#### Measurement of Temperature, Physics tutorial

Heat and Temperature

Heat is the form of energy that can be converted into other forms of energy. It is as well termed as 'thermal energy' and for all time flows from a body at a higher temperature to a body at a lower temperature, when the two bodies are in contact. This is a measure of the internal energy of a body.

The quantity of heat included in a body based on the mass of the body and its temperature. The unit of heat is joule (J).

Temperature is the degree of coldness or hotness of a body. It is associated to the energy of movement (that is, kinetic energy). It is as well a measure of the average kinetic energy of the molecules of a body. The unit of temperature is degree Celsius (oC) or Kelvin (K).

Principle employed in Temperature Measurement:

In computing the temperature of a body we utilize the principle that certain physical properties of some substances differ with temperature. Any physical property of a substance that differs in a known manner and can simply be measured is used in an instrument termed as 'thermometer' to measure the temperature. The substance whose physical property which is employed is termed as a thermometric substance. The table below represents a summary of the kinds of thermometers and their thermometric substances.

Table: Thermometers and Thermometric Substances

 S.NO. Types of Thermometers Thermometric substance Physical Property 1. Liquid-in-glass thermometer Mercury or Alcohol Change in volume of liquid with temperature 2. Gas thermometer Gas Change of gas pressure at constant volume by temperature 3. Resistance thermometer Resistance wire Change in electrical resistance of wire by temperature 4. Thermocouple Two metals (copper and constantan) Change in electric potential difference between the two metal junctions at various temperatures. 5. Bimetallic thermometer Two dissimilar metals (iron and copper) The differential expansion of the two metals of the bimetallic strip.

Fixed Temperature Points of a Thermometer:

A thermometer consists of two reference temperatures or 'fixed points', namely:

a) The upper fixed temperature point: The upper fixed point of a thermometer is the temperature of steam from pure water boiling at standard atmospheric pressure of 760 mm of mercury.

b) The lower fixed temperature point: The lower fixed point of a thermometer is the temperature of pure melting ice at the standard atmospheric pressure of 760 mm of mercury.

c) The fundamental interval (or temperature interval) is the difference in temperature between the upper and lower fixed points of a thermometer.

The basic interval of a thermometer is generally calibrated to give readings of temperature values among the upper and lower fixed points. The calibration of this interval based on the scale of temperature selected for the thermometer.

Types of Temperature Scales:

The three kinds of scales which are in common use are as follows:

A) Fahrenheit Scale:

• Lower and upper fixed points are 32oF and 212oF correspondingly.
• Fundamental interval is splitted into 180 equal parts (that is, 212 - 32 = 180) each of which states one degree Fahrenheit (1oF) in this scale.

B) Celsius scale:

• Lower and upper fixed points are 0oC and 100oC correspondingly.
• Fundamental interval is splitted into 100 equal parts or degree, each equivalent to 1oC.

C) Kelvin or absolute scale:

• Lower and upper fixed points are 273K and 373K correspondingly.
• Fundamental interval is splitted into 100 equivalent parts or units each of which is termed as one Kelvin (K).

Definition of absolute zero: The absolute zero temperature is the temperature at which the volume of a fixed mass of gas at constant pressure that is steadily cooled beneath 0 oC, would theoretically become zero.

Conversion Formulas:

i) Conversion from Fahrenheit to Celsius:

C = (F - 32) x (5/9)

ii) Conversion from Celsius to Fahrenheit:

F = C x (9/5) + 32

iii) Conversion from Kelvin to Fahrenheit:

F = [(9/5) (K - 273)] + 32

Constant Volume Gas Thermometer Scale:

(i) Upper fixed point is the triple point of water:

Define: The triple point of water is the temperature in which the ice liquid water and water vapor coexist in equilibrium form.

(ii) Lower fixed point is the absolute zero or Ok (-273oC):

The scale is generally calibrated at these two fixed points and other temperatures are obtained through measuring the pressure of the gas at unknown temperature and making utilization of the definition of temperature in the scale given below.

Assume that the unknown temperature = T

Temperature of the triple point of water = Ttr = 273.16K

Pressure of gas at the unknown temperature = PT

Pressure of gas at triple point of water = Ptr

By using, T1/T2 = P1/P2

T/Ttr = Pr/Ptr

T/273.16 = PT/Ptr

T = (PT/Ptr) x 273.16

For basic work, where ice point is employed rather than the triple point, we have:

T = (PT/Pice) x 273.16

Standard Thermometer Scale:

Early experiments evaluate temperature by means of mercury thermometers and frequently found that various instruments gave dissimilar readings for the similar temperature. Other kinds of thermometers like the platinum resistance or the gas thermometers that were employed later had the similar problem. It became clear that one kind of thermometer based on one scale of temperature would have to be taken as standard. Gas thermometers, either the constant volume or constant pressure kinds, exhibited the closest agreement over a broad range of temperatures. They were as well much sensitive, accurate and highly reproduceable. It was noticed that as the pressure was lowered (approaching to zero); all gas thermometers point out the similar reading.

Lord Kelvin proposed that the standard scale of temperature must be based on an imaginary ideal gas having properties which were those of real gases at very low that is, it followed Boyle's law. He stated that the product of the pressure and volume of this ideal gas must be employed as the thermometric property of the gas. Therefore, when P1, P2 are the pressures and V1, V2 the volumes of the gas at temperatures T1, T2, then,

T1/T2 = P1V1/P2V2

If the volume is kept constant, then we have

T1/T2 = P1/P2

that provides a definition of temperature on the constant - volume gas thermometer scale. If though, pressure is kept constant, we have

T1/T2 = V1/V2

That provides a definition of the temperature on the constant-pressure gas thermometer scale.

International Practical Temperature Scale (IPTS):

Measuring temperatures on the standard thermometer scale (or ideal gas scale) by employing the constant-volume gas thermometer is a tedious work out.

The international temperature scale (ITS) was thus proposed and adopted as a more practical scale for general utilization. The scale comprises of eleven primary fixed points ranging from the triple point of hydrogen (13.81K) to the freezing point of gold (1337.58K) that have been precisely determined on the ideal gas scale through a constant volume gas thermometer and as well some other secondary fixed points. Particular kinds of thermometer are specified for measuring temperatures over a particular range by using agreed formulas. At fixed points, there is agreement among the IPTS and the Kelvin scale, the differences at the intervening temperatures being generally negligible.

Types of Thermometer:

Thermistor thermometer: An electronic component termed as the Thermistor is employed. Resistance in the Thermistor reduces as temperature rises, so that a larger current points out a higher temperature.

Clinical thermometer: Mercury-in-glass thermometer build up for measuring body temperature. There is a small bend close to the bulb to prevent mercury from falling back after the thermometer is taken out of the mouth.

Rotary thermometer: This thermometer makes utilization of a bimetallic strip which comprises of two strips of various metals joined altogether surface to surface. The strip bends as one metal expands more than the other beneath temperature change. As temperature rises, the coiled bimetallic strip bends more to rotate a pointer around on the scale.

Mercury-in-glass thermometer:

Mercury is placed within a bulb at the bottom of a sealed narrow glass tube. If temperature increases, mercury expands and rises up in the narrow glass tube. This responds to temperature change quickly. It must be handled with care as mercury is poisonous.

Resistance thermometer:

Electrical resistance of a metal wire rises as temperature rises, so that a smaller current points out a higher temperature. This can measure temperatures of over a thousand degrees Celsius and can be employed in industry to assess the temperatures of ovens and furnaces.

Alcohol-in-glass thermometer:

Colored and pressurized alcohol is placed within a bulb at the bottom of a sealed narrow glass tube. If temperature increases, alcohol expands and increases up in the narrow glass tube. It responds to temperature changes gradually. Alcohol is non-poisonous.

Digital thermometer:

The temperature measured through a Thermistor is displayed digitally. It is generally employed clinically to measure the body temperature.

Optical Pyrometers:

If it is needed to make accurate measurements of very high temperature, optical pyrometers are employed. This is done by observing the radiation from the hot body and the procedure is termed as pyrometer and the instrument employed a radiation pyrometer or optical pyrometer.

Optical pyrometers make utilization of the principle that extremely hot substances change color at certain known temperatures. For instance the temperature of steel, if it is below red heat, can be judged by its color. Temperatures below red heat can also be estimated by the use of paints that change colors at known temperatures.

Radiation pyrometers can be employed to measure temperatures (example of furnaces) just above red-heat that is around 600oC. They fall into two main classes:

1) Optical radiation pyrometers that respond only to visible light.

2) Total radiation pyrometers that respond to the net radiation from the hot body, light and heat.

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