Thermocouples (continued)

Introduction to Temperature Sensors

ISAT 300 Instrumentation and Measurement

02/21/2000

Language of Thermocouples

Temperature Range -270oC to 2320oC depends on the type of the

thermocouple Passive

Dose not require external power source Non-intrusive

Does not affect the system much Linearity

In general, it is a nonlinear function of temperature Sensitivity

From 0.011 mV/oC for type R to 0.076 mV/oC for type E

Millivolt Output of Common Thermocouples (Reference Junction at 0oC)

-20

-10

0

10

20

30

40

50

60

70

80

90

-250 250 750 1250 1750

Temperature (C)

Ou

tpu

t (m

V)

K

T

J

E

R

S

Type Materials Lead wirecolor

Operatingrange(oC)

Approximatesensitivity(mV/oC)

T Copper/constantan Blue -250 to 400 0.052

E Chromel/constantan Purple -270 to 1000 0.076

J Iron/constantan Black -210 to 760 0.050

K Chromel/alumel Yellow -270 to 1372 0.039

R Platinum/platinum-13% rhodium

Green -50 to 1768 0.011

S Platinum/platinum-10% rhodium

Green -50 to 1768 0.012

E Tungsten, 5%rhenium/tungsten,26% rhenium

White,Red trace

0 to 2320 0.020

Characteristics of Standard Thermocouples

Common Sheathed Thermocouple Probe

Place the wires and junction and ceramic insulation inside a stainless steel or inconel sheath to protect the thermocouple wires from damage or chemical contamination.

Thermopile

When n thermocouples are connected in series in a device called a thermopile

Which increases the sensitivity of the system, however, it provides a method to average several thermocouples which are distributed in a spatial region.

C 0 1 2 3 4

20 0.798 0.838 0.879 0.919 0.960

Example:

A type K thermocouple with an ice reference gives a voltage reading of 0.900 mV. What is its temperature?

Thermoelectric voltage in mV

0.040 mV

0.900

0.021 mVC 53.22

1 040.0

021.0C 22

CT

C 0 1 2 3 4

300 2.401 2.410 2.420 2.430 2.440

Example:

A type R thermocouple with an ice reference gives a voltage reading of 2.415 mV. What is its temperature?

Thermoelectric voltage in mV

2.415C 5.301

1 010.0

005.0C 301

CT

12.207

30.10

42.307

-10

0

10

20

30

40

50

60

-500 0 500 1000 1500

Temperature (C)

Ou

tpu

t Vo

ltag

e (m

V)

The Importance of 0oC Reference Junction

C 0 1 2 3 4

30 0.171 0.177 0.183 0.189 0.195

Example:

A type R thermocouple with an ice reference gives a voltage reading of 2.415 mV. What would it read

with a 30 °C reference?

Thermoelectric voltage in mV

mV 244.2mV 171.0mV 415.2 V

C 0 1 2 3 4

280 2.207 2.217 2.226 2.236 2.246

Example:

A type R thermocouple with 30 °C reference gives a voltage reading of 2.244 mV. What is its temperature?

Thermoelectric voltage in mV

0.010 mV

2.244

0.008 mVC 8.310

30 1 010.0

008.0C 280

CCT

NO!

C 0 1 2 3 4

300 2.401 2.410 2.420 2.430 2.440

Thermoelectric voltage in mV

2.415 = 2.244 + 0.171C 5.301

1 010.0

005.0C 301

CT

Example:

A type R thermocouple with 30 °C reference gives a voltage reading of 2.244 mV. What is its temperature?

Correct the voltageFIRST!

First Order System A change at the input is NOT seen immediately at the output.

Example: Move a temperature probe from cold water to hot water.

CoolBath

HotBath

CdT t

d t

T T t

Rm c

dT t

d thA T T t

CJ

C

RC

WT (t)T

p w p pw p

o

o

p

w

( ) ( ) ( )[ ( )]

, o r, ,

w h ere , in is th e h ea t cap acity o f th e p ro b e .

in is th e th erm al resis tan ce o f th e p ro b e .

is th e tem p era tu re o f p ro b e , an d is th e tem p era tu re o f w ater.

CdT t

d t

T T t

RdT t

d t CRT t

CRT

p w p

p

p w

( ) ( )

( )( )

is a tran sien t h ea t co n d u ctio n eq u atio n ,

w h ich can b e rew ritten as 1 1

A Differential Equation

Assumed that the water temperature of the hot bath (Tw) does not cool down much (non-intrusive), and can be treated as a constant.

Then this equation simply just a first-order differential equation, a time dependent temperature equation of Tp(t), with an initial condition of Tp(0)=Tpo.

Solution for This Differential Equation

Here, C is the heat capacity, R is the thermal resistance of the temperature probe, they are the probe material properties should be given or known to us.

T h e so lu tio n fo r th is d ifferen tia l eq u atio n is

N o w , if w e ap p ly th e in itia l co n d itio n to

th is so lu tio n . w e w ill g e t , w h ere , = C R .

T t C e T

T t T T e T

p

t

w

p w po

t

po

( ) .

( ) ( )( )

1

o r, w e co u ld rearran ge it as T t T

T Te

p po

w po

t( )

1

The Time Constant, Response for Varying Values of

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Time

Res

po

nse

= 1.0 = 0.5

= 0.2

T t T

T Te

p po

w po

t( )

1

For t=, thermocouple reaches 63.2% of the steady-state or final value.