that 1 is hotter than 2,2 hotter
18 Chapter 1 Getting Started Fig. 1.12 Relationships among the absolute, atmospheric, gage, and vacuum pressures. Atmospheric pressure p (gage) p (absolute) patm (absolute) p (absolute) p (vacuum) Zero pressure Zero pressure Absolute pressure that is less than the local atmospheric pressure Absolute pressure that is greater than the local atmospheric pressure 1.7 Temperature In this section the intensive property temperature is considered along with means for measuring it. A concept of temperature, like our concept of force, originates with our sense perceptions. Temperature is rooted in the notion of the “hotness” or “coldness” of objects. We use our sense of touch to distinguish hot objects from cold objects and to arrange objects in their order of “hotness,” deciding that 1 is hotter than 2, 2 hotter One in three Americans is said to have high blood pressure. Since this can lead to heart disease, strokes, and other serious medical complications, medical practitioners recommend regular blood pressure checks for everyone. Blood pressure measurement aims to determine the maximum pressure (systolic pressure) in an artery when the heart is pumping blood and the minimum pressure (diastolic pressure) when the heart is resting, each pressure expressed in millimeters of mercury, mmHg. The systolic and diastolic pressures of healthy persons should be less than about 120 mmHg and 80 mmHg, respectively. The standard blood pressure measurement apparatus in use for decades involving an inflatable cuff, mercury manometer, and stethoscope is gradually being replaced because of concerns over mercury toxicity and in response to special requirements, including monitoring during clinical exercise and during anesthesia. Also, for home use and self-monitoring, many patients prefer easy-to-use automated devices that provide digital displays of blood pressure data. This has prompted biomedical engineers to rethink blood pressure measurement and develop new mercury-free and stethoscope-free approaches. One of these uses a highly sensitive pressure transducer to detect pressure oscillations within an inflated cuff placed around the patient’s arm. The monitor's software uses these data to calculate the systolic and diastolic pressures, which are displayed digitally. BIOCONNECTIONS
1.7 Temperature 19 than 3,and so on.But however sensitive human touch may be,we are unable to gauge Ext_Int_Properties this quality precisely. A.3-Tab e A definition of temperature in terms of concepts that are independently defined or accepted as primitive is difficult to give.However,it is possible to arrive at an objective understanding of equality of temperature by using the fact that when the temperature of an object changes,other properties also change. To illustrate this,consider two copper blocks,and suppose that our senses tell us that one is warmer than the other.If the blocks were brought into contact and iso- lated from their surroundings,they would interact in a way that can be described as a thermal (heat)interaction.During this interaction,it would be observed that the thermal (heat)interaction volume of the warmer block decreases somewhat with time,while the volume of the colder block increases with time.Eventually,no further changes in volume would be observed,and the blocks would feel equally warm.Similarly,we would be able to observe that the electrical resistance of the warmer block decreases with time and that of the colder block increases with time:eventually the electrical resistances would become constant also.When all changes in such observable properties cease. the interaction is at an end.The two blocks are then in thermal equilibrium.Consid- thermal equilibrium erations such as these lead us to infer that the blocks have a physical property that determines whether they will be in thermal equilibrium.This property is called temperature,and we postulate that when the two blocks are in thermal equilibrium, temperature their temperatures are equal. It is a matter of experience that when two objects are in thermal equilibrium with a third object,they are in thermal equilibrium with one another.This statement,which is sometimes called the zeroth law of thermodynamics,is tacitly assumed in every zeroth law of measurement of temperature.If we want to know if two objects are at the same thermodynamics temperature,it is not necessary to bring them into contact and see whether their observable properties change with time,as described previously.It is necessary only to see if they are individually in thermal equilibrium with a third object.The third object is usually a thermometer. 1.7.1 Thermometers Any object with at least one measurable property that changes as its temperature changes can be used as a thermometer.Such a property is called a thermometric thermometric property property.The particular substance that exhibits changes in the thermometric property is known as a thermometric substance. A familiar device for temperature measurement is the liquid-in-glass thermometer pictured in Fig.1.13a,which consists of a glass capillary tube connected to a bulb filled with a liquid such as alcohol and sealed at the other end.The space above the liquid is occupied by the vapor of the liquid or an inert gas.As temperature increases, the liquid expands in volume and rises in the capillary.The length L of the liquid in the capillary depends on the temperature.Accordingly.the liquid is the thermometric substance and L is the thermometric property.Although this type of thermometer is commonly used for ordinary temperature measurements,it is not well suited for appli- cations where extreme accuracy is required. More accurate sensors known as thermocouples are based on the principle that when two dissimilar metals are joined,an electromotive force (emf)that is primarily a function of temperature will exist in a circuit.In certain thermocouples,one ther- mocouple wire is platinum of a specified purity and the other is an alloy of platinum and rhodium.Thermocouples also utilize copper and constantan (an alloy of copper and nickel),iron and constantan,as well as several other pairs of materials.Electrical- resistance sensors are another important class of temperature measurement devices. These sensors are based on the fact that the electrical resistance of various materials changes in a predictable manner with temperature.The materials used for this pur- pose are normally conductors(such as platinum,nickel,or copper)or semiconductors
1.7 Temperature 19 than 3, and so on. But however sensitive human touch may be, we are unable to gauge this quality precisely. A definition of temperature in terms of concepts that are independently defined or accepted as primitive is difficult to give. However, it is possible to arrive at an objective understanding of equality of temperature by using the fact that when the temperature of an object changes, other properties also change. To illustrate this, consider two copper blocks, and suppose that our senses tell us that one is warmer than the other. If the blocks were brought into contact and isolated from their surroundings, they would interact in a way that can be described as a thermal (heat) interaction. During this interaction, it would be observed that the volume of the warmer block decreases somewhat with time, while the volume of the colder block increases with time. Eventually, no further changes in volume would be observed, and the blocks would feel equally warm. Similarly, we would be able to observe that the electrical resistance of the warmer block decreases with time and that of the colder block increases with time; eventually the electrical resistances would become constant also. When all changes in such observable properties cease, the interaction is at an end. The two blocks are then in thermal equilibrium. Considerations such as these lead us to infer that the blocks have a physical property that determines whether they will be in thermal equilibrium. This property is called temperature, and we postulate that when the two blocks are in thermal equilibrium, their temperatures are equal. It is a matter of experience that when two objects are in thermal equilibrium with a third object, they are in thermal equilibrium with one another. This statement, which is sometimes called the zeroth law of thermodynamics, is tacitly assumed in every measurement of temperature. If we want to know if two objects are at the same temperature, it is not necessary to bring them into contact and see whether their observable properties change with time, as described previously. It is necessary only to see if they are individually in thermal equilibrium with a third object. The third object is usually a thermometer. 1.7.1 Thermometers Any object with at least one measurable property that changes as its temperature changes can be used as a thermometer. Such a property is called a thermometric property. The particular substance that exhibits changes in the thermometric property is known as a thermometric substance. A familiar device for temperature measurement is the liquid-in-glass thermometer pictured in Fig. 1.13a, which consists of a glass capillary tube connected to a bulb filled with a liquid such as alcohol and sealed at the other end. The space above the liquid is occupied by the vapor of the liquid or an inert gas. As temperature increases, the liquid expands in volume and rises in the capillary. The length L of the liquid in the capillary depends on the temperature. Accordingly, the liquid is the thermometric substance and L is the thermometric property. Although this type of thermometer is commonly used for ordinary temperature measurements, it is not well suited for applications where extreme accuracy is required. More accurate sensors known as thermocouples are based on the principle that when two dissimilar metals are joined, an electromotive force (emf) that is primarily a function of temperature will exist in a circuit. In certain thermocouples, one thermocouple wire is platinum of a specified purity and the other is an alloy of platinum and rhodium. Thermocouples also utilize copper and constantan (an alloy of copper and nickel), iron and constantan, as well as several other pairs of materials. Electricalresistance sensors are another important class of temperature measurement devices. These sensors are based on the fact that the electrical resistance of various materials changes in a predictable manner with temperature. The materials used for this purpose are normally conductors (such as platinum, nickel, or copper) or semiconductors. thermal (heat) interaction thermal equilibrium temperature zeroth law of thermodynamics thermometric property Ext_Int_Properties A.3 – Tab e