Thermometers

TemperatureTemperature

A2 Level PhysicsA2 Level Physics

Mukesh N. TekwaniMukesh N. [email protected]@hotmail.com

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ThermodynamicsThermodynamics

A branch of physics in which thermal A branch of physics in which thermal effects are studied using effects are studied using macroscopicmacroscopic quantities.quantities.

MacroscopicMacroscopic quantities are: quantities are: • PressurePressure• TemperatureTemperature• VolumeVolume• Internal energyInternal energy

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Kinetic TheoryKinetic Theory

Kinetic theory is also concerned with Kinetic theory is also concerned with thermal effects.thermal effects.

But here we assume the existence of But here we assume the existence of atoms and molecules.atoms and molecules.

The laws of mechanics and statistics are The laws of mechanics and statistics are applied to a large number of these applied to a large number of these molecules.molecules.

Microscopic levelMicroscopic level

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Thermal EquilibriumThermal Equilibrium

If a body (X) at a higher temperature is in If a body (X) at a higher temperature is in contact with a body (Y) at a lower temperature, contact with a body (Y) at a lower temperature, then X will transfer heat energy to the lower then X will transfer heat energy to the lower temp object (Y)temp object (Y)

This process will continue till the objects attain This process will continue till the objects attain the same temperature.the same temperature.

The temp of both objects will become same.The temp of both objects will become same. This thermal state in which both bodies are at This thermal state in which both bodies are at

the same temp is called the same temp is called thermalthermal equilibriumequilibrium..

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Using Physical Properties to Using Physical Properties to Measure TemperatureMeasure Temperature

Many Many physical propertiesphysical properties change with change with temperaturetemperature• Change in Change in volumevolume (e.g. expansion of a liquid) (e.g. expansion of a liquid)• Change in Change in lengthlength of a mercury column of a mercury column• Change in Change in resistanceresistance of a wire of a wire• Change in Change in pressurepressure of a gas at constant volume of a gas at constant volume

All these properties can be used in different All these properties can be used in different types of thermometerstypes of thermometers

A thermometer is an instrument for A thermometer is an instrument for measurement of temperature. measurement of temperature.

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Imp DefinitionsImp Definitions

The physical property on which a particular The physical property on which a particular thermometer is based is called the thermometer is based is called the thermometric propertythermometric property..

Thermometric substanceThermometric substance is the material used in is the material used in the thermometer, whose property varies with the thermometer, whose property varies with temperaturetemperature

Thermometric property should vary linearly Thermometric property should vary linearly with temp over a reasonable range of tempwith temp over a reasonable range of temp

The range of linearity of the thermometric The range of linearity of the thermometric property is called the property is called the thermometric rangethermometric range..

E.g., mercury is a thermometric substanceE.g., mercury is a thermometric substance

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Temperature ScalesTemperature Scales

Each type of thermometer can be used to Each type of thermometer can be used to establish its own temp scale.establish its own temp scale.

How is this done?How is this done?• Every substance Every substance changes statechanges state at a at a fixedfixed

temperaturetemperature. E.g., solid-to-liquid OR liquid-to-. E.g., solid-to-liquid OR liquid-to-gasgas

• These fixed temperatures can be used to These fixed temperatures can be used to define reference temperatures. These define reference temperatures. These reference temperaturesreference temperatures are called are called fixed fixed pointspoints..

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Temperature ScalesTemperature Scales

We take the value of the thermometric We take the value of the thermometric property at the two fixed points and property at the two fixed points and divide the range into a number of EQUAL divide the range into a number of EQUAL steps or degrees.steps or degrees.

This way we set up an “empirical scale” This way we set up an “empirical scale” of thermometer.of thermometer.

Empirical => ‘derived from experiment’Empirical => ‘derived from experiment’

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Temperature ScalesTemperature Scales

E.g., suppose we consider the fixed points E.g., suppose we consider the fixed points as the melting point of ice (0as the melting point of ice (000) and boiling ) and boiling point of water (100point of water (10000))

Divide the range from 0 to 100 into 100 Divide the range from 0 to 100 into 100 equal degrees. This gives the empirical equal degrees. This gives the empirical scale of temperature for that scale of temperature for that thermometer.thermometer.

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Disagreement between ThermometersDisagreement between Thermometers

The choice of thermometric susbstance The choice of thermometric susbstance and thermometric property and the and thermometric property and the assumed relation between the property assumed relation between the property and temperature leads to an individual and temperature leads to an individual temp scale.temp scale.

Measurements made with such a Measurements made with such a thermometer may not agree with thermometer may not agree with measurements made by any other temp measurements made by any other temp scalescale

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Disagreement between ThermometersDisagreement between Thermometers

This disagreement is removed by the This disagreement is removed by the following:following:• Using a particular thermometric substanceUsing a particular thermometric substance• Using a particular thermometric propertyUsing a particular thermometric property• A particular relation between that property A particular relation between that property

and the temp scale. E.g., a linear relation and the temp scale. E.g., a linear relation between length of a mercury column and between length of a mercury column and temptemp

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Determining an unknown TempDetermining an unknown Temp

Consider the following graph which shows Consider the following graph which shows the variation of a property P with temp.the variation of a property P with temp.

Pt

P100

P0

t1 0 t 100 t2

Degrees CDegrees C

Thermometric range

= t2 – t1

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Determining an unknown TempDetermining an unknown Temp

From the st line graph, we get:From the st line graph, we get:

= const = const

100 - 0100 - 0

P100 - P0

= const = const

t - 0t - 0

Pt - P0

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Determining an unknown TempDetermining an unknown Temp

= const = const

100 - 0100 - 0

P100 - P0

= const = const

t - 0t - 0

Pt - P0

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Determining an unknown TempDetermining an unknown Temp

Equating the LHS of these eqns we getEquating the LHS of these eqns we get

t = t = 100 x (P100 x (Ptt – P – P00))

(P(P100100 – P – P00))

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Thermometric PropertiesThermometric Properties

LengthLength varies linearly with temperature varies linearly with temperature• Give formulaGive formula• Used in liquid-in-glass thermometersUsed in liquid-in-glass thermometers

PressurePressure varies linearly with temperature varies linearly with temperature• Give formulaGive formula• Used in constant volume gas thermometersUsed in constant volume gas thermometers

VolumeVolume varies linearly with temperature varies linearly with temperature• Give formulaGive formula• Used in constant pressure gas thermometersUsed in constant pressure gas thermometers

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Thermometric PropertiesThermometric Properties

ResistanceResistance varies linearly with temp varies linearly with temp• Give formulaGive formula• Used platinum resistance thermometersUsed platinum resistance thermometers

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ThermometersThermometers

Factors to consider while choosing a thermometerFactors to consider while choosing a thermometer• AccuracyAccuracy• SensitivitySensitivity (distance between divisions on the scale) (distance between divisions on the scale)• RangeRange of temps it can measure of temps it can measure• Speed of responseSpeed of response – measure rapidly varying – measure rapidly varying

temperaturestemperatures• Sensitive part of the thermometer should be small so Sensitive part of the thermometer should be small so

that it does not absorb much heat from the objectthat it does not absorb much heat from the object• It shuld be easy to read – no complicated calibrations It shuld be easy to read – no complicated calibrations

/ settings/ settings

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Platinum Wire ThermometersPlatinum Wire Thermometers

These are based on the variation of electrical resistance These are based on the variation of electrical resistance due to temperaturedue to temperature

Resistance of a metal wire increases with increase in Resistance of a metal wire increases with increase in temp. temp.

RRtt = R = R00 ( 1 + ( 1 + t) t) Range of temp they can measure is from -260 C to Range of temp they can measure is from -260 C to

1700 C1700 C Temp sensor or material is a coil of fine Temp sensor or material is a coil of fine platinumplatinum wire wire

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Platinum Wire ThermometersPlatinum Wire Thermometers

AdvantagesAdvantages of platinum resistance thermometers: of platinum resistance thermometers:• High accuracy High accuracy • LL ow drift ow drift

• Wide operating rangeWide operating range

Disadvantages of Platinum Thermometers• Not very sensitive to small changes in temp• Slow response time

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ThermistorThermistor

A thermistor is a type of resistor whose resisatnce changes with temperature

ThermTherm (heat / temp) + Resistor = Thermistor Semiconductors are used in these devices The electrical resistance decreases very rapidly with

increasing temp. Thus, we say that thermistors have a negative temp

coeff. of resistance (NTC)

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ThermistorsThermistors

AdvantagesAdvantages of thermistors: of thermistors:

• Sensitivity is high • Their size is very Their size is very smallsmall – hence can be used to measure temp of – hence can be used to measure temp of

small objectssmall objects

Disadvantages of Thermistors• Their scale is non-linear

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ThermocoupleThermocouple

This makes use of the thermoelectric effect Thermoelectric device - A thermoelectric device creates a

voltage when there is a different temperature on each side When the junctions of two different conductors, such as copper When the junctions of two different conductors, such as copper

and constantan wire are at different temperatures, an emf and constantan wire are at different temperatures, an emf (voltage) is developed.(voltage) is developed.

The relation between emf and temp diff is not linear.The relation between emf and temp diff is not linear. The emf generated is small – typically about 5 mV for a temp diff The emf generated is small – typically about 5 mV for a temp diff

of 100 Cof 100 C Advantages:Advantages:

• Can be used to measure rapidly changing temps. Can be used to measure rapidly changing temps. • Can be used to measure temp of small objectsCan be used to measure temp of small objects