Types of Temperature Scales and Its Formulas

Temperature is one of the seven fundamental physical quantities in physics. A substance's temperature is defined as its degree of hotness. As a result, temperature refers to how hot or cold a body is. Different temperature scales, such as the Celsius, Kelvin, and Fahrenheit scales, are used to express a substance's temperature. To convert temperature from one scale to another, there are several formulas. The numerous forms of temperature scales and their formulas will be discussed here.

What is Temperature?

The degree of hotness of a body is measured by temperature. We can compare two bodies and determine one is hotter than the other based on their temperature values. Kelvin is the SI unit of temperature (K). Celsius and Fahrenheit are the two temperature units. Heat energy transfers from the body with a higher temperature to the one with a lower temperature when two bodies with differing temperatures come into contact. When two bodies of the same temperature come into touch with each other, no heat energy is transferred between them.

Different types of Temperature Scales

Temperature scales are divided into three categories. The Celsius, Fahrenheit, and Kelvin scales are the three. The formula can be used to convert a temperature value from one scale to another. Let's take a closer look at the many types of temperature scales.

Celsius Temperature Scale

There is one lower fixed point of 0 degrees Celsius and one upper fixed point of 100 degrees Celsius on the Celsius temperature scale. The centigrade temperature scale is another name for the Celsius temperature scale. It's because the lower fixed point of 0 degrees Celsius and the upper fixed point of 100 degrees Celsius are separated by a hundred degrees. The lower fixed point in the Celsius temperature system is 0 degrees Celsius, which is the freezing point of water at 1 atm atmospheric pressure. The upper fixed point in the Celsius temperature scale is 100 degrees Celsius, which is the boiling point of water at normal atmospheric pressure. Anders Celsius, a Swedish astronomer, established the Celsius temperature scale. The temperature in degrees Celsius is represented by the symbol °C. As a result, we can write that water's freezing point is 0 degrees Celsius and its boiling point is 100 degrees Celsius. All around the world, the Celsius temperature scale is frequently used.

Fahrenheit Temperature Scale

Daniel Gabriel devised the Fahrenheit temperature scale in 1744 while working on alcohol and mercury thermometers. In Fahrenheit, the temperature is expressed in degrees Fahrenheit (°F). The freezing point of water at normal atmospheric pressure is 32 degrees Fahrenheit, which is the lower fixed point on the Fahrenheit temperature scale. The boiling point of water at normal atmospheric pressure is 212 degrees Fahrenheit, which is the upper fixed point on the Fahrenheit temperature scale. Between the lower fixed point of 32 °F and the higher fixed point of 212 °F, there are 180 intervals. In the United States, the Fahrenheit temperature scale is widely used.

Kelvin Temperature Scale

Lord Kelvin invented the Kelvin scale in 1848. Kelvin is the S.I. temperature unit, denoted by K without a degree notation. The Kelvin temperature scale was inspired by the concept of absolute zero. The absolute zero temperature is the lowest temperature that any substance in the cosmos can reach. It is the lowest temperature at which the molecules have the least amount of energy. In the kelvin temperature scale, absolute zero is equal to 0 K. In the Kelvin temperature scale, absolute zero K equals -273.15 °C. In the Kelvin temperature scale, 1 K equals 1/273.16 of the temperature of the triple point of water.

Water has a freezing point of 273.15 K and a boiling point of 373.15 K on the kelvin temperature scale.

The Conversion of Temperature Scales Using the Formula

The temperature of a body can be converted from one temperature scale to another. Let's have a look at a few different temperature scale formulas.

The relation between the temperature in degree Celsius and the temperature in degree Fahrenheit is given by,

$\Rightarrow T_{^oF}= \frac{9}{5} \times T_{^oC} + 32$

Where,

$T_{^oF}$ - The temperature in Fahrenheit scale.

$T_{^oC}$ - The temperature in Celsius scale

The relation between the temperature in degree Celsius and temperature in kelvin scale is given by,

TK = 273.15 + $T_{^oC}$

Where,

TK - The temperature in the Kelvin scale.

$T_{^oC}$ - The temperature in Celsius scale

The relation between the temperature in Fahrenheit scale and the temperature in kelvin scale is given by,

$T_K= \frac{5}{9}\times \left ( T_{^oF} - 32 \right ) + 273.15$

Where,

$T_{^oF}$ - The temperature in Fahrenheit scale.

TK - The temperature in kelvin scale

Examples:

1. The temperature of a body is given as 80 ℃. Express this temperature on the Fahrenheit scale.

Ans:

The temperature of the body in degree Celsius = $T_{^oC}$ = 80oC

The relation between the temperature in degree Celsius and the temperature in degree Fahrenheit is given by,
$\Rightarrow T_{^oF}= \frac{9}{5} \times T_{^oC} + 32$...(1)

Where,

$T_{^oF}$ - The temperature in Fahrenheit scale.

$T_{^oC}$ - The temperature in Celsius scale

Substitute the value for temperature in degree Celsius in the equation (1) and simplify to calculate the temperature in Fahrenheit scale.

$\Rightarrow T_{^oF}= \frac{9}{5} \times T_{^oC} + 32$

$\Rightarrow T_{^oF}= \frac{9}{5} \times 80 + 32$

$\Rightarrow T_{^oF}= 144 + 32$

$\Rightarrow T_{^oF}= 176^oF$

⇒T℉ = 95 T℃ + 32

⇒T℉ = 95 80 + 32

⇒T℉ = 144 + 32

⇒T℉ = 176 ℉

Therefore, the temperature of the body in Fahrenheit scale is 176 ℉

2. Find the corresponding temperature for 298.15 K on the Celsius scale and Fahrenheit.

Ans:

The temperature in kelvin scale = TK = 298.15 K

The relation between the temperature in degree Celsius and temperature in kelvin scale is given by,

$\Rightarrow T_{^oF}= 273.15 \times T_{^oC}$...(1)

Where,

TK - The temperature in the Kelvin scale.

$T_{^oC}$ - The temperature in Celsius scale

Substitute the values for temperature in Kelvin scale in equation (1) and simplify to calculate the temperature in Celsius scale.

$\Rightarrow T_{k}= 273.15 + T_{^oC}$

$298.15 = 273.15 + T_{^oC}$

$T_{^oC} = 25^oC$

Therefore, the temperature in the Celsius scale is 25oC

The temperature in Celsius scale $T_{^oC}$ = 25oC

The relation between the temperature in degree Celsius and the temperature in degree Fahrenheit is given by,

$\Rightarrow T_{^oF}= \frac{9}{5} \times T_{^oC} + 32$...(2)

Where,

$T_{^oF}$ - The temperature in Fahrenheit scale.

$T_{^oC}$ - The temperature in Celsius scale

Substitute the value for temperature in degree Celsius in equation (2) and simplify to calculate the temperature in Fahrenheit scale.

$\Rightarrow T_{^oF}= \frac{9}{5} \times T_{^oC} + 32$

$\Rightarrow T_{^oF}= \frac{9}{5} \times 25 + 32$

$\Rightarrow T_{^oF}= 45 + 32$

$\Rightarrow T_{^oF}= 77{^oF}$

Therefore, the temperature of the body in Fahrenheit scale is 77 ℉

Conclusion

A body's temperature is a measurement of how hot it is. To express the temperature of a body, we use many temperature scales. The Celsius temperature scale, Fahrenheit temperature scale, and Kelvin temperature scale are three different forms of temperature scales. Using the formulas given above, we may convert the temperature of a body in one temperature scale to another temperature scale. On the Celsius scale, water has a freezing point of 0°C, 32°F on the Fahrenheit scale, and 273.15 K on the Kelvin scale. At normal atmospheric pressure, the boiling point of water is 100°C on the Celsius scale, 212°F on the Fahrenheit scale, and 373.15 K on the Kelvin scale. As a result, the temperature of a body has distinct values on different temperature scales.