Temperature Measurement

Gerald Recktenwald, Evan ThomasPortland State University

Department of Mechanical Engineering

Temperature Measurement

• Liquid bulb thermometers

• Gas bulb thermometers

• bimetal indicators

• RTD: resistance temperature detectors (Platinum wire)

• thermocouples

• thermistors

• IC sensors

• Optical sensors

Pyrometers⊲ ⊲ Infrared detectors/cameras liquid crystals⊲

IC Temperature Sensors

• Semiconductor-based temperature sensors or thermocouple reference-junctioncompensation

• Packaged suitable for inclusion in a circuit board

• Variety of outputs: analog (voltage or current) and digital

• More useful for a manufactured product or as part of a control system than aslaboratory instrumentation.

Thermistors

A thermistor is an electrical resistor used tomeasure temperature. A thermistor designed suchthat its resistance varies with temperature in arepeatable way.A simple model for the relationship betweentemperature and resistance is

ΔT = kΔR

A thermistor with k > 0 is said to have a positivetemperature coefficient (PTC). A thermistor withk < 0 is said to have a negative temperaturecoefficient (NTC).

Photo from YSI web site:www.ysitemperature.com

Thermistors

Advantages

• Output is directly related to absolute temperature - no reference junction needed.

• Relatively easy to measure resistance

• Sensors are interchangeable (±0.5◦C)

Disadvantages

• Possible self-heating error

⊲ Each measurement applies current to resistor from precision current source ⊲ Measure voltage drop ΔV , then compute resistance from known current and ΔV . Repeated measurements in rapid succession can cause thermistor to heat up⊲

• Can be more expensive than thermocouples for comparable accuracy: $10 to $20/eachversus $1/each per junction. Thermistors costing less than $1 each are available fromelectronic component sellers, e.g. Digikey or Newark.

• More difficult to apply for rapid transients: slow response and self-heating

Thermistors

50Data

Calibration uses the Steinhart-Hart equation

Nominal resistance is controllable bymanufacturing.

Typical resistances at 21◦C:10 kΩ, 20 kΩ, . . . 100 kΩ.

45 Curve Fit

40

35

30

25

20

15

10

5

05 10 15 20 25 30

Resistance (kΩ)

Thermistors

Two-wire resistance measurement:

Resistance in the lead wires can lead to inaccurate temperature measurement.

Ohmmeter

ThermistorI

RT V

Thermistors

Four-wire resistance measurement eliminates the lead resistance1

Ohmmeter

Rlead

Thermistor

RTRlead I

Rlead

Rlead

V

1Sketch adapted from Hints for Making Better Digital Multimeter Measurements, Agilent Technologies Corporation,www.agilent.com.

Thermocouples

• Principle of operation

• Wire types: B, E, J, K, N, R, S, T

• Formats: prefab, homemade, fast response, slow response

• Circuit diagrams: reference junction compensation

• Good practice

Heat

Metal A

Metal BVAB

+

-

Type K • Chromel {90% nickel and 10% chromium} • Alumel {95% nickel, 2% manganese, 2% aluminum and 1% silicon}• 41 µV/°C • −200 °C to +1350 °C / -330 °F to +2460 °F range.

Seebeck Effect

Temperature gradient in a conductor induces a voltage potential

T2

E12

Voltmeter

T1

E12 = σ(T2 − T1) (1)

where σ is the average Seebeck coefficient for the range T1 ≤ T ≤ T2.

Seebeck Effect

Perturb T2 while holding T1 fixed:

(2)

Subtract Equation (1) from Equation (2) to get

(3)

Rearrange

(4)

σ is an intrinsic property of the material, so

(5)

Seebeck Effect

Applying the limit yields the derivative:

so

(6)

Equation (6) is the definition of the Seebeck Coefficient

Nominal values of Seebeck Coefficient

σ values are small, so the voltage output from thermocouples is small, typically on theorder of 10−3 V.

Reference Junction

Thermocouples are only capable ofmeasuring temperature differences.

To measure the temperature of anobject, we need a known referencetemperature. The thermocouple isused to measure the temperaturedifference between the object andthe known reference temperature.

Physical Circuit:x

Tt Tr

1 Cu2

Voltmeter 5 Cu 4

Conceptual T(x) Plot:

Tj

Tt 1

Cu

Tr 2

material P Tj

3material N

3

5

Cu

4

x

Ejr

emf relativeto referencejunction

Etr

0

Ice Point Reference Junction

Ice-point reference junction used in the thermal lab:

Glass tube, partiallyfilled with oil

Ice/watermixture

Insulated thermos

Calibration Curves

Working with calibration data

• Integrals are never evaluated.• Data is tabulated and curve fit

• Standard polynomial curve fitsand coefficients are available forcommon thermocouple types

Calibration data for T-Typethermocouples:

E (mV) T (◦C)

0.0000 0

2.0357 50

4.2785 100

6.7041 150

9.2881 200

12.0134 250

14.8619 300

17.8187 350

20.8720 400

Temperature Data Acquisition and Analysis

Evan ThomasPortland State University

Department of Mechanical Engineering

Resolution – the number of bits involved in an analog to digital conversion. Conversion time – the time it takes for an ADC to convert an analog voltage sample to a digital code.Quantization error – The rounding error between the true analog value and the recorded digital value.

Analog to Digital Conversion

Voltage 2-Bit Digital Representation0 to 2.5 002.5 to 5 015 to 7.5 107.5 to 10 11

Digital Data• Hexadecimal numbers

– Save space

• Signing bit– Represent negative numbers– Known as twos complement

Decimal Hexadecimal0 01 12 23 34 45 56 67 78 89 910 A11 B12 C13 D14 E15 F

Bits Unsigned value 2's complement value0111 1111 127  127 0111 1110 126  126 0000 0010 2 2 0000 0001 1 1 0000 0000 0 0 1111 1111 255  −1 1111 1110 254  −2 1000 0010 130  −126 1000 0001 129  −127 1000 0000 128  −128 

Digital Data

R Project• The R Project for Statistical Computing is a free, open source and powerful

statistically, analysis and plotting software program. It can perform many of the tasks of Excel, Stata, MatLab and SAS, and integrate with many other systems including online datasets and MySQL databases.

• In this lab, we will use R to:– Download data from MySQL data tables– Import data from lab calibration runs– Plot data– Derive calibration curve