Temperature Scales (Celsius and Fahrenheit) and its Derivation

The exact relationship between degrees Celsius and Fahrenheit is to be established. There are two parts of the lesson. One is to establish the relationship and the other is to compare the established formula with an estimate. The exact formula is F = 1.8C +32, whereas the estimate formula is F = 2C + 30 ( in words, double and add 30). Straight line graphs are to be plotted on the graph paper provided.

The steps of the derivation are given, but require explanations as to why each step follows the previous step, until one arrives at the required exact relationship.

Note: While the ice (freezing) and the steam (boiling) points of pure water are 0 and 100 degrees Celsius respectively, the corresponding points for the Fahrenheit scale are 32 and 212 degrees.

Points of discussion:

1. At 10 degrees Celsius, both the exact and the estimate formula produce the sam value of degrees Fahrenheit - 50 degrees Fahrenheit
2. Impurities will lower the freezing point of water and raise the boing point.
3. Work out the one particular temperature at which both scales read the same value.