l temperature

7/31/2019 L Temperature

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Temperature

Measurement


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Introduction

Temperature along with pressure is an important parameter thatgoverns many physical phenomena.

Hence the measurement of temperature is a very important activity in

the laboratory as well as in industry.

The lowest temperature that is encountered is very close to 0 K and

the highest temperature that may be measured is about 1,00,000 K.

This represents a very large range and cannot be covered by asingle measuring instrument.

Hence temperature sensors are based on many different principlesand the study of these is the material of this presentation.


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We take recourse to thermodynamics to provide a definition for

temperature of a system.

Thermodynamics is the studies of systems in equilibrium andtemperature is an important intensive property of such systems.

Temperature is defined via the zeroth law of thermodynamics.

A system is said to be in equilibrium if its properties remain invariant.

Consider a certain volume of an ideal gas at a specified pressure.

When the state of this volume of gas is disturbed it will eventuallyequilibrate in a new state that is described by two new values ofvolume and pressure.


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Even though we may not be able to describe the system as it isundergoing a change we may certainly describe the two end states

as equilibrium states.

Imagine two such systems that may interact through a wall thatallows changes to take place in each of them.

The change will manifest as changes in pressure and/or volume.

If, however, there are no observable changes in pressure andvolume of each one of them when they are allowed to interact asmentioned above, the two systems are said to be in equilibrium

with each other and are assigned the same temperature.


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Zeroth law of Thermodynamics:

The zeroth law ofthermodynamics states that if asystem C is in equilibriumseparately with twothermodynamic systems A andB then A and B are also in

equilibrium with each other.

At once we may conclude thatsystems A and B are at thesame temperature!

Thermometry thus consists ofusing a thermometer (systemC) to determine whether or nottwo systems (A and B in theabove) are at the same

temperature.


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Assume that one of the coordinates of the system (Y) is fixed at a valueequal to Yo.

Then there is only one sate that will correspond to any given isotherm.

If the system is allowed to equilibrate with a system characterized bydifferent isotherms, the property X will change as indicated by the pointsof intersection X1, X2 and so on.

These will then correspond to the respective temperatures T1, T2 and soon.

We refer to Xas the thermometric propertyand the system as athermometer.


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Constant volume gas thermometer:

Fig. 3: Schematics of constant volume gas thermometer.


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It consists of a certain volume of a gas contained in a rigid vessel.

The vessel is connected to a U tube manometerwith a side tubeand height adjustable reservoiras shown.

The volume is kept constant by making the meniscus in the left limbof the U tube always stay at the mark made on the left limb of the Utube.

The right limb has a graduated scale attached to it as shown.

The gas containing vessel is immersed in a constant temperatureenvironment.

The graduated scale helps in determining the pressure of theconfined gas in terms of the manometer head.


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The following experiment may be performed.

Choose the pressure of the gas (Ptp) to have a definite value when theconstant temperature environment corresponds to standard fixed statesuch as the triple point of water(or the ice point at one atmosphere

pressure).

Now move the thermometer into an environment at the steam point(boiling point of water at one atmosphere).

The pressure of the gas (Pst) has to be adjusted to a higher value than itwas earlier by adjusting the height of the reservoir suitably so as to makethe meniscus in the left limb of the U tube stay at the mark.

The above experiment may be repeated by taking less and less gas to

start with by making the pressure at the triple point of water to have asmaller and smaller value (the vessel volume is the same in all the cases).

The experiment may also be repeated with different gases in the vessel.

The result of such an experiment gives a plot as shown in Figure 4.


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Gas thermometer characteristics:

Fig. 4: Characteristics of gas thermometer.


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The ratio of the pressure of the gas corresponding to thesteam point to that at the triple point of water tends to aunique number as Ptp 0 (the intercept on the pressure

ratio axis) independent of the particular gas that has beenused.

This ratio has been determined very accurately and is givenby:

The gas thermometer temperature scale is defined basedon this unique ratio and by assigning a numerical value of:

0366049.1 tptp

st PasPP

CKorTtp

01.016.273


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The defining relation is:

This last value is referred to as the single fixed point for thermometry orthe primary fixed point.

At this temperature ice, liquid water and water vaporall coexist, if in addition,the pressure is maintained at 4.58 mm Mercury column or 610.65 Pa.

The ice point is at 273.15 K or 0C and was used in early times as theprimary fixed point in thermometry.

In ordinary laboratory practice the ice point is easier to achieve and hence iscommonly used.

0 tptp

st

tp

st asPPP

TT


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Practical thermometry

As mentioned earlier, the range of temperatures encounteredin practice is very wide.

It has not been possible to device a single thermometercapable of measuring over the entire range.

Since all thermometers must be pegged with respect to thesingle fixed point viz. the temperature at the triple point ofwater it is necessary to assign temperature values to asmany reproducible states as possible using the constantvolume gas thermometer.

Subsequently these may be used to calibrate otherthermometers that may be used to cover the range oftemperatures encountered in practical thermometry.

These ideas are central to the introduction of InternationalTemperature Scale 1990 (or ITS90, for short).


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Specification of ranges and corresponding thermometersaccording to ITS 90.

Between 0.65 K and 5.0 K T90 is defined in terms of the vapour pressuretemperature relations 3He and 4He.

Between 3.0 K and the triple point of neon (24.5561 K) T90 is defined by

means of a helium gas thermometer calibrated at three experimentally

reliable temperatures having assigned numerical values (defining fixedpoints) and using specified interpolation procedures.

Between the triple point of equilibrium hydrogen (13.8033 K) and the

freezing point of silver (961.78 C) T90 is defined by means of platinum

resistance thermometers calibrated at specified sets of defining fixed pointsand using specified interpolation procedures.

Above the freezing point of silver (961.78C) T90 is defined in terms of a

defining fixed point and the Planck radiation law.


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Secondary fixed points used in ITS90

Fig. 3: Secondary fixed points used in ITS90


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Classification of measuring instruments

Several are listed here.

Thermoelectric thermometer Based on thermoelectricity - Thermocouple thermometers using two wires

of different materials

Electric resistance

Resistance thermometer using metallic materials like Platinum, Copper,

Nickel etc.

Thermistors consisting of semiconductor materials like Manganese-

Nickel-cobalt oxide mixed with proper binders

Thermal expansion

Bimetallic thermometer

Liquid in glass thermometer using mercury or other liquids

Pressure thermometers

Pyrometry and spectroscopic methods

Radiation thermometry using a pyrometer

Special methods like spectroscopic methods, laser based methods,

interferometry etc.


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Thermoelectric thermometry


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Introduction

Thermoelectric thermometry is based on thermoelectric effects orthermoelectricity discovered in the 19th century.

They are:

Seebeck effect discovered by Thomas Johann Seebeck in 1821.

Peltier effect discovered by Jean Charles Peltier in 1824.

Thomson effect discovered by William Thomson (later Lord Kelvin)in 1847.


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Thermo Electric Effects

Consider two wires of dissimilar

materials connected to form a circuit

with two junctions.

Let the two junctions be maintained

at different temperatures as shown

by the application of heat at the twojunctions. An electric current will flow

in the circuit as indicated with heat

absorption at one of the junctions and

heat rejection at the other. This is

referred to as the Peltier effect. The power absorbed or released at

the junctions is given by

P = QP= AB *I

where AB is the Peltier voltage


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The direction of the current will decide whether heat is

absorbed or rejected at the junction.

For example, if the electrons move from a region of lower

energy to a region of higher energy as they cross the junction,

heat will be absorbed at the junction.

This again depends on the nature of the two materials that

form the junction.


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Consider now a single conductor of

homogeneous material in which a

temperature gradient exists. The

current I is maintained by heat

absorption or heat rejection along the

length of the wire. If the direction of the

current is as shown the electrons

move in the opposite direction.

If T2

> T1

, the electrons move from a

region of higher temperature to that at

a lower temperature. In this case heat

will be rejected from the wire.

The expression for heat rejected is

where QT is the Thomson heat and

A is the Thomson coefficient for the

material.


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If we cut conductor B (or A) as

indicated the Seebeck emf

appears across the cut. This emf

is due to the combined effects ofthe Peltier and Thomson effects.

We may write the emf appearing

across the cut as

l temperature

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