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Conversion of temperature from one scale to other

Let l cm be the length between the mercury levels in the capillary tube between the lower fixed point and upper fixed point.Thus on the Celsius scale, l cm length of mercury corresponds to 100°C ,while on Fahrenheit scale,l cm length of mercury corresponds to 180° F 

i.e., for each degree,the length is l/180.

If  C and F be the readings of the temperature of the same body on the Celsius and Fahrenheit scales,then

length of expanded mercury in the Celsius thermometer = (C - 0) x l/100, and 

length of expanded mercury in the Fahrenheit thermometer = (F - 32) x  l/180.

Since the length of expanded mercury on the two scales must be same,

Therefore (C - 0) x l /100 = (F - 32) x l /180

or                            C / 5 = F - 32 / 9

With this relation, temperature on Celsius scale can be converted into the corresponding temperature on the Fahrenheit scale or viceversa.

To convert the Celsius scale into the kelvin scale,we have to add 273 to the Celsius scale.