Temperature measurement

Transcription

1 emperature measurement BASICS Interest in emperature measurements appeared definitively later as respect to other quantities. emperature is an intensive quantity (a quantity strictly correlated to temperature must be used).

2 emperature measurement Wikipedia In the physical sciences, an intensive property (also called a bulk property, intensive quantity, or intensive variable), is a physical property of a system that does not depend on the system size or the amount of material in the system: it is scale invariant. By contrast, an extensive property (also extensive quantity, extensive variable, or extensive parameter) is one that is additive for independent, noninteracting subsystems. It is directly proportional to the amount of material in the system. For example, density is an intensive property of a substance because it does not depend on the amount of that substance; mass and volume, which are measures of the amount of the substance, are extensive properties. 2

3 emperature measurement By contrast to quantities like mass, time, lenght, temperature cannot be measured by comparison with temperature reference. A different approach is hence required WE NEED O USE EMPERAURE SCALES, WHICH CAN BE DEFINED BY EXPLOIING PHYSISCAL LAW AND IMPLEMENED BY PHYSICAL DEVICES EXPLOIING SUCH PHYSICAL LAWS

4 emperature measurement All temperature scales, including the modern thermodynamic temperature scale used in the International System of Units, are calibrated according to thermal properties of a particular substance or device. he following ingredients must be fixed: a substance or a thermometric property; (two) well-defined temperature points; defining temperature increments via a (linear) interpolation function of the response of the thermometric device. For example, both the old Celsius scale and Fahrenheit scale were originally based on the linear expansion of a narrow mercury column within a limited range of temperature, each using different reference points and scale increments.

5 emperature measurement Celsius scale and Fahrenheit scale Substance: mercury; temperature points: melting (32 F, 0 C) and boiling (212 F, 100 C)point of water; Linear interpolation function from Celsius to Fahrenheit [ F] = [ C] From Fahrenheit to Celsius [ C] = ([ F] 32) 5 9

6 emperature measurement Empirical scales Empirical scales are based on the measurement of physical parameters that express the property of interest (to be measured) through some formal, most commonly a simple linear, functional relationship. Es. expansion of a narrow mercury column!!!

7 emperature measurement Different empirical scales may not be compatible with each other, except for small regions of temperature overlap. Example If an alcohol thermometer and a mercury thermometer have same two fixed points, namely the freezing and boiling point of water, their reading will not agree with each other except at the fixed points, as the linear 1:1 relationship of expansion between any two thermometric substances may not be guaranteed.

8 emperature measurement An ideal temperature scale should not depend on the adopted substance or the quantity adopted to estimate temperature! A solution could be the use of thermodinamic laws: he thermodinamic temperature scale

9 emperature measurement he thermodinamic temperature scale Because of Carnot theorem, any reversible heat engine operating between temperatures 1 and 2 must have the same efficiency, meaning, the efficiency is the function of the temperatures only: Q 1 /Q 0 = 1 / 0 Q 0, 0 Q 1, 1 If the emperature point is fixed (riple point of water 0 =273,16K), a relationship between the target temperature and the heat exchange can be estimated.

10 emperature measurement riple point of water 0 =273,16K

11 emperature measurement he thermodinamic temperature scale based on the Carnot cycle is ideal. By using the same triple point of water the GAS LAW can be exploited. PV=nR n gas moles; R gas universal constant GAS hermometers can exploit: A volume costant approach: P/P 0 =/ 0 A pressure costant approach: V/V 0 =/ 0

12 Gas hermometer Atmosphere Pressure P P 0 P/P 0 =/ 0 is the target temperature; he Volume of the Gas will change as a function of the temperature. he GAS volume inside the bulb must be constant. he height, h, of tank R is changed in order to maintain fixed the mercury height in the left hand side column (the gas volume is kept constant) Restoring the Gas Volume will change the Gas pressure. he new gas pressure, P, is estimated by: P 0 = P + ρgh P = P 0 - ρgh Where P 0 is the atmosphere pressure. he calibration procedure (triple point of water) allows the estimation of a proportional constant C such that: = C P 12

13 emperature measurement SIP (IS-90) Since, the thermodinamic temperature scale is very complex to be implemented, the SIP emperature Scale has been defined. Measurement units emperature intervals emperature points Interpolating functions Interpolating instruments (hermometer) 13

14 emperature measurement IS-90: Interpolating Instruments [0.65 K 5,0 K] Vapor pressure thermometer (using 3 He and 4 He); [3,0K K] Helium constant volume thermometer; [13,8033K C] Platinum Resistive hermometer; Above C Monocromatic Pyrometer 14

15 emperature measurement Other principles for temperature measurement Magnetic thermometry It works properly below 2K where gas thermometry cannot be used and it exploits the relationship between the magnetic material c susceptivity and temperature Acustic thermometry which exploits the dependence of sound velocity in gas by the gas temperature itself V 02 =g 0 R/M Noise thermometry which exploits the thermal noise in a resistor: V eff2 =4kRDf with k= 1, J/K -1. Radiation thermometry.

16 emperature measurement Resistive thermometry It is based on the following law r(t)= r(t 0 )(1+aDt+bDt 2 + ) r(t 0 )(1+aDt) Nickel: poor linearity, high responsivity; Copper: good linearity, easy oxidation at high temperature; Platinum: offers a good compromise between linearity, stability and responsivity.

17 emperature measurement Resistive thermometry

18 emperature measurement Primary Standard Platinum Resistance hermometer, SPR High cost Poor robustness Range: [ 200 C, 1000 C] Accuracy: ±0.001 C

19 La misura della temperatura Secondary Standard Platinum Resistance hermometer, SPR Range: [ 200 C, 500 C] Accuracy: ±0.03 C a= C 1 Industrial Platinum Resistance hermometer Range: [ 200 C, 500 C] Accuracy: da ±0.25 C a ±2.5 C

20 emperature measurement Wire-wound elements for resistive thermometer Range: [ 200 C, 660 C] he coil diameter provides a compromise between mechanical stability and allowing expansion of the wire to minimize strain and consequential drift. he sensing wire is wrapped around an insulating mandrel or core. he winding core can be round or flat, but must be an electrical insulator. he coefficient of thermal expansion of the winding core material is matched to the sensing wire to minimize any mechanical strain. he sensing wire is connected to a larger wire, usually referred to as the element lead or wire. his wire is selected to be compatible with the sensing wire so that the combination does not generate an emf that would distort the thermal measurement.

21 emperature measurement hard fired ceramic oxide tube Coiled elements elements for resistive thermometer small coil of platinum sensing wire Range: [ 200 C, 850 C] hese devices have largely replaced wire-wound elements in industry. his design has a wire coil which can expand freely over temperature, held in place by some mechanical support which lets the coil keep its shape. his strain free design allows the sensing wire to expand and contract free of influence from other materials; It is similar to the SPR, the primary standard upon which IS-90 is based, while providing the durability necessary for industrial use.

22 emperature measurement Platinum thin film sensor hin film elements have a sensing element that is formed by depositing a very thin layer of resistive material, normal platinum, on a ceramic substrate; his layer is usually just 10 to 100 angstroms (1 to 10 nanometers) thick and it is coated with an epoxy or glass that helps protect the deposited film and also acts as a strain relief for the external lead-wires. Disadvantages not as stable as their wire wound or coiled counterparts; limited temperature range due to the different expansion rates of the substrate and resistive deposited giving a "strain gauge" effect that can be seen in the resistive temperature coefficient. Range: [-50 C, 400 C] Accuracy: da ± 0.5 C a ±2.0 C a= C

23 emperature measurement Resistive thermometers Metal based sensors (RD): r(t)= r(t 0 )(1+aDt+bDt 2 + ) r(t 0 )(1+aDt) Example Platinum: a3.912 x 10-3 /K e b x 10-7 /K 2 Above parameters guarantee that for temperature up to 650 C the linear term dominates (10 time greater than the quadratic term) Semiconductor based sensors : r r o e E 1 k 1 - o he temperature coefficient (Ω/Ω)/K is positive for metallic sensors and negative for semiconductors.

24 emperature measurement Resistive thermometers For metal sensors (RD) : r(t)= r(t 0 )(1+aDt+bDt 2 + ) r(t 0 )(1+aDt) R R R rl S l r( t0 ) ( 1 adt S R ( 1 x ) 0 ) R 0 ( 1 adt ) he resistivity increases with temperature due to thermal agitation

25 emperature measurement hermistor (NC, PC) Semiconductor PC sensors (Barium itanate) strongly doped: he resistivity increases with temperature due to thermal agitation. Semiconductor NC sensors (Nickel, Cobalt, Manganesium) poorly doped he resistivity decreases with temperature due to increasement of free charges mobility. R R 0 1 B e - 1 o Where B is the Characteristic emperature R 0 =is the 25 C 25

26 emperature measurement NC thermistor R R 0 1 B e - 1 o Semiconductor temperature sensors are lighter that RD sensors, more responsive and strongly non linear. Operating range: [ 100 C e 450 C]

27 emperature measurement raditional electronics hermistors (NC, PC) R=R partitore //R carico he trend is non linear Anyway it is possible to linearize a well defined operating range by propoerly choose the R value

28 emperature measurement Examples: hermistors (NC, PC) ypical applications of PC sensors for overtemperature.

29 emperature measurement Self-Heating in resistive sensors he thermal dissipation is due to the flowing current and it can be estimated by: Example: RD: R=100 Ω, =6 mw/k. = P D /D(mW/K) Which is the maximum smaller than 0.1 C.? current causing a self-heating error D P D 2 I R 0.1 C0.006W / K D I 2. 4 R 100 ma 29

30 emperature measurement hermoelectric thermometry Absolute Seebeck Effect (1822): Given an electrical conductor, between two points, a and b, with different temperatures an electromotive force e.m.f. appears: a, a M E M de M ( )d b, b E M ( a, b ) b ( a )d is the homson coefficient and depends on the material.

31 emperature measurement hermoelectric thermometry hermocouples: Such devices are active sensors composed of two materials with a common junction. a, a M N E M E N E b, b c, c he e.m.f. E depends on the materials and the junction temperatures. 31

32 emperature measurement hermoelectric thermometry Relative Seebeck effect a, m M N E M E N E b, r c, r E m m M d - Nd - r E M ( m, r r )- E N ( m : arget temperature under measurement; m M N m r, r : Reference temperature r ) d

33 emperature measurement hermoelectric thermometry Relative Seebeck effect a, m M N E M E N E b, r c, r Example: in case of a hermocouple with the cold junction at 20 C and the hot junction at 100 C, known the two e.m.f. are 0,79 mv and 4,28 mv, E will be: E= 4,28-0,79= 3,49 mv

34 emperature measurement hermocouple Conductors Positive Conductors Negative ype B Platinum-30% rhodium Platinum-6% rhodium E Nickel-chromium alloy Copper-nickel alloy J Iron Copper-nickel alloy K Nickel-chromium alloy Nickel-aluminum alloy N Nickel-chromium-silicon Nickel-silicon-magnesium alloy alloy R Platinum-13% rhodium Platinum S Platinum-10% rhodium Platinum Copper Copper-nickel alloy 34

35 emperature measurement hermoelectric thermometry J K 35

36 emperature measurement hermoelectric thermometry Realistic hermocouple Circuits he true nature of the Seebeck phenomenon is the occurrence of a source emf that, for accurate thermometry, must be measured in open-circuit mode that suppresses current. In practical thermometry, no realistic thermocouple circuit has only two dissimilar materials. Some have many dissimilar materials and several of these can be expected to contribute some Seebeck emf. hermometry circuits can have one or two separate reference junctions. 36

37 emperature measurement hermoelectric thermometry Single reference junction E B E A E E A his configuration allows for very accurate measurements where the cold junction can be at fixed temperature (triple point of water, water and ice) or it can be independently measured. Hypothesys: i = a = f : to avoid Seebeck effects inside the instrument c = d : to avoid Seeback effects dur to the C material; Under such constraints: E m r E B A' E d B r m E A A d r i m r A d B d m - r m r B d A d i m m r A d B - A d 37

38 emperature measurement hermoelectric thermometry Double reference junctions s wo reference junctions must be at the same temperature. C and D are two conductors used to convey signals into the reader (extension leads). On the basis of C and D conductors the reference junctions can be: e,c or b,f. he instrument must have a compensation system to compensate for r. 38

39 emperature measurement hermoelectric thermometry Double reference junctions 0 i s Reference junctions could be e,c or b,f. 1) C e D Neutral Extension Leads: they are of the same material with same Seebeck coefficient, c = D. E - s i E D D E d B - m s E A B d E C m s A d s i C d Reference junctions: e, c. 39

40 emperature measurement hermoelectric thermometry Double reference junctions 0 i s 2) C e D Matching Extension Leads: c = A e B = D E - m i s i E A D D d E d - B - m i m s E B A B d d E C m s A d Reference junctions: b, f. s i C d 40

41 emperature measurement hermoelectric thermometry Double reference junctions 0 i s 3) C e D Compensating Extension Leads: C and D are choosen in orser to assure: CD = AB. he advantage as respect to matching extension leads is that they can be conventional materials. E - s i s i E D D CD d d E B - - m s m s E A B AB d E C d m s m i A d AB d s i C d 41

42 emperature measurement hermoelectric thermometry Relative Seebeck effect a, m M N E M E N E b, r c, r E f M, N, m, r Where f is non linear function. AENION!!!! In order to measure absolute temperature m, the temperature r must be known (measured).

43 emperature measurement hermoelectric thermometry he model f: E f,,, As always, we are interested to f -1!!!! M =a 0 +a 1 E+a 2 E 2 +a 3 E 3 N m r Model parameters are available in the literature and are related to a well defined value, 0 (0 C), of r. In case r 0 a compensation procedure (numerical or electronic) must be adopted. 43

44 emperature measurement hermoelectric thermometry he model =a 0 +a 1 E+a 2 E 2 +a 3 E 3 44

45 emperature measurement hermoelectric thermometry Cold junction compensation a, m Fe E Fe E Cn Cn b, r V FeCn is related to a cold junction at 0. V FeCn c, a In case of a cold junction at a temperature, a the V FeCn must be corrected by adding the voltage value, Vb, provided by the thermocouple when the temperature of the hot junction is a and the cold junction at 0. Example: if the cold and hot junctions are at the same temperature a (e.g. environmental) V FeCn =0, while it should be the value tabled for a : V FeCn a o such aim the following compensation approach is used: V= V FeCn +Vb 45

46 emperature measurement hermoelectric thermometry 46

47 emperature measurement Cold junction compensation Fig. 6.1 V b Es. FeCn hermocouple V It must be: Since: V IrCn V b Vb V IrCn a VIrCn Ka c a V b R ' 1 -V R 1 R ' R1 ' R1 R R ( 1 a ) 0 V b 2 R4 - ' R R 3 4 K a c Some design constraints can be used to fix circuit parameters: Es. ype J thermocouple to be compensated in a range [10 C-40 C.] From the able in the previous slide it could be evinced that K=( )/(40-10) V/ C; For the linearized bridge is: hence c=0. V b K (i.e. V b (0)=0 ) and 47

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49 emperature measurement hermoelectric thermometry class I and class II hermocouples

50 emperature measurement hermoelectric thermometry A series configuration of thermocouples will increases the responsivity A parallel configuration will provide the mean temperature value 50

51 emperature measurement hermocouples vs RD 51