Relation Between Celsius and Fahrenheit - Detailed Guide

Relationship Between Celsius an Frahrenheit

The conversion formula for a temperature that is expressed on the Centigrade scale (C) to its Fahrenheit scale (F) representation is or the relationship between Celsius and Fahrenheit scale is:

$F=\left(\frac{9}{5} \times C\right)+32$

Celsius temperature scale is also known as centigrade temperature scale , it is the scale based on 0 for the freezing point of water and 100 for the boiling point of water.

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What is Centigrade?

Celsius is also called a centigrade. It is also the unit of temperature. It is based on 0° for the freezing point of water and 100° for the boiling point of water. The formula used to convert the temperature from the Fahrenheit ( °F ) scale to the Celsius ( °C ) value is :

$C=\frac{5}{9}(F-32)$

The Celsius scale is used generally when the metric system of units is used , also it has wide use in science field everywhere.

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What is Fahrenheit Scale?

Fahrenheit is a scale used for measuring temperature degree, in which water freeze down at 32 degrees and boils at 212 degrees. It is represented by the symbol °F. It was invented by physicist Daniel Gabriel Fahrenheit in the year 1724.

The given formula can be used to convert degree Celsius to it’s Fahrenheit :

$F=\left(\frac{9}{5} \times C\right)+32$

Fahrenheit is widely used in the United States by the National Weather Service of the US.

Derivation of Celsius to Fahrenheit Formula
To derive the relation:
Difference in Fahrenheit scale:

$
212-32=180
$

Difference in Celsius scale:

$
100-0=100
$

Thus, ratio:

$
\frac{C}{100}=\frac{F-32}{180}
$

Solving:

$
F=\frac{9}{5} C+32
$

Relationship between celsius and fahrenheit

Celsius and fahrenheit scale is formulated as:

°C = 5/9 (°F − 32)

Similarly, we found relation between fahrenheit scale and celsius scale (convert farahenheit to celsius )

°F = ( 9/5 x °C ) + 32

Difference between celsius and fahrenheit

Celsius scale

• Celsius is the scale of temperature in which 0 o C represents the melting point of ice while 100 o C represents the boiling point of water.
• The absolute zero in the Celsius scale is 273.15 o C.

Fahrenheit scale

• Fahrenheit is a scale of temperature in which 32 o F represents the melting point of water.
• The absolute zero in Fahrenheit is - 459.67 o C

Also, now we can draw a celsius vs fahrenheit graph

Celsius vs Fahrenheit graph

Absolute Zero in Both Scales

• Absolute zero in Celsius = −273.15°C

• Absolute zero in Fahrenheit = −459.67°F

Applications of Temperature Conversion

• Weather forecasting
• Scientific experiments
• Industrial processes
• Cooking and food industry
• Medical thermometers

Solved Examples on Celsius-Fahrenheit Conversion

Example 1: Convert $\mathbf{2 5}^{\boldsymbol{\circ}} \mathbf{C}$ to Fahrenheit
Solution:
We use the formula:

$
F=\frac{9}{5} C+32
$

Substitute $C=25$ :

$
\begin{gathered}
F=\frac{9}{5} \times 25+32 \\
F=45+32=77^{\circ} F
\end{gathered}
$

Example 2: Convert $68^{\circ} \mathrm{F}$ to Celsius
Solution:

We use the formula:

$
C=\frac{5}{9}(F-32)
$

Substitute $F=68$ :

$
\begin{gathered}
C=\frac{5}{9}(68-32) \\
C=\frac{5}{9} \times 36=20^{\circ} \mathrm{C}
\end{gathered}
$

NCERT Physics Notes:

• NCERT Notes Class 11th Physics
• NCERT Notes Class 12th Physics
• NCERT Notes For All Subjects

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