Chapter 7 THERMOELECTRIC THERMOMETRY

Thomson refers to this as the specific heat of electricity because of an apparent analogy between and the usual specific heat c of thermodynamics.

Note that represents the rate at which heat is absorbed , or evolved , per unit temperature difference per unit current , whereas c represents the heat transfer per unit temperature difference per unit mass .

The Thomson coefficient is also seen to represent an emf per unit difference in temperature. Thus the total Thomson voltage set up in a single conductor may be expressed as

7.1 Historical Development of Basic RelationsThomas Johann Seebeck , the German physicist , discovered

in 1821 the existence of thermoelectric currents while observing electromagnetic effects associated with bismuth-copper and bismuth-antimony circuits [1],[2].

His experiments showed that , when the junctions of two dissimilar metals forming a closed circuit are exposed to different temperatures , a net thermal electromotive force is generated that induces a continuous electric current .

The Seebeck effect concerns the net conversion of thermal energy into electrical energy with the appearance of an electric current. The Seebeck voltage refers to the net thermal electromotive force set up in a thermocouple under zero-current conditions. The direction and magnitude of the Seebeck voltage E, depend on the temperatures of the junctions and on the materials making up the thermocouple. For a particular combination of materials, A and B, and for a small temperature difference, dt, the Seebeck voltage may be written

,s A BdE dt(7.1)

where αA,Bis a coefficient of proportionality called the Seebeck coefficient. (This is commonly called the thermoelectric power). Thus the Seebeck coefficient represents, for a given material combination, the net change in thermal emf caused by a unit temperature difference; that is ,

,0

limit s sA B

T

E dE

t dt

(7.2)

Thus if determined by calibration,

then .

Note that, based on the validity of the experimental

relation,

(7.11)

where t1 < t2 < t ,

It follows that is entirely independent of the reference

temperature employed .

In other words, for a given combination of materials, the

Seebeck coefficient is a function of temperature level only.

2

2

1btatE

2bta

2

2 1 1

tt t

s

t t t

E dT dT dT

Jean Charles Athanase Peltier, the French physicist, discovered in 1834 peculiar thermal effects when he introduced small, external electric currents in Seebeck’s bismuth- antimony thermocouple .

His experiments show that when a small electric current is passed across the junction of two dissimilar metals in one direction, the junction is cooled (i.e., it acts as a heat sink) and thus absorbs heat from its surroundings.

When the direction of the current is reversed, the junction is heated (i.e., it acts as a heat source) and thus releases heat to its surroundings.

The Peltier effect concerns the reversible evolution, or absorption, of heat that usually takes place when an electric current crosses a junction between two dissimilar metals. (In certain combinations of metals, at certain temperatures, there are thermoelectric neutral points where no Peltier effect is apparent).

This Peltier effect takes place whether the current is introduced externally or is induced by the thermocouple itself.

The Peltier heat was early found to be proportional to the current and may be written

PdQ Id (7.12)

Where л is a coefficient of proportionality known as the Peltier coefficient or the Peltier voltage.

Note thatл represents the reversible heat that is absorbed, or evolved, at the junction when unit current passes across the junction in unit time, and that it has the dimensions of voltage.

The direction and magnitude of the Peltier voltage depend on the temperature of the junction and on the materials making up the junction ; however ， л at one junction is independent of the temperature of the other junction .

External heating, or cooling, of the junctions results in the converse of the Peltier effect.

Even in the absence of all other thermoelectric effects, when the temperature of one junction (the reference junction) is held constant and the temperature of the other junction is increased by external heating , a net electric current will be induced in one direction .

If the temperature of the latter junction is reduced below the reference junction temperature by external cooling, the direction of the electric current will be reversed.

Thus the Peltier effect is seen to be closely related to the Seebeck effect.

Peltier himself observed that, for a given electric current, the rate of absorption, or liberation, of heat at a thermoelectric junction depends on the Seebeck coefficient a of the two materials.

Note that the Peltier thermal effects build up a potential difference that opposes the thermoelectric current, thus negating the perpetual-motion question.

William Thomson (Lord Kelvin), the English physicist, came to the remarkable conclusion in 1851 that an electric current produces different thermal effects, depending on the direction of its passage from hot to cold, or from cold to hot, in the same metal.

By applying the (then) new principles of thermodynamics to the thermocouple and by disregarding (with tongue-in-cheek) the irreversible and conduction-heating processes,

Thomson reasoned that, if an electric current produced only the reversible Peltier heating effects, the net Peltier voltage would equal the Seebeck voltage and would be linearly proportional to the temperature difference at the junctions of the thermocouple .

This reasoning led to requirements at variance with observed characteristics (i.e., dEs/dt constant).

Therefore, Thomson concluded that the net Peltier voltage was not the only source of emf in a thermocouple circuit but that the single conductor itself, whenever it is exposed to a longitudinal temperature gradient, must also be a seat of emf. A. C.

Becquerel had at that time already discovered a thermoelectric neutral point, that is, Es = 0, for an

iron-copper couple at 280 . Thomson agreed with ℃Becquerel’s conclusion and started his thermodynamic reasoning from there.

The Thomson effect concerns the reversible evolution, or absorption, of heat occurring whenever an electric current traverses a single homogeneous conductor, across which a temperature gradient is maintained, regardless of external introduction of the current or its induction by the thermocouple itself.

The Thomson heat absorbed, or generated, in a unit volume of a conductor is proportional to the temperature difference and to the current; that is,

where σ is a coefficient of proportionality called the Thomson coefficient.

2

1

T

T

T

dQ dT Id

(7.13)

where its direction and magnitude depend on temperature level, temperature difference, and material considered.

Note that the Thomson voltage alone cannot sustain a current in a single homogeneous conductor forming a closed circuit, since equal and opposite emfs will be set up in the two paths from heated to cooled parts.

2

1

T

T

T

E dT (7.14)

Soon after his heuristic reasoning, Thomson succeeded in demonstrating indirectly the existence of the predicted Thomson emfs (see Figure 7. 1).

He sent an external electric current through a closed circuit formed of a single homogeneous conductor that was subjected to a temperature gradient and found the heat to be slightly augmented or diminished by the reversible Thomson heat in the paths from

Figure7.1 Thomson experiment to demonstrate existence of reversible emfs in a single conductor.

(1) Points A and B can be found, when the switch is open, having the same temperature.

(2)When an electric current is passed through the copper bar, point A becomes cooler while point B becomes hotter.

(3) That is, Joule heating is slightly affected by the reversible Thomson emf , which either opposes or adds to the external emf when the copper bar is preferentially heated.

(4) Thomson concluded that hot copper was electrically positive with respect to cold copper, cold to hot or from hot to cold, depending on the direction of the current and the material under test.

In summary, thermoelectric currents may exist whenever the junctions of a circuit formed of at least two dissimilar materials are exposed to different temperatures.

This temperature difference is always accompanied by irreversible Fourier heat conduction;

The passage of electric currents is always accompanied

by irreversible Joule heating effects.

At the same time, the passage of electric currents is always accompanied by reversible Peltier heating or cooling effects at the junctions of the dissimilar metals;

The combined temperature difference and passage of electric current is always accompanied by reversible Thomson heating or cooling effects along the conductors.

The two reversible heating-cooling effects are manifestations of four distinct emfs that make up the net Seebeck emf:

where the three coefficients, α,π,σ are related by the Kelvin relations.

, 2 , 1 ,s A B A B A B A BE t t dT dT dt (7.17)

7.2 The Kelvin Relations

Assuming that the irreversible and heat-conduction effects can be completely disregarded (actually, they can only be minimized, since, if thermal conductivity is decreased , electrical resistivity usually is increased, and vice versa , see Figure 7.2) , the net rate of absorption of heat required by the thermocouple to maintain equilibrium in the presence of an electric current is

2

1 2 1( )net

A B s

Qq dT I E I

(7.15)

This is in accord with the first law of thermodynamics, according to which heat and work are mutually convertible.

Thus the net heat absorbed must equal the electric work accomplished or, in terms of a unit charge of electricity, must equal the Seebeck emf Es, which may be expressed in the differential form

( )s A BdE d dT (7.16)

The second law of thermodynamics may also be applied to the thermocouple cycle (the unit charge of electricity again being considered) as

where ΔQ represents the various components of the net heat absorbed (i.e., the components of Es), and Tabsolute is

the temperature at which the heat is transferred across the system boundaries.

0reversibleabsolute

QS

T

(7.18)

Equation 7.10 can be expressed in the differential form

Combining the differential expressions for the first and second laws of thermodynamics, we obtain the Kelvin relations

from which we can determine, α,π,Δσ , when

Es is obtained as a function of T.

( )0A B

reversibledS d dTT T

, ,s

A B absolute absolute A B

dET T

dT

2

2( ) s

A B absolute

d ET

dT

(7.19)

(7.20)

(7.21)

is taken to represent the thermoelectric characteristic of a thermocouple whose reference junction is maintained at 0 in which the coefficients ℃ a and b are obtained, for example , by the curve fitting of calibration data , then

An example of the use of these coefficients is given

in Figure 7.3.

21

2sE at bt

( )

( )

( )absolute

absolute

a bt

T a bt

T b

(7.22)

(7.23)

(7.24)

(7.25)

Given the two constants, a and b, as determined with respect to platinum,

By way of illustration, consider the following combinations of materials: iron-copper and

iron-constantan, with their measuring junctions at 200 and their reference junctions at 0 :℃ ℃

Metal a ， μ V/℃ b, μ V/℃Iron(I) +16.7 -0.0297

Copper(Cu) +2.7 +0.0079

Constantan(C) -34.6 -0.0558

tan tan

16.7 ( 34.6) 51.3 /

0.0297 ( 0.0558) 0.0261 /

I Cu I Cu

I Cu I Cu

Iron cons

a a a V C

b b b V C

16.7 2.7 14 /

0.0297 0.0079 0.0376 /

I Cu I Cu

I Cu I Cu

Iron copper

a a a V C

b b b V C

Since Seebeck voltage

Figure 7.3 Determination of various thermoelectric quantities applied to thermocouples

21

2sE at bt

2114(200) ( 0.0376)(200)

22048

s

s

Iron copper

E

E V

2

tan tan

151.3(200) (0.0261)(200)

210,782

s

s

Iron cons

E

E V

Note how different combinations of materials give widely different thermal emfs. Now we proceed to write expressions for α,π and Δσ to note how the separate emfs combine to give the ( net ) Seebeck emf. Since Seebeck coefficient,

Tba BABABA ,,,

0

200

0

200

14 ( 0.0376)(0) 14 /

14 ( 0.0376)(200) 6048 /

tan tan

51.3 0.0261(0) 51.3 /

51.3 0.0261(200) 56.52 /

Iron copper

V C

V C

Iron cons

V C

V C

Note that it is the great difference in Seebeck coefficients (thermoelectric powers) for the two combinations that accounts for the difference in thermal emfs:

Since

=Peltier coefficient

=Peltier voltage

,

R

T

s A B

T

E dT

, ,A B absolute A BT

Note that, in the case of the iron-copper ( I-Cu ) couple, , where as in the more usual I-C couple, .

hotcold

coldhot

0

200

0

200

273(14) 3822

473(6.48) 3065

Iron-const an tan

273(51.3) 14,005

473(56.52) 26,734

Iron copper

V

V

V

V

Since =Thomson coefficient ,

and

＝ Thomson coefficient

Figure 7.3 continued

, ,A B A B absoluteb T

2 2,

1( )

2R

T

T A B R

T

E dT b T T

We sum the various components

2 2

2 2

0.0376(273 473 ) 2805

2tan tan

0.0261(273 473 ) 1947

2

T

T

Iron copper

E V

Iron cons

E V

2

2 1

1

3065 3822 2805 2048

tan tan

26,734 14,005 1947 10,782

s

s

s

E dT SeebeckVoltage

Iron copper

E V

Iron cons

E V

These figures, of course, check with the original calculations. Note that, in the I-Cu case, the net Thomson emf far outweighs in importance the net Peltier emf, whereas in the I-C case , the converse is true .

Figure 7.3 (concluded)

7. 3 Microscopic Viewpoint of Thermoelectricity

What gives rise to these thermoelectric effects ? Recall from your chemistry that when the loosely bound outer (valence) electrons of a material absorb enough energy from external sources, they may become essentially free from the influence of their nuclei.

Once free, these electrons can absorb any amount of energy supplied to them, and it is usual to suppose that the free electrons in a metal act collectively as an idealized gas (see Chapter2) 。

Even at a common temperature, however, the energies and densities of the free electrons in different materials need not be the same.

Thus when two different materials in thermal equilibrium with each other are brought in contact, there usually will be a tendency for electrons to diffuse across the interface.

The electric potential of the material accepting electrons would become more negative at the interface, whereas that of the material emitting electrons would become more positive. In other words, an electric field would be set up by the electron displacement that opposes the osmotic process.

When the difference in potential across the interface just balances the thermoelectric (diffusion) force, equilibrium with respect to a transfer of electrons would be established.

If two different homogeneous materials are formed into a closed circuit and the two junctions are maintained at the same temperature, the resultant electric fields would exactly oppose each other, and there would be no net electron flow.

However, if these two junctions are maintained at different temperatures , a net diffusion current will be induced in coincidence with a net electric field (the random motion of the free electrons is on the average in the direction of the net potential gradient , and this gives rise to the electric current).

From conservation principles, the power to drive this electric current could only come from a net absorption of thermal energy from the surroundings by the free electrons of the materials, since there is no observable change in the nature or composition of the thermoelectric materials.

But what accounts for this net absorption of heat? Why does the thermocouple act as a heat engine (i.e., a device that makes available as work some portion of the thermal energy acquired from a source)?

Consider first a closed circuit of a single material (thus avoiding for a time the thermoelectric effects). Under the influence of a temperature gradient alone, the material will conduct a thermal current. But all the thermal energy absorbed by the circuit at one zone is rejected by the circuit at another zone.

Thus the Fourier effect exhibits no accumulation of heat in the steady state, and cannot account for a thermally induced electric current in a thermocouple circuit.

Again, under the influence of a voltage gradient alone, this same single material closed circuit will con- duct an electric current.

But the only thermal effect associated with this current is the inevitable heat generation. Thus the Joule effect exhibits no absorption of heat from outside the circuit and cannot account for a thermally induced electric current in a thermocouple circuit.

Evidently, when examining the mechanism by which a closed circuit formed of two unlike materials acts as a heat engine, we need concern ourselves only with the reversible thermoelectric effects. (Perhaps similar reasoning guided Thomson when he successfully obtained the valid Thomson relations by intuitively disregarding the irreversible Joule and Fourier processes.)

From this viewpoint, the resultant electric current in the thermocouple circuit having its junctions maintained at different temperatures agrees in direction with the natural (Peltier) potential gradient at the hot junction , and thus tends to wipe out ( do away with the need for ) this field .

At the cold junction, this same thermally induced current must cross the interface against the natural potential gradient, and this tends to build up a stronger field of opposition there.

In terms of the idealized gas, the free electrons expand isothermally across the hot junction interface because the flow is in the direction of the Peltier potential gradient there.

This expansion tends to cool the hot junction but, in face of the isothermal restriction and in accord with the first law of thermodynamics, the hot junction absorbs just enough heat from its surroundings to maintain its temperature.

These Peltier (junction) effects, although usually predominating, do not tell the complete story. As Thomson first pointed out, there will be thermoelectric heating effects along each of the materials making up the circuit whenever an electric current and a temperature gradient exist.

The Thomson effect may be visualized as follows. If a single conductor is preferentially heated, electrons usually tend to leave the hot end more frequently than the cold.

Just as we found at the junctions, an opposing electric field would be set up along the single conductor by this diffusion of electrons.

Thus whenever an electric current occurs in a closed thermocouple circuit, it must either agree with or oppose these Thomson (material) potential gradients, and this accounts for heating and cooling effects in addition to the Peltier (junction) effects discussed previously.

Hence the thermocouple in a temperature gradient does qualify as a heat engine in that there will always be a net absorption of heat from its surroundings per unit time , and we see once more that it is just this excess of thermal power arising entirely from reversible thermoelectric effects that sustains the thermoelectric current in the circuit .

7 .4 Macroscopic Viewpoint of Thermoelectricity

The historical viewpoint presented thus far has avoided the real irreversible I2R and heat conduction effects in order to arrive at the useful and experimentally confirmed Kelvin relations. We now discuss how the present-day irreversible thermodynamic viewpoint removes this flaw in our reasoning.

Basically, we judge whether a given process is reversible or irreversible by noting the change in entropy accompanying a given change in the thermodynamic state. Thus, if , we say the process is irreversible ; or , stated in a more useful manner ,

absoluteq TQds /

or

systerm across producedboundary inside

dS dS dS

qs o i

absolute absolute

Q FdS dS dS

T T

(7.26)

(7.27)

Hence only in the absence of entropy within the system boundaries do we have the reversible case, ,

which may be handled adequately by classical thermodynamics in the steady and quasi-steady states .

Evidently the rate of production of entropy per unit volumeξis an important quantity in irreversible thermodynamics . It may be expressed as

where Adx is the area times the differential length.

/reversible q absoluteds Q T

1 1i

absolute

dS F

Adx d Adx T

(7.28)

Another significant quantity, the product Tabsolute （ called the dissipation) , can always be split either

into two terms or into a sum of two terms , one associated with a flow J, and the other associated with a force X.

Furthermore, in many simple cases a linear relation is found (by experiment) to exist between the flow and force terms so defined; for example, in the one- dimensional, isothermal, steady flow of electric charges, , across a potential gradient-dE/dx , it may be shown that

dQe /

absolute e e

I dET J X

A dx

(7.29)

where Je and Xe represent, respectively, the electric flow and force terms, as defined by the entropy production method. (D.G. Miller gives an excellent review of the thermodynamic theory of irreversible processes .

We follow his development closely. The term Je represents the electric current density and the term Xe the electric field strength or the electromotive force.

These are, of course, related by the linear Ohm's law (i.e., Je = LeXe, where Le represents the electrical conductivity).

Again, in the one-dimensional, steady flow of thermal charges across a temperature gradient - dT/dx, it may be shown that

dQq /

1absolute q q

absolute

Q dTT J X

A T dx

(7.30)

where Jq and Xq represent, respectively, the thermal flow and force, as defined by the entropy production method. The term Jq represents the thermal current density, and the term Xq represents the thermomotive force.

These are, of course, related by the linear Fourier’s law (i.e., Jq = LqXq where Lq represents the product of the thermal conductivity and the absolute temperature).

It has been found that even in complex situations it may always be stated that

When several irreversible transport processes occur

simultaneously (e.g., the electric and thermal conduction in a

thermocouple), they will usually interfere with each other.

Therefore, the linear relations must be generalized to

include the various possible interaction terms.

absolute k kT J X (7.31)

Thus for the combined electric and thermal effects we

would write

We have just seen that an entropy production necessarily accompanies both the and heat conduction effects (i.e., they are irreversible); therefore, the Kelvin relations could not follow from reversible thermodynamic theory without certain intuitive assumptions. intuitive assumptions.

Or, in general

e ee e eq qJ L X L X

p qe e qq qJ L X L X

i ij jJ L X

(7.32)

(7.33)

(7.34)

By reasoning that the electric and thermal currents were independent, Thomson tacitly assumed that Leq ＝ Lqe as we shall show subsequently.

Experimentally, this reciprocal relationship was often found to be true. The American chemist Lars Onsager proved, in 1931, from a statistical-mechanics viewpoint, that the assumption

is always true when the linear relations between flows Jk and forces Xk are valid . (For this work Onsager subsequently was awarded a Nobel Prize.)

The Onsager reciprocal relation forms the basis of irreversible thermodynamics .

ij jiL L (7.35)

By applying these concepts to the processes involved in the thermocouple, we are led rationally and unambiguously

to the Kelvin relations .

Thus whenever the junctions of a thermocouple are maintained at different temperatures, we expect that an electric potential difference, an electric current, and a thermal current will be present .

The dissipation for this thermoelectric process is simply the sum of the electric and thermal terms previously given. That is

1absolute

absolute

I dE Q dTT

A dx A T dx

(7.36)

The generalized linear laws for this case have also been given as

Recalling that the Seebeck emf is determined under conditions of zero electric current, the Seebeck the coefficientsαmay be expressed in terms of the Onsager coefficients as

eqe ee

absolute

LdE dTJ L

dT T dx

qqq qe

absolute

LdE dTJ L

dT T dx

(7.37)

(7.38)

0

eqs

I ee absolute

LdE

dT L T

(7.39)

Recalling that the Peltier coefficientπ represents the heat absorbed or evolved with the passage of an electric current across an isothermal junction, this too may be expressed in terms of the Onsager coefficients as

Finally we recall that Thomson found experimentally (and expressed in the Kelvin relations) that the Seebeck and Peltier coefficients are related, Thus

0

q qe

e eedT

J L

J L

(7.40)

0

sabsolute

I

dET

dT

(7.41)

In terms of the Onsager coefficients, this requires that

which indicates that the experimental results agree with those which are predicted by the entropy-production linear-law Onsager reciprocal relation approach;

In other words, by irreversible thermodynamics, without using any intuitive assumption. The Kelvin relations, also in accord with experiment, must follow.

qe eqabsolute

ee ee absolute

L LT

L L T

qe eqL L

(7.42)

(7.43)

7.5 Laws of Thermoelectric Circuits

We have seen that, in 1821, T. J. Seebeck discovered "thermomagnetism" when the junctions between two different metals forming a closed circle were subjected to a temperature difference.

Just a few years later, in 1826, A.C. Becquerel read a paper to the Royal Academy of Sciences in Paris describing the first recorded suggestion to make use of Seebeck’s discovery as a means of measuring temperature.

It was not until 1885, however, that the problem of measuring high temperatures was successfully attacked by Henry LeChatelier.

He determined experimentally that the use of a platinum wire against a platinum rhodium alloy wire gave the most satisfactory "thermo-electric” results . LeChatelier’s work is still the basis of modern standard thermoelectric thermometry.

Numerous investigations of thermoelectric circuits ,in which accurate measurements were made of the current , resistance , and electromotive force have resulted in the establishment of several basic laws.

These laws have been established experimentally beyond a reasonable doubt and may be accepted in spite of any lack of a theoretical development.

Law of Homogeneous Materials A thermoelectric current cannot be sustained in a circuit

of a single homogeneous material however it varies in cross section by the application of heat alone

A consequence of this law is that two different materials are required for any thermocouple circuit.

Experiments have been reported suggesting that a nonsymmetrical temperature gradient in a homogeneous wire gives rise to a measurable thermoelectric emf.

A preponderance of evidence, however, indicates that any emf observed in such a circuit arises from effects of local inhomogeneities.

Furthermore, any current detected in such a circuit when the wire is heated in any way whatever is taken as evidence that the wire is inhomogeneous.

Law of Intermediate Materials

The algebraic sum of the thermoelectromotive forces in a circuit composed of any number of dissimilar materials is zero if all of the circuit is at a uniform temperature.

A consequence of this law is that a third homogeneous material can always be added in a circuit with no effect on the net emf of the circuit as long as its extremities are at

the same temperature.

Therefore, it is evident that a device for measuring the thermo-electromotive force may be introduced into a circuit at any point without affecting the resultant emf, provided all of the junctions that are added to the circuit by introducing the device are all at the same temperature.

It also follows that any junction whose temperature is uniform and that makes good electrical contact does not affect the emf of the thermoelectric circuit regardless of the method employed in forming the junction (see Figure 7.4).

Figure 7.4 The emf is unaffected by the third material C

Another consequence of this law may be stated as follows. If the thermal emfs of any two metals with respect to a reference metal (such as C) are known, the emf of the combination of the two metals is the algebraic sum of their emfs against the reference metal (see Figure 7.5).

Law of Successive or Intermediate Temperature

If two dissimilar homogeneous materials produce a thermal emf of E1: when the junctions are at temperatures

T1, and T2, and a thermal emf of E2 when the junctions are at

T2 and T3,the emf generated when the junctions are at T1 and

T3 will be E1 + E2 .

One consequence of this law permits a thermocouple calibrated for a given reference temperature to be used with any other reference temperature through the use of a suitable correction (see Figure 7.6).

Another consequence of this law is that extension wires having the same thermoelectric characteristics as those of the thermocouple wires can be introduced in the thermocouple circuit (say from region T2 to region T3 in

Figure 7.6) without affecting the net emf of the thermocouple.

7.6 Elementary Thermoelectric Circuits

Two continuous, dissimilar thermocouple wires extending from the measuring junction to the reference junction, when used with copper connecting wires and a potentiometer connected as shown in Figure 7.7, make up the basic thermocouple circuit.

The ideal circuit given in Figure 7.8 is for use when more than one thermocouple is involved. Note that each thermocouple is made up of two continuous wires between the measuring and reference junctions. This circuit should be used for all precise work in thermoelectric thermometry.

A circuit that requires only one reference junction is known in Bureau of Standards publications as a zone-box circuit. A diagram of one is shown in Figure 7.9.

Such a circuit should not be used when uncertainties under 1F are required.

The usual thermocouple circuit, however, includes measuring junctions, thermocouple extension wires, reference junctions, copper connecting wires, a selector switch, and a potentiometer, as indicated in Figure 7.10.

The uncertainties introduced by this circuit should be expected to be greater than 1 .℉

Many different circuit arrangements of these components also are acceptable, depending on given circumstances, and some are shown in Figure 7.11a, b, and c. These circuits can be characterized briefly as follows:

a. Thermopile, for sensing average temperature level.

Advantages: magnifies thermoelectric power by the number of couples in series, enabling the detection of small changes in temperature level; one observation gives, by calibration, the arithmetic mean of temperatures sensed by N individual measuring junctions, when total emf is divided by N.

Precautions: the emf may be too great for the indicator; a short circuit may escape detection (giving erroneous readings); this thermopile gives no indication of temperature distribution; and the temperature / emf calibrations of all couples must be identical.

b. Parallel arrangement, for sensing average temperature level.

Advantage: one observation gives, by calibration, the arithmetic mean of the temperatures sensed by N individual measuring junctions.

Precautions: gives no indication of temperature

distribution; the temperature/emf calibrations of all couples must be identical and linear; and all couples must have equal resistances.

c. Thermopile, for sensing average temperature differences.

Advantages: the signal is magnified by the number of couples in series ( permits detection of very small temperature differences), and one observation, by calibration , gives the arithmetic mean of the temperature differences sensed by two groups of N measuring junctions

when the total emf is divided by N.

Precautions: temperature level is not indicated; a short circuit may escape detection; and the temperature/emf calibrations of all couples must be identical. A typical ice bath is shown in Figure 7.12.

Various circuits for using potentiometers, compensated to indicate temperature directly and uncompensated to indicate voltages directly, are shown in Figure 7.13.

Grounded Thermocouple Circuits

Relatively little attention has been paid to electrical effects that are extraneous to the basic thermocouple circuit. Prime examples of external effects not always considered are: effects of electrical and magnetic fields, cross-talk effects, and effects connected with common mode voltage rejection.

An excellent discussion of these noise effects in general instrument circuits and of methods for reducing them is given by Klipec . (On common mode voltage rejection see also .) A brief review of these effects follows :

1. Electric fields radiated from voltage sources are capacitively coupled to thermocouple extension wires and cause an alternating noise signal to be superimposed on the desired signal.

Electric noise is minimized by shielding the thermocouple extension wire and grounding the shield.

2. Magnetic fields radiated from current-carrying conductors produce noise current and hence noise voltage in the thermocouple circuit. Magnetic noise is minimized by twisting the thermocouple extension wires.

3. Adjacent pairs of a multipair cable tend to pick up noise when pulsating d.c. signals are transmitted. Cross-talk noise is minimized by shielding the individual pairs of thermocouple extension wires.

4. Electrical connections made between a thermocouple and a grounded instrument may introduce common mode noise if different ground potentials exist along the wire path.

Common mode noise is minimized by grounding the thermocouple and its shielding at a single point as close as practical to the measuring junction.

Several arrangements of thermocouple/extension wire/shield/ground combinations, acceptable from the noise viewpoint, are shown in Figure 7.14.

It is evident from the foregoing that the grounding of thermocouple circuits is an important consideration. It is a fact that grounding is often done improperly.

It is shown in Section 7.9, under circuit analysis, that the introduction of multiple grounds in a thermocouple circuit can lead to serious temperature errors, errors that are over and above those associated with thermoelectro-motive force generation, with static and dynamic calibrations, with heat transfer effects, and so on.

Circuits for Rotating Parts

Often in engineering the temperature of a rotating part must be obtained. There are several methods for accomplishing this task.

A rotating transformer may be used where in one coil remains stationary while the other rotates, and hence the signal is passed electrically from rotating to stationary parts.

Radio telemetry may be employed wherein a rotating transmitter sends the temperature signal from a rotating sensor to a stationary indicating device by means of a radio frequency signal, antenna, and receiver system.

However, the most usual method is by a slip ring arrangement wherein the electrical signal from a rotating thermocouple is passed to the stationary world by means of rotating slip rings and fixed brushes.

These three methods are illustrated in Figure 7.15. The slip ring circuit that has proven to be useful for the highest accuracy temperature measurement of a rotating part is shown in Figure 7.16a.

This makes use of a separate rotating thermocouple to sense the temperature in the zone where the necessary transition takes place between the thermocouple wires from the measuring junctions and the copper wires of the slip ring assembly.

In Figure 7.16b, the accuracy of the basic slip ring circuit is compromised through the built-in assumption that a common temperature exists at both the rotating and the fixed terminals of the slip ring assembly.

If this can be safely posited, or if the temperature difference across the slip ring can be tolerated in the

overall measurement accuracy (e.g., a 2°Δt across the

slip ring will introduce a 2°error in the measurement), the simplification of circuit b over a may be warranted.

A third arrangement, wherein the rotating zone thermocouple of Figure 7.16a is replaced by a fixed zone thermocouple extending into the slip ring assembly may sometimes be used if it is felt that such a fixed zone thermocouple adequately proclaims the temperature in the rotating portion of the slip ring assembly.

A fourth arrangement, wherein a rotating resistance thermometer (RTD, see Chapter 6) is used in place of any of the above rotating or fixed zone thermocouple junctions, can be used to advantage if it is important that copper wires be used throughout the slip ring assembly .

A slip ring circuit is analyzed, thermoelectrically, in Section 7.9.

7.7 Circuit Component Uncertainties

Typical uncertainties that can accompany the various

circuit components are discussed briefly below .

Measuring Junction

The junction of a thermocouple that is at the temperature to be measured is referred to as the measuring junction.

Each measuring junction has its own peculiar characteristics depending on such factors as materials, methods of joining, age, and history of junction. Yet the measuring uncertainties introduced by this junction are small;

They are accounted for in the overall circuit calibration (to be discussed), and do not introduce extraneous insidious uncertainties in a temperature measurement.

Thermocouple Extension Wires

Extension wires are thermoelements inserted between the measuring junction and the reference junction that have approximately the same thermoelectric properties as the thermocouple wire with which they are used (the A' and B' wires of Figure 7.10).

The use of extension wires introduces at their extremities at least four extraneous thermoelectric junctions in each

thermocouple circuit.

Even with normal usage, the resulting uncertainties can amount to as much as, depending on the temperatures at the ends of the extension wires, and on the particular wires used.

Such large uncertainties can be minimized by calibrating with given extension wires and then using the same wires in the field, maintaining (as nearly as possible) the same temperatures at their extremities in both circumstances.

These uncertainties can be entirely avoided by not introducing any extension wires in the thermocouple proper.

Selector Switch

When placed in any circuit other than the basic circuit the switch can introduce uncertainties of ±1.5 . It is not ℃enough to keep a switch at a uniform temperature, nor even at a constant temperature.

To minimize uncertainties, the switch must be kept at the same temperature in the field as it was during the calibration. The uncertainties can be avoided entirely by placing the switch in the copper extension Wires leading from the reference junctions to the potentiometer.

Reference Junctions

The junction of a thermocouple that is maintained at a known temperature is referred to as the reference junction.

In any but the basic circuit, reference junctions can introduce uncertainties of ±1 . ℉

These can be minimized by using the same reference junction in the field as was used in the calibration.

The uncertainties can be avoided entirely by using a proper thermocouple, that is, one for which the measuring and reference junctions are simply the extremities of the thermocouple wires.

Copper Connecting Wires

Copper wires used to connect the reference junctions of a thermocouple to the switch or potentiometer are called copper connecting wires.

These wires cause no uncertainty when they are used between the reference junctions and the potentiometer

Potentiometer

A potentiometer is used to measure the emf generated by the thermocouple. A standardized current is passed through a wire of fixed resistance. The wire is calibrated by marking the corresponding voltage drop along its length.

Thus any unknown external emf (such as that encountered in the thermocouple circuit) can be compared with the known voltage drop along the calibrated wire.

A sliding contact on the calibrated wire facilitates the comparison, whereas a galvanometer indicates the balance (null) condition by absence of needle deflection. With reference to Figure 7.17, operation of the potentiometer is as follows.

The switch is placed on (1), and the current from the working cells is adjusted by rheostat C until the galvanometer indicates the null. Under this condition the current through the calibrated wire is "standardized."

The switch is then placed on (2), and the slide on the calibrated wire is adjusted until the galvanometer again indicates the balance condition.

The unknown voltage is now determined by the position of the slide on the calibrated wire.

Since no current flows in the external circuit, the resistance of that circuit introduces no error in the voltage measurement.

An increase in external circuit resistance, however, does decrease the sensitivity of the potential measurement.

This component introduces no uncertainty that is not accounted for in the overall calibration.

7.8 Thermoelectric Reference Tables

Only a few of the large number of possible combinations of materials are actually used in thermoelectric thermometry.

These are chosen on the basis of their standing in the Thermoelectric Series, their Seebeck coefficients (i.e., thermoelectric powers), and on their stability and reproducibility as evidenced by the establishment of

Thermocouple Reference Tables. In the following section, these three tabulations are presented.

Thermoelectric Series

The various conductors have been tabulated in an order such that, at a specified temperature, each material in the list is thermoelectrically negative with respect to all above it and positive with respect to all below it (see Table 7.1).

Although this tabulation resembles the electrochemical electromotive force series, the position of a material in one series bears no relation to that in the other.

Seebeck Coefficients

Nominal thermoelectric powers of various thermoelements with respect to Platinum 67 (a standard maintained at the NBS), and of various common thermocouple types, are presented in Tables 7.2 and 7.3.

These are quite useful in the analysis of circuits such as those dealt with in Section 7.9. Curves to present this same

information graphically are given in Figures 7.18 and 7.19.

Thermocouple Reference Tables

Thermocouple reference values represent in both form and magnitude the nominal characteristics of particular thermocouple types.

Thermocouple wires are carefully selected and matched to conform with these tables within prescribed limits. The printed scales of all direct temperature-indicating potentiometers are based on such tables.

Calibration curves, in the form of voltage -or temperature-difference plots, are obtained by comparing calibration data with reference values

A satisfactory table of reference values for use with thermocouples must be capable of easy and unique generation for a number of reasons:

(1) the values are used by many people;

(2) their storage in computer applications must not present a problem; and

(3) since interpolation must be used, unique values at all arbitrary points must be available.

The last requirement means that a mathematically continuous functional relation must exist between the temperatures and voltages with which the table is concerned.

Satisfactory reference values must also agree closely with the characteristic of the thermocouple type being considered so that differences in values change slowly and smoothly.

The established reference tables adequately fulfill all these requirements. Unique polynomials are available for generating tables for each of the seven thermocouples now in common use.

These are given in Tables 7.4 and 7.5 for easy reference.

A short discussion of each thermocouple type follows .

TYPE T (copper / constantan).

This type can be represented by an eighth-degree equation as in Table 7.4a. This is used to generate exact values of voltage as a function of temperature from 0 to 400 . ℃ ℃

The inverse relation, for temperature as a function of voltage, is generated over the same temperature range by another polynomial also given in the table.

This procedure is necessarily inexact, but will yield reference temperatures to within known uncertainty bands. For type T, temperatures are given to 0.2 from 0 to ℃ ℃400 .℃

TYPE J (iron/constantan).

Output of this type can be determined as a function of temperature from by a seventh-degree equation in Table 7.4b.

The resulting values are exact by definition. This shows the inverse relation for temperature as a function of voltage over the same temperature range. For type J, temperatures are given to 0.1 from 0 to 760 .℃ ℃ ℃

TYPE E (chromel /constantan).

Thermocouples of this type can be represented by a ninth-degree polynomial as in Table 7.4c.

Voltage generated as a function of temperature from 0 ℃to 1000 can be calculated, as can temperature as a ℃function of voltage using the inverse relationship . For the latter case , temperatures are given to 0.1 from 0 to ℃ ℃

1000℃ .

TYPE K (chromel / alumel).

Outputs of these thermocouples can be represented by the equation in Table 7.4d.

An eighth -degree equation with an exponential term is used to generate values of voltage as a function of temperature from 0 to 1372 . The inverse relation ℃ ℃provides reference temperatures accurate to 0.02 from ℃400 to 1100 .℃ ℃

TYPE B (platinum-30% rhodium / platinum).

An eighth-degree equation, given in table 7.5a is used to generate these voltages as a function of temperature from 0 to 1820 . ℃ ℃

Type R (platinum-13% rhodium / platinum).

Two third-degree equations are required to generate voltage as a function of temperature from 630 to 1665 , ℃ ℃as shown in Table 7.5b.

TYPE S (platinum-10% rhodium / platinum).

From the antimony point to the gold point, that is, from 630.74 to 1064.43 , a second-degree equation is used to ℃ ℃generate voltages for this type thermocouple. From 1064 ℃to 1665 , a third-degree equation is used. The required ℃coefficients of these polynomials are given in Table 7.5c.

A table generated by the polynomials given in Tables 7.4 and 7.5, for six of the most commonly used types of thermocouples, is presented as Table 7.6. Prior to the publication of the NBS polynomials of Tables 7.4 and 7.5, there was no unique , internationally accepted, mathematical generation scheme available that would reproduce the

established thermocouple reference table values .

One method that found wide acceptance in the ISA , ASME , ASTM , and industry in general , was based on the trial-and-error establishment of a few key values of voltage and temperature and a series of equations of specified degree to interpolate voltages between the key points .

Today this generation scheme is no longer required and is only of historical interest. NBS Monograph 125[29] is the accepted standard for the nominal characteristic for all conventional thermocouple types.

7.9 Thermoelectric Circuit Analysis

An important phase of each temperature measurement by means of thermocouples is the thermoelectric circuit analysis. This operation can be systematized by observing the following set of rules.

1. Draw an equivalent circuit, numbering all thermoelectric junctions, and show an assumed direction of current.

2. Indicate the direction of the potential drop at each junction, guided by the outputs of each material with respect to platinum-67 (see Figure 7.18).

3. Compute the net emf in terms of the potentials at each junction (assigning a plus sign if the potential drop is in the same direction as the assumed current).

4. Combine the voltages algebraically to a form that allows easy reference table look-up (i.e., combine in terms of usual thermocouple combinations).

5. Compute the errors.

The examples that follow illustrate the application of these rules, and have been chosen to represent common and yet serious thermocouple circuit errors.

Example 1.

Use of Incorrect Extension Wires. A chromel-alumel (Ch-Al) thermocouple was connected by mistake with iron-constantan (I-C) extension wires to a potentiometer in such a manner that the output emf was on scale.

The actual temperatures were at measuring junction ， TM ＝ 60 ; at reference junction℉ ， TR ＝ 32 ; and at the ℉

junction between the thermocouple and extension wires ， TJ ＝ 130 . What was the error in the measurement?℉

1. Draw an equivalent circuit (see Figure7.20).

2. Indicate direction of all potential drops (dotted arrows

in Figure 7.20)

3,4. Compute net emf:

1 2 3 4

1 60

2 130

3 32

4 130 130 130 130

( 1) 0.619

( ) 3.329

( ) 0

( 1) ( 1) ( ) ( )

2.206 3.329 2.820

1.697 ( 7.21)

0.619 3.329 0 1.697 4.40

net

F

F

F

F F F F

net

E E E E E

E Ch A mV

E Ch C mV

E I C mV

E I A ch A Ch C I C

mV

mV seeFigure

E

7mV

whereas the correct emf should have been:

5. Compute errors

60 F 32 F( ) ( ) 0.619mVE Ch Al Ch Al － ＝

net voltage error =4.407-0.619=3.788mV

net voltage error =225 60 165 F, (on 1 )

net voltage error =183 60 123 F, (on I )

Ch A scale

Cscale

It goes without saying that, on either thermocouple scale, It goes without saying that, on either thermocouple scale, errors of this magnitude cannot be tolerated.errors of this magnitude cannot be tolerated.

Example 2.

Use of Incorrect Polarity Wires. The extension wires of a chromel-alumel thermocouple were inadvertently interchanged. The actual temperatures were at measuring junction ， TM ＝ 980 ; at reference junction ℉ ， TR ＝ 32 ; and at the junction between the thermocouple and ℉extension wires ， TJ ＝ 100 . ℉

What was the error in the measurement??

1, 2. Draw an equivalent circuit (see Figure 7.20).

3, 4. Compute net emf:

whereas the correct emf should have been

1 2 3 4

1 60

2 130

3 32

4 130 130 130 130

( 1) 0.619

( ) 3.329

( ) 0

( 1) ( 1) ( ) ( )

2.206 3.329 2.820

1.697 ( 7.21)

0.619 3.329 0 1.697 4.40

net

F

F

F

F F F F

net

E E E E E

E Ch A mV

E Ch C mV

E I C mV

E I A ch A Ch C I C

mV

mV seeFigure

E

7mV

980 32( 1) ( 1) 21.777

F FE Ch A Ch A mV

Once again, a most common thermocouple circuit error, namely interchanging extension wires, is seen to lead to a very serious temperature measuring error.

net voltage error =26.637-7.958=18.679mV

net temperature error =700-255 445 F

5. Compute errors

Example 3.

Use of Improper Grounding. A chromel-constantan thermocouple, grounded at its measuring junction according to Figure 7.14, was inadvertently grounded at its reference junction also. The actual temperatures were: at measuring junction, TM = 700 ; at reference junction, ℉ TR =32 . ℉

What is the predicted error in the measurement?

1. Draw an equivalent circuit:

Figure7.22 illustrates the multigrounded circuit under consideration. Figure7.23 depicts the equivalent circuit that represents the multigrounded thermocouple.

2. In this example, the direction of all potential drops is indicated by electrical cell symbols, where the drop is from minus to plus at the junction.

3, 4. Compute net emf: A voltage summation is written around the outer ground loop to obtain the current in the loop as follows.

( ) ( ) 0pq M g n pn ME E iR iR E (7.44)

Where （ Epg ） M signifies the emf set up by the positive thermoelement and the ground wire at the measuring junction temperature , and so on . Thus

Note that chromel is the positive element with respect to constantan and that copper is assumed to be the grounding wire.

Given the ground loop current, the net voltage set up by the doubly grounded thermocouple circuit can be determined as follows.

( ) ( )pn M pg M

g n

E Ei

R R

(7.45)

where （ Epg ） M signifies the emf set up by the positive

thermoelement and the ground wire at the measuring

junction temperature , and so on . Thus

The pertinent resistance values are:

for constantan

for copper

( ) ( )net g pg M n pn ME iR E iR E

2.902nR 0.0646gR

(7.46)

700

700 700

( ) ( ) 26.637

( ) ( ) ( )

( ) 26.637 19.095 7.542

26.637 7.5426.437

0.0646 2.902( ) 6.437(0.0646) 7.542 7.958

pn M Ch C F

pg M Ch Cu Ch C Cu CF F

pg M

net g pg M

E E mV

E E E E

E mV

i mV

E iR E mV

The pertinent voltage values are:

5. The temperature error for this doubly grounded thermocouple can be estimated as follows

net voltage error =26.637-7.958=18.679mV

net temperature error =700-255 445 F

. This error is obviously much larger than any other error

associated with thermocouple circuits, and it is clear that doubly grounded thermocouple circuits are to be avoided at all costs.

Example 4.

Rotating thermocouple circuit analysis. A rotating iron-constantan thermocouple is connected through a slip ring to a stationary potentiometer and reference junction.

The unknown temperature at the transition between the thermocouple wires and the copper slip ring wires is accounted for by a special rotating iron-constantan thermocouple connected as shown in Figure 7.16a.

The actual temperatures were: at measuring junction ， TM ＝ 500 ; at reference junction℉ ， TR ＝ 32 ; and at the ℉

slip ring, TJ=150 .What was the error in the measurement? ℉

1, 2. Draw an equivalent circuit (see Figure7 .24 ） .3, 4. Compute net emf:

1 2 3 4

1 980

2 100

3 32

4 100

( 1) 21.777

( 1) 1.520

( 1) 0

( 1) 1.520

21.777 1.520 0 1.520 18.737

net

F

F

F

F

net

E E E E E

E Ch A mV

E Ch A mV

E Ch A mV

E Ch A

E mV

Since this is the voltage required, there are no circuit errors in this example.