Scales of Temperature and Their Conversions

Temperature is a measure of the average kinetic energy of the particles in a substance. It is one of the fundamental quantities in physics and is measured using various scales. The most commonly used temperature scales are Celsius, Fahrenheit, and Kelvin.

Celsius (°C)

The Celsius scale, also known as the centigrade scale, is used by most countries worldwide and is considered the standard unit of temperature for the International System of Units (SI). It is named after the Swedish astronomer Anders Celsius. The scale is defined by two points: the freezing point of water at 0°C and the boiling point of water at 100°C, both at one atmosphere of pressure.

Fahrenheit (°F)

The Fahrenheit scale is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit. It is used primarily in the United States. On the Fahrenheit scale, the freezing point of water is 32°F and the boiling point is 212°F, placing the boiling and freezing points of water exactly 180 degrees apart.

Kelvin (K)

The Kelvin scale is the base unit of temperature in the International System of Units (SI). It is named after the Scottish physicist and engineer Lord Kelvin. The Kelvin scale is an absolute temperature scale where 0 K is absolute zero, the point at which no more thermal energy can be extracted from a system. The freezing point of water on the Kelvin scale is 273.15 K and the boiling point is 373.15 K.

Rankine (°R)

The Rankine scale is similar to the Kelvin scale in that it is an absolute temperature scale. It is named after the Scottish engineer and physicist William John Macquorn Rankine. The scale uses the Fahrenheit degree as its unit increment but, like the Kelvin scale, starts at absolute zero. Therefore, the freezing point of water is 491.67°R and the boiling point is 671.67°R.

Differences and Important Points

Here is a table summarizing the differences between the temperature scales:

Scale	Freezing Point of Water	Boiling Point of Water	Increment	Absolute Zero
Celsius (°C)	0°C	100°C	1°C	-273.15°C
Fahrenheit (°F)	32°F	212°F	1°F	-459.67°F
Kelvin (K)	273.15 K	373.15 K	1 K	0 K
Rankine (°R)	491.67°R	671.67°R	1°R	0°R

Formulas for Temperature Conversion

To convert between these temperature scales, you can use the following formulas:

Celsius to Fahrenheit

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

Fahrenheit to Celsius

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

Celsius to Kelvin

$$ K = C + 273.15 $$

Kelvin to Celsius

$$ C = K - 273.15 $$

Fahrenheit to Kelvin

$$ K = \frac{5}{9}(F - 32) + 273.15 $$

Kelvin to Fahrenheit

$$ F = \frac{9}{5}(K - 273.15) + 32 $$

Celsius to Rankine

$$ R = \left(\frac{9}{5}C\right) + 491.67 $$

Rankine to Celsius

$$ C = \frac{5}{9}(R - 491.67) $$

Fahrenheit to Rankine

$$ R = F + 459.67 $$

Rankine to Fahrenheit

$$ F = R - 459.67 $$

Examples

Let's go through some examples to understand how to use these formulas:

Example 1: Celsius to Fahrenheit

Convert 25°C to Fahrenheit.

$$ F = \frac{9}{5} \times 25 + 32 $$ $$ F = 45 + 32 $$ $$ F = 77°F $$

Example 2: Fahrenheit to Celsius

Convert 77°F to Celsius.

$$ C = \frac{5}{9} \times (77 - 32) $$ $$ C = \frac{5}{9} \times 45 $$ $$ C = 25°C $$

Example 3: Celsius to Kelvin

Convert 100°C to Kelvin.

$$ K = 100 + 273.15 $$ $$ K = 373.15 K $$

Example 4: Kelvin to Celsius

Convert 0 K to Celsius.

$$ C = 0 - 273.15 $$ $$ C = -273.15°C $$

Understanding these temperature scales and how to convert between them is essential for scientific measurements, cooking, and many other applications where temperature plays a crucial role.