The Celsius and Fahrenheit scales are both defined by the fr

The Celsius and Fahrenheit scales are both defined by the freezing and boiling points of water at standard atmospheric pressure. Given that the freezing point of water is exactly 0 degree C and 32 degree F and that the boiling point of water is exactly 100 degree C and 212 degree F, derive the equation that will convert a Celsius temperature into a Fahrenheit temperature. Also derive the equation that will convert a Fahrenheit temperature into a Celsius temperature.

Solution

For two temperature scale. We can write,

{Given Temperature in (°C) - Freezing point point of water in (°C)}/{Boiling temperature of water in (°C) - Freezing point point of water in (°C)}   

= {Given Temperature in (°F) - Freezing point point of water in (°F)} / {Boiling temperature of water in (°F) - Freezing point point of water in (°F)}   

{T (°C) - 0 (°C)} / {100 (°C) - 0 (°C)} = {F (°F) - 32 (°F) }/{ 212 (°F) - 32 (°F)}

T (°C) = 9/5 {F -32}                                                Where T is Temperature in °C and F is Temperature in °F

F- 32 = 5/9 * T (°C)

F = 5/9 * T (°C) + 32