Relation Between Celsius and Fahrenheit: Definitions, Temperature, Examples, History, Units, Scales, Derivation, Conversion

Relation Between Celsius and Fahrenheit Overview

The two most commonly used temperature scales are Fahrenheit and Celsius. The Fahrenheit scale expresses or writes the temperature in degrees Fahrenheit, whereas the Celsius scale expresses or writes the temperature in degrees Celsius. Fahrenheit and Celsius have a direct proportional connection. Furthermore, both Fahrenheit and Celsius have distinct values for the freezing point of water, and each scale has a different unit difference.

What is a Temperature?

Temperature is a physical measure that quantifies our feelings of hotness and coolness. A thermometer is used to measure temperatures. Thermometers are calibrated on a variety of temperature scales that have traditionally been defined by various reference points and thermometric substances. The most prevalent scales are the Celsius scale (previously known as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being used mostly for scientific reasons. The kelvin is one of the seven basic units of the International System of Units (SI).

Relation Between Celsius and Fahrenheit: Definition

What is Celsius?

The degree Celsius is the unit of temperature on the Celsius scale (formerly known as the centigrade scale outside of Sweden). A particular temperature on the Celsius scale or a unit used to denote a difference or range between two temperatures are both represented by the sign "degree Celsius" (°C). It was created in 1742 by the Swedish astronomer Anders Celsius (1701–1744), who gave it his name. The measure was once known as centigrade, which comes from the Latin words centum, which means 100, and gradus, which means steps, until it was changed to honor Celsius in 1948. Since 1743, the freezing point of water has been measured at 0 °C, and the boiling point at 1 atm has been measured at 100 °C. The numbers were originally inverted, with the boiling point at 0 degrees and the freezing point at 100 degrees, until 1743. Jean-Pierre Christin suggested the 1743 scale reversal.

What is Fahrenheit?

The temperature scale known as the Fahrenheit scale was first proposed in 1724 by scientist Daniel Gabriel Fahrenheit (1686–1736). The unit is the degree Fahrenheit, represented by the sign °F. There are several reports of how he initially created his scale, but according to the original study, the lowest defining point, 0 °F, was chosen to correspond to the freezing point of a brine solution generated from a combination of water, ice, and the salt ammonium chloride. His best estimate of the average human body temperature, first set at 90 °F and then 96 °F (about 2.6 °F less than the current figure due to a later revision of the scale), was the other limit established.

Relation Between Celsius and Fahrenheit: Examples

The examples of Celsius and Fahrenheit are given below-

History and Importance of Celsius and Fahrenheit Scales 

The Fahrenheit and Celsius scales were developed by scientist Daniel Gabriel Fahrenheit, who established the Fahrenheit scale in 1724. The major focus of this physicist was to estimate the average inside temperature of a human body as well as the temperature of brine at which it freezes (Paoletti, 2020). According to Fahrenheit, the typical temperature of a human's inside body is close to 90 °F. The estimated inner body temperature of a person was later updated to 96 °F, which was extremely close to the actual inner body temperature.

Anders Celsius, a Swedish astronomer, established the centigrade scale in 1742. The present name, "Celsius scale," is derived from the name of the originator of this scale. At the time of its development, the Celsius scale was mostly used as a 100-point system (Sekerák et al. 2020). This scale was initially intended to calculate the temperature difference between boiling water and melting snow.

Relation Between Celsius and Fahrenheit: Units 

Temperature scale units are important for distinguishing temperatures from one scale to another. The following are some of the units of Celsius and Fahrenheit-

1. On the Celsius scale, the temperature is represented by °C.
2. On the Fahrenheit scale, the temperature is represented by °F.

What are the Centigrade and Fahrenheit Scales?

Anders Celsius, a Swedish astronomer, invented the Celsius scale in 1742. Because of the 100-degree space between the stated points, it is also known as the centigrade scale. The temperature should be represented in degrees Celsius on the Celsius scale. The Fahrenheit scale is atemperature scale established by scientist Daniel Gabriel Fahrenheit in 1724. Fahrenheit is the unit of measurement.

Relation Between Celsius and Fahrenheit: Derivation

The following mathematical equation can be used to demonstrate the derivation of the relationship between the two temperature units, Celsius and Fahrenheit. Because the freezing point of water in Celsius is 0 °C and 32 °F in Fahrenheit, we get the equation,

C − 0 = F − 32

We obtain it by dividing it by the entire number of intervals in the scale (100 degrees for Celsius and 180 degrees for Fahrenheit)-

 (C − 0) / 100 = (F − 32) / 180

C / 100 = (F − 32) / 180

C / 5 = (F − 32) / 9

In the above-proven equations,

F = Temperature in Fahrenheit.

C = Temperature in Celsius.

Relation Between Celsius and Fahrenheit: Conversion

Conversion from Celsius to Fahrenheit

The conversion from Celsius to Fahrenheit may be represented mathematically as-

F = (9/5 x C) + 32

Where, 

F is the temperature in Fahrenheit.

C is the temperature in degrees Celsius.

Conversion from Fahrenheit to Celsius

The conversion from Fahrenheit to Celsius may be represented mathematically as-

C = 5/9 (F - 32)

Where, 

F is the temperature in Fahrenheit.

C is the temperature in degrees Celsius.

Relation Between Celsius and Fahrenheit

The Celsius and Fahrenheit scales have a strong link since both are extensively used to measure the temperature of liquids, bodies, and other things. The proportionate relationship between these two scales highlights an essential point. When the degree of temperature is increased on one scale, the rate of temperature is seen to increase on the other (Huda, 2021). As a result, if the temperature of an object decreases on the Fahrenheit scale, the temperature on the Celsius scale also decreases. The following table gives details about Celsius and Fahrenheit-

Points to Remember

1. F = (9 / 5 C) + 32 is the formula for converting Celsius to Fahrenheit.
2. C = 5 / 9 (F 32) is the formula for converting Fahrenheit to Celsius.
3. The Celsius scale has 100-degree increments, while the Fahrenheit system has 180-degree increments.
4. The Fahrenheit scale temperature must be represented in degrees Fahrenheit.
5. The temperature should be represented in degrees Celsius on the Celsius scale.
6. Water has a boiling temperature of 100 degrees Celsius and a freezing temperature of 212 degrees Fahrenheit.
7. Water has a freezing point of 0 °C on a Celsius scale and a freezing point of 32 °F on a Fahrenheit scale.

Sample Questions related to the Relation Between Celsius and Fahrenheit

Sample Question 1: What is the boiling point of water on the Fahrenheit and Celsius scales?

Solution: The Fahrenheit scale and the centigrade scale both use different thermometers and different scale values to measure temperature, so the boiling point of water varies on both scales. For example, the boiling point of water on the Celsius scale is 100 degrees Celsius, while it is 212 degrees Fahrenheit on the Fahrenheit scale.

Sample Question 2: What is the Fahrenheit equivalent of 30 °C? Use the formula application to demonstrate. 

Solution: The following formula should be used to convert 30 °C to Fahrenheit, which is 

F = (9 / 5 X C) + 32

F denotes the temperature in Fahrenheit.

while C denotes the temperature in degrees Celsius.

In this instance, the value of C is 30. 

As a result, we will substitute the value of C in the formula to obtain the value of F.

F = (9 / 5 X 30) + 32

F = ( 9 X 6) + 32

F = 54 + 32

F = 86

So, 30° C = 86° F

Sample Question 3: What exactly is the Kelvin Scale? Also, using the Kelvin scale, provide the freezing and boiling points.

Solution: The Kelvin scale, like the Centigrade and Fahrenheit scales, is used to measure temperature and has its own relationship to the other two scales. The freezing point on the Kelvin scale is 273 degrees Celsius, whereas the boiling point is 373 degrees Celsius. The unit of kelvin is represented by k here.

Sample Question 4: What is the Fahrenheit equivalent of 20 °C?

Solution: The formula for converting °C to °F is

TF = 9/5(TC) + 32

TF = 9/5(20) + 32

TF = 36 + 32

TF = 68 °F

The Fahrenheit equivalent of 20 °C is 68 °F.

At -40°, Celsius and Fahrenheit are the same, but at normal temperatures, Fahrenheit will be greater than Celsius.

Sample Question 5: Ques. On the centigrade scale, which unit is used to represent temperature?

Solution: Celsius is used to represent centigrade temperature units, such as 2 degrees Celsius.

Sample Question 6: What's the difference between Celsius and Fahrenheit? 

Solution: The Celsius and Fahrenheit units are precisely proportional to each other, which means that when the corresponding temperature in the Celsius unit rises, so will the temperature in Fahrenheit, and vice versa.

Sample Question 7: Convert 30 degrees Celsius to Fahrenheit.

Solution: The formula for converting °C to °F is

TF = 9/5(TC) + 32

     = 30° × 9

     = 270°

     = 270° ÷ 5

     = 54°

     = 54 + 32

     = 86° F

Therefore, 30 °C = 86 °F.