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# Fahrenheit|Definition & Meaning

## Definition

**Fahrenheit** is a linear **scale** for measurement of **temperature** that maps zero degree Celsius (**melting point of ice**) to **thirty two degree Fahrenheit** and 100 degree Celsius (**boiling point of water**) to **two hundred and twelve degree Fahrenheit**.

There are **many scales** of measuring temperature that have been in use in **different parts** of the **world** during different timelines. However, three units are most **commonly used** today. These include **Celsius, Fahrenheit,** and **Kelvin** scales. The following **figure** shows these scales **side by side. **

**Figure 1: Celsius, Fahrenheit and Kelvin scales**

As shown in the figure above, all **three scales** are related to each other through the **freezing** and **boiling point of water.** Consequently, all three scales are **linear,** and they can be completely defined by these **two points.**

The water freezes at **zero degree Celsius, thirty-two degrees Fahrenheit** and two hundred seventy-three Kelvin. It boils at a **hundred degrees Celsius, two hundred and twelve degrees Fahrenheit** and three hundred and seventy-three Kelvin.

## Explanation of Fahrenheit Scale

All three of these scales have their own **significance** and **utilization** in terms of **applications.** While **Celsius** is used **worldwide** and **Kelvin** is the **system international** unit of temperature, **Fahrenheit** is the unit of choice when it comes to **United States.**

This scale is named after the renowned Polish physicist **Daniel Gabriel Fahrenheit** who invented the first ever **precision thermometers** in the seventeenth century. The scale is symbolized by** capital letter F**. Following figure shows some important temperature readings on this scale.

**Figure 2: Important Temperature Readings on Fahrenheit Scale**

Fahrenheit scale is the scale of choice in the **medical community.** Commonly used thermometer that we use for our **body temperature** to measure the **fever** is also graded in **Fahrenheit scale.** The normal human body temperature is **98.6 degree Fahrenheit.**

The wide use of the **Fahrenheit** scale in the **USA** and the resistance to the adoption of the **Kelvin** or **Celsius** scale do have some logical reasons. One of the key reason is that the **Fahrenheit scale** is more suitable and **intuitive** in describing the **outdoor temperature** compared to the other scales.

It can be noticed that in many parts of the **habitable world,** the temperature does fall below zero degrees Celsius whereas in Fahrenheit, most areas are covered.

Similarly, on a **hot summer day,** the temperature is around a hundred degrees Fahrenheit in the USA. Therefore, the **adoption of Fahrenheit** is more suitable. The zero mark on this scale represents **cold days** of **winter,** while the 100-degree mark represents **hot summer days.**

Another notable reason for the use of **Fahrenheit** is that the **resolution** of the scale is **larger than Celsius.** Therefore more precise measurements can be noted on the Fahrenheit scale compared with Celsius or Kelvin.

## Inter-conversion of Temperature Scales

Since all **three scales** of temperature are used in mostly all parts of the world, it is worthwhile to learn the interconversion** formulae** for these scales. As students of **mathematics** and **science,** we come across many such situations where an instrument measures in one scale of temperature while our formulae require the other one.

Or, there may be a situation when a **scientist** from **one part** of the **world** has to **share temperature data** with **other scientists** in other parts of the globe. So it is important to **understand** how these scales are related **mathematically. The following** headings **summarize** these **interconversions.**

### Inter-conversion Between Fahrenheit and Celsius Scales

As explained earlier, both scales are **linear,** and the **relationship** can be drawn based on the temperature values of any **two physical phenomena.** Since we know the **freezing** and **boiling points** of **water** in both scales, we can formulate an equation of the line as follows:

**F = 1.8 C + 32 … … … … (1)**

**The following figure** explains this **relationship:**

**Figure 3: Inter-conversion between Fahrenheit and Celsius Scales**

Which can be **re-arranged** to obtain the following formula:

**C = 0.556 ( F – 32 ) … … … … (2)**

### Inter-conversion Between Fahrenheit and Kelvin Scales

Since we know the **freezing** and **boiling points** of **water** in both scales, we can formulate an **equation** of the line as follows:

**F = 1.8 ( K – 273.15 ) + 32 … … … … (3)**

**The following figure** explains this **relationship:**

**Figure 4: Inter-conversion between Fahrenheit and Kelvin Scales**

Which can be **re-arranged** to obtain the following formula:

**K = 0.556 ( F – 32 ) + 273.15 … … … … (4)**

## Examples of Inter-conversion

Since **temperature conversion** is a very commonly seen problem in real life as well as in many **scientific problems,** let us consider some **numerical examples.**

### (a) Conversion from Celsius to Fahrenheit Scale

A **can of water** is heated up to a temperature of **80 degrees Celsius**. Find the value of temperature in **Fahrenheit scale.** Using the formula no. 1 above:

**F = 1.8 ( 80 ) + 32 = 176 degree Fahrenheit**

### (a) Conversion from Fahrenheit to Celsius Scale

A **piece of ice** is cooled to a temperature of **10 degrees Fahrenheit**. Find the value of temperature in the **Celsius scale.** Using the formula no. 2 above:

**C = 0.556 ( 20 – 32 ) = -6.67 degree Celsius**

### (a) Conversion from Kelvin to Fahrenheit Scale

The** boiling point of a certain alcohol** is **350 Kelvin**. Find the value of temperature in **Fahrenheit scale.** Using the formula no. 3 above:

**F = 1.8 ( 350 – 273.15 ) + 170.33 degree Fahrenheit**

### (a) Conversion from Fahrenheit to Kelvin Scale

The **melting point of iron is 2800 degrees Fahrenheit**. Find the value of temperature in the **Kelvin scale.** Using the formula no. 4 above:

**K = 0.556 ( 2800 – 32 ) + 273.15 = 1812.158 Kelvin**

## Numerical Problems Involving Fahrenheit Temperatures

**Part (a):** Convert **70 degree Celsius** to Fahrenheit

**Part (b):** Convert** 200 degree Fahrenheit** to Celsius

**Part (c):** Convert **273.15 Kelvin** to Fahrenheit

**Part (d):** Convert **1000 Fahrenheit** to Kelvin

### Solution Part (a)

**F = 1.8 C + 32**

**F = 1.8 ( 70 ) + 32**

**F = 158 degrees Fahrenheit**

### Solution Part (b)

**C = 0.556 ( F – 32 )**

**C = 0.556 ( 200 – 32 )**

**C = 93.33 degree ****Celsius**

### Solution Part (c)

**F = 1.8 ( K – 273.15 ) + 32**

**F = 1.8 ( 273.15 – 273.15 ) + 32**

**F = 32 degrees Fahrenheit**

### Solution Part (d)

**K = 0.556 ( F – 32 ) + 273.15**

**K = 0.556 ( 1000 – 32 ) + 273.15**

**C = 810.93 degrees ****Celsius**

*All images/mathematical drawings were created with GeoGebra.*