# Relationship between Temperature Scales

## Relationship between Temperature Scales

### Relationship between Fahrenheit and Celsius

##### To determine the relationship between Fahrenheit and Celsius, we could draw a graph of F (temperature in °F) versus C (temperature in °C), for C in the range 0 ≤ C ≤ 100.

Using the general equation for a straight line:

#### y = m x + c

using the general straight line equation and above graph, the following equation obtained

We can now also express Celsius in terms of Fahrenheit. From Equation -1:

Now we solved the basic formulas for conversion of Celsius to Fahrenheit or vice versa. Using the same above procedure we can also calculate the relationship between different temperature scales.

### Quickly Convert Between Temperatures:

• Celsius to Fahrenheit: Multiply the temperature by 2 and then add 30
• Fahrenheit to Celsius: subtract 30 from the temp. and then divide by 2
• Kelvin to Fahrenheit: Subtract 273.15, multiply by 1.8, then add 32
• Fahrenheit to Kelvin: Subtract 32, multiply by 5, divide by 9, then add 273.15
• Kelvin to Celsius: Add 273
• Celsius to Kelvin: Subtract 273

Example -1

#### Convert the absolute zero of temperature (–273.15 °C), to degrees Fahrenheit.

F = (9/5)C + 32 = (9/5)×(-273.15) + 32 = -459.67 °F ≈ -460 °F

Example -2

#### Convert 86 °F into degrees Celsius, Rankine and Kelvin.

C = (5/9)(F – 32) = (5/9)×(86 – 32) = 30 °C

R = F + 460 = 86 + 460 = 546 R

K = C + 273 = 30 + 273 = 303 K

Example -3

#### Determine the temperature in degrees Fahrenheit that would translate into the same value in degrees Celsius.

In Equation -2 (or Equation -1), set C = F:

F = (5/9)(F – 32) ⇒ 9F = 5F – 160 ⇒ 4F = -160 ⇒ F = -40 °F

Example -4

#### Convert 0 °F to degrees Celsius.

C = (5/9)(F – 32) = (5/9)(0 – 32) = -17.78 °C