# Thermometer

## What is a Thermometer?

A thermometer is defined as a device which is used to measure the temperature of a body. Temperature is basically a measure of the amount of kinetic energy of the particles possessed by the body or system.

The process of measurement of temperature of anything is called Thermometry. Nowadays, there are many different types of thermometers are used in thermometry.

Following are of most important –

1. Glass tube thermometer.
2. Thermistor.
3. Thermocouple.
5. Pyrometer etc.

### Thermometry

The branch of physics which deals with the measurement of temperature is called thermometry.

• Temperature is a measure of amount of kinetic energy possessed by a body.
• Thermometry is the process of measuring of this energy by using thermometers.

### Thermometric Property

The property of a material which has linear relation with rise of temperature is called thermometric property. A thermometer uses the thermometric property of a material to measure temperature.

Example –

1. Due to thermal expansion height of a mercury column in a glass tube changes linearly with rise in temperature. This property is used in the working principle of a glass tube mercury thermometer.
2. By Charle’s law, the pressure of a gas changes linearly with rise in temperature at constant volume. This property is used in the working principle of a Constant volume gas thermometers.
3. By Boyle’s law, the volume of a gas changes linearly with rise in temperature at constant pressure. This property is used in the working principle of Constant pressure gas thermometers.
4. By Ohm’s law, the electrical resistance of a metal wire changes linearly with rise in temperature. This property is used in the working principle of Platinum resistance thermometers.
5. By Seebeck effect, e.m.f produced in a thermocouple is proportional to the temperature difference of junctions. This property is used in the working principle of thermoelectric thermometer uses

## Thermometer Scale

A thermometer scale is consists of a graduated temperature scale between two fixed points. To construct a temperature scale, following fixed points are chosen –

1. Lower fixed point – It is the temperature at which pure ice melts at standard pressure.
2. Upper fixed point – It is the temperature at which pure water boils at standard pressure.

Range between these two fixed temperatures is called fundamental interval. Fundamental interval is sub divided into equal divisions.

Different types of commonly used thermometer scales are tabulated below –

 Thermometer scale Lower fixed point Upper fixed point Range CELSIUS SCALE 0 \degree C 100 \degree C 100 divisions. FAHRENHEIT SCALE 32 \degree F 212 \degree F 180 divisions. REAUMER SCALE 0 \degree R 80 \degree R 80 divisions. KELVIN SCALE 273 \degree K 373 \degree C 100 divisions.

### Conversion of Thermometer Scales

A relation between different thermometer scales has derived for used in conversion of the temperature from one scale to another scale.

• This relation is based on the principle of thermal expansion of substance.
• Thermal expansion between upper and lower fixed points is common for all the scales of measurement.

Let, ( T_C, \ T_F, \ T_R, \ T_K ) are the temperatures of a body measured in Celsius, Fahrenheit, Reaumer and Kelvin scales respectively.

Then, \left ( \frac {\text {Temperature of body - Lower fixed point}}{\text {Range}} \right ) will be common for all scales.

Therefore, \left ( \frac { T_C - 0 }{ 100 } \right ) = \left ( \frac { T_F - 32 }{ 180 } \right ) = \left ( \frac { T_R - 0 }{ 80 } \right ) = \left ( \frac { T_K - 273 }{ 100 } \right )

## Absolute Scale of Thermometer

According to Charle’s law, if ( V_{t} ) and ( V_{0} ) are the volumes at ( t \degree C ) and ( 0 \degree C ) respectively of a given mass of a gas at constant pressure ( P ) , then –

V_t = V_0 \left ( 1 + \frac { t }{ 273 } \right )

Therefore, volume of gas below ( 0 \degree C ) will be less than ( V_0 ) .

Thus, volume of gas at ( - t \degree C )  will be –

V_{-t} = V_0 \left ( 1 - \frac { t }{ 273 } \right )

Therefore, a decrease in temperature results in decrease in volume of the gas. This has been shown by plotting the volume of a given mass of gas against temperature at constant pressure as shown in figure.

• The graph is a straight line.
• If we extrapolate the straight line it meets the temperature axis at ( - 273 \degree C ) , where volume of gas becomes zero.

Hence, a gas occupies zero volume at ( - 273 \degree C ) .

Therefore, a temperature of less than ( - 273 \degree C )  is not possible to achieve, because the volume of gas will become negative which is not feasible.

• Hence, the possible lowest temperature of ( - 273 \degree C ) at which a gas have zero volume and zero pressure and entire molecular motion of gas stops, is called the absolute zero temperature.
• Kelvin suggested a new scale of temperature starting with ( - 273 \degree C ) as its lower fixed point. This scale of temperature is known as Kelvin scale or absolute scale of temperature.

In this scale ice point or triple point of water is assigned a value of ( 273 \degree K ) .

Therefore, \quad T (K) = ( t \degree C + 273 )

## Types of Thermometer

Thermometers are classified according to the thermometric material used in it. Thermometers are of following types –

### 1.Liquid Thermometer

• Thermometric property –  Linear expansion of liquid column with rise in temperature.
• Governing thermometric relation

T = \left [ \left ( \frac { l_t - l_0 }{ l_{100} - l_0 } \right ) \times 100 \degree C \right ]

Where, ( l ) is the length of liquid column.

Examples

1. Mercury thermometer.
2. Alcohol thermometer.

### 2.Gas Thermometer

• Thermometric property –  Linear change in pressure of gases with rise in temperature at constant volume.
• Governing thermometric relation

T = \left [ \left ( \frac { P_t - P_0 }{ P_{100} - P_0 } \right ) \times 100 \degree C \right ]

Where, ( P ) is the pressure of gas at constant volume.

Examples

1. Helium gas thermometer.
2. Nitrogen gas thermometer.

1. These thermometers are more sensitive than liquid thermometers because gas expansion is large with small change in temperature.
2. These are most accurate and used to calibrate other thermometers.
3. These thermometers can be used for a wide range of measurement such as ( -270 \degree C ) using helium gas and up to ( 1600 \degree C ) using nitrogen gas.

### 3.Resistance Thermometer

• Thermometric property –  Linear variations of electrical resistance or resistivity of conductors with rise in temperature.
• Governing thermometric relation

T = \left [ \left ( \frac { R_t - R_0 }{ R_{100} - R_0 } \right ) \times 100 \degree C \right ]

Where, ( R ) is the electrical resistance of a conductor.

Examples

1. Platinum resistance thermometer.
2. Germanium resistance thermometer.

It works on the principle of wheat stone bridge.

### 4.Thermocouple Thermometer

T = \left [ \left ( \frac { ξ_t - ξ_0 }{ ξ_{100} - ξ_0 } \right ) \times 100 \degree C \right ]

Where, ( ξ ) is the induced e.m.f due to thermo-electric effect.

Examples

1. Chromel – Alumel thermometer.
2. Iron – Constantan thermometer.

Normal range of thermo-electric thermometer is ( - 200 \degree C ) \ to \ ( 1600 \degree C ) . In industrial applications these are used as probes and thermo-sensors.

### 5.Optical Pyrometers

These are non contact type radiation thermometers. These are used to measure very high temperature.

• Thermometric property –  Variations of radiation energy with change in temperature.
• Governing thermometric relation  –

\lambda_{m} T = b ( A constant).

This constant is called Wien’s constant.

Where, ( \lambda_{m} ) is the wavelength of radiation of source.

Pyrometers are of two types –