Scales of Temperature – Types, Formula & Conversion

Scales of temperature is a basic concept that every individual should be aware of. Any object with comparatively more internal energy (energy possessed by its molecules) is considered to have a high temperature, whereas an object with comparatively less internal energy is considered to have a low temperature. The temperature of a body is measured by a device called a thermometer. There are different scales of measuring temperature. For example, a clinical thermometer usually measures temperature in degree Celsius or degree Fahrenheit.

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What are Temperature Scales?

Temperature scale is a parameter that is used to measure temperature. A thermometer is used to measure the temperature of a body on various scales. Every thermometer has temperature scales marked in them which is hence used to measure the body temperature. There are different units that are used for the purpose of measuring temperature. The most common scale for measuring temperature is the Celsius scale. It expresses the temperature in degrees Celsius.

Fig: scales of temperature

What are the Different Scales of Temperature?

There are four main scales used to measure temperature. They are discussed as follows:

1. Kelvin Scale: The British physicist William Thompson who was also known as Lord Kelvin, invented the Kelvin scale. Kelvin scale of temperature is based on the kinetic theory of molecular motion. On the Kelvin scale, absolute zero is the temperature when no molecular motion takes place. Absolute zero is the coldest possible temperature. Thezing point (ice point) of water on this scale is \({\rm{273}}\,{\mkern 1mu} {\rm{K,}}\) and the boiling point (steam point) of water is \({\rm{373}}\,{\mkern 1mu} {\rm{K,}}\) In between the two points, there are \({\rm{100}}\) equal divisions on the Kelvin scale. This scale does not have negative values. Kelvin scale is widely used in scientific calculations. Kelvin is the SI unit of temperature and is represented by the letter \({\rm{‘K’}}{\rm{.}}\)
2. Celsius Scale: The Swedish astronomer Celsius invented this scale. On the Celsius scale, thezing point (ice point) of water is taken as \({\rm{0}}\,^\circ {\mkern 1mu} {\rm{C}},\) and the boiling point (steam point) of water is taken as \({\rm{100}}\,^\circ {\mkern 1mu} {\rm{C}}.\) In between the two points, there are \({\rm{100}}\) equal divisions on the Celsius scale.
3. Fahrenheit Scale: This scale was introduced by the German physicist Daniel Gabriel Fahrenheit. On this scale, thezing point of water is taken as \({\rm{32}}\,^\circ {\mkern 1mu} {\rm{F,}}\) and the boiling point of water is taken as \({\rm{212}}\,^\circ {\mkern 1mu} {\rm{F}}{\rm{.}}\) In between the two points, there are \({\rm{180}}\) equal divisions on the Fahrenheit scale.
4. Reaumur Scale: Reaumur scale is invented by Rene-Antoine Ferchault de Reaumur. Thezing point of water on this scale is marked as zero, and the boiling point of water is taken as \({\rm{80}}\,^\circ {\rm{Re}}\) In between the two points, there are \(80\) equal divisions on the Reaumur scale.

Commonly Used Scales of Temperature

The commonly used scales of temperature are the Celsius scale and the Fahrenheit scale. There are two types of thermometer, namely laboratory thermometer and clinical thermometer. The human body temperature is measured by a clinical thermometer which shows the temperature in degree Celsius \(\left( {^\circ {\rm{C}}} \right)\) and degree Fahrenheit \(\left( {^\circ {\rm{F}}} \right)\) The range of a clinical thermometer is from \(35\,^\circ {\mkern 1mu} {\rm{C}}\) to \(42\,^\circ {\mkern 1mu} {\rm{C}}\) The normal human body temperature is \({\rm{37}}\,^\circ {\mkern 1mu} {\rm{C}}\) to \({\rm{98}}.{\rm{6}}\,^\circ {\mkern 1mu} {\rm{C}}\) In order to measure the temperature in laboratories, a laboratory thermometer is used. It ranges from \({\rm{ – 10}}\,^\circ {\rm{C}}\) to \({\rm{110}}\,^\circ {\mkern 1mu} {\rm{C}}\)

A thermometer uses mercury as a heat-sensitive material that rises up when brought in contact with a body. The division of thermometric scale up to which the mercury rises gives the reading of the temperature of the body. Some thermometers use alcohol (ethanol) to measure extremely low temperatures.

Relationship Between Different Scales of Temperature – Formula

Thezing point or ice point of water is taken as the lower fixed point while making a temperature scale for the thermometer, and the boiling point of water is taken as the upper fixed point of the temperature scale.

The formula below gives the relationship between the Kelvin scale, Celsius scale and Fahrenheit scale:

\(\frac{{C\, – \,LFP}}{{UFP\, – \,LFP}}\, = \,\frac{{K\, – \,LFP}}{{UFP\, – \,LFP}}\, = \,\frac{{F\, – \,LFP}}{{UFP\, – \,LFP}}\)

Where \(LFP\, = \) Lower fixed point on a particular scale

\(UFP\, = \) Upper fixed point on a particular scale

\(C\, = \) Temperature on the Celsius scale

\(F\, = \) Temperature on the Fahrenheit scale

\(K\, = \) Temperature on the Kelvin scale

\(\frac{{C{\mkern 1mu} – {\mkern 1mu} 0}}{{100{\mkern 1mu} – {\mkern 1mu} 0}}{\mkern 1mu} = {\mkern 1mu} \frac{{K{\mkern 1mu} – {\mkern 1mu} 273}}{{373 – 273}} = \frac{{F{\mkern 1mu} – {\mkern 1mu} 32}}{{212{\mkern 1mu} – {\mkern 1mu} 32}}\)

\(\Rightarrow \,\frac{C}{{100}} = \frac{{K – 273}}{{100}} = \frac{{F – 32}}{{180}}\)

1. Relationship Between Celsius Scale and Kelvin Scale: From the above formula, we get the relationship between the three scales of temperature. The relationship between the Celsius scale and the Kelvin scale is given by \(C\, = \,K\, – \,273\).
2. Relationship Between Fahrenheit Scale and Kelvin Scale: The relation between the Fahrenheit scale and the Kelvin scale is given by \(F = \,\frac{9}{5}(K\, – \,273)\, + \,32\).
3. Relationship Between Celsius and Fahrenheit Scale: The relationship between the Celsius and the Fahrenheit scale is given by \(F\, = \left( {\frac{9}{5}\, \times C} \right)\, + 32\). Note that the lower fixed point in all temperature scales is equal, and the upper fixed point in all temperature scales is equal.

Conversion of Scales of Temperature – Examples

Q.1. Convert \({\rm{0}}\,^\circ {\mkern 1mu} {\rm{C}}\) to \(^\circ {\rm{F}}\)
Sol: Given the temperature on the Celsius scale \({\rm{ = }}\,{\mkern 1mu} 0{\,^{\rm{o}}}{\rm{C}}\)
The formula for converting degree Celsius to degree Fahrenheit is given by \(F\, = \,\left( {\frac{9}{5} \times C} \right) + 32\)
By putting the given value of temperature, we get:
\(F\, = \,\left( {\frac{9}{5} \times 0} \right) + 32\)
\(\Rightarrow F = 32{\mkern 1mu} \,^\circ {\rm{F}}\)

Q.2. Convert \({\rm{45}}\,{{\mkern 1mu} ^{\rm{o}}}{\rm{F}}\) to \(^{\rm{o}}{\rm{C}}\)
Sol: Given the temperature on the Fahrenheit scale \(= 45\,{{\mkern 1mu} ^{\rm{o}}}{\rm{C}}\)
The formula for converting degree Fahrenheit to degree Celsius is given by \(C\, = \,\frac{5}{9}(F\, – \,32)\)
By putting the given value of temperature, we get:
\(C\,\, = \,\frac{5}{9}(45\, – \,32)\)
\(\Rightarrow C = \frac{5}{9} \times 13 = 7.222\,{{\mkern 1mu} ^{\rm{o}}}{\rm{C}}\)

Q.3. Convert \(250\,{\rm{K}}\,{\rm{to}}\,^\circ {\rm{C}}.\)
Sol: Given the temperature on the Kelvin scale \(= 250\,{\rm{K}}\)
The formula for converting Kelvin to degree Celsius is given by
\(C\, = \,K\, – \,273\)
By putting the given value of temperature in the above formula, we get:
\(C{\mkern 1mu} {\mkern 1mu} = {\mkern 1mu} 250{\mkern 1mu} – {\mkern 1mu} 273{\mkern 1mu} = {\mkern 1mu} \, – 23\,^\circ {\rm{C}}\)

Q.4. Convert \(120\,^\circ {\rm{F}}\,{\rm{to}}\,^\circ {\rm{C}}\)
Sol: Given the temperature on the Fahrenheit scale \(= 120\,^\circ {\rm{F}}\)
The formula for converting degree Fahrenheit to degree Celsius is given by
\(C\, = \,\frac{5}{9}(F\, – \,32)\)
By putting the given value of temperature, we get:
\(C\, = \,\frac{5}{9}(120\, – \,32)\)
\(\Rightarrow C{\mkern 1mu} = \,\frac{5}{9} \times 88{\mkern 1mu} = {\mkern 1mu} 48.889\,^\circ {\rm{C}}\)

From this article, we can conclude that different scales of temperature are used to measure the degree of hotness or coldness of a substance. The most commonly used temperature scale is the Celsius scale. It measures the temperature of a body in the unit called degree Celsius or degree centigrade. The use of different scales of temperature depending upon a person’s convenience helps him measure extremely high or low temperature.

Scales of Temperature FAQs

Frequently asked questions related to scales of temperature is listed as follows:

Q.3. Why are there three different temperature scales?
Ans: Different temperature scales make it easy to measure extremely high or low temperatures and measure the accurate value of temperature. For example, we will get a recurring number when we convert \(120{\mkern 1mu} \,^\circ {\rm{F}}\) to degree centigrade. Therefore, this will not allow us to get an accurate value on the Celsius scale.

Q.4. What is absolute zero on a Kelvin scale?
Ans: Absolute zero or \(0\,{\rm{K}}\) is the temperature at which the kinetic energy of molecules is equal to zero. No molecular motion takes place at absolute zero. Absolute zero is the lowest possible temperature.

Q.5 What are the five temperature scales?
Ans: The five temperature scales are as follows:
a. Kelvin scale
b. Celsius scale
c. Fahrenheit scale
d. Reaumur scale
e. Rankine scale

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