Question

A faulty mercury in glass thermometer indicate that the ice point of pure water is 0.8°c and steam point is 99.5°c under standard atmospheric pressure.Deduce an expression in the form of y=mx +c,where m and c are constant to relate the faulty temperature reading F°c to the correct temperature T°c

Answer 1

$T=mF+c,$ we know that water becomes ice when temperature is 0°c ans boils when temperature is 100°c. Therefore,

$0 = m\cdot0.8 + c, \;\; 100 = m\cdot99.5 + c$ . Subtracting the first equation from the second, we get

$100 = m\cdot98.7, \;\; m = 1.013.$

$c =- 0.8m =- 0.8\cdot1.013 \approx -0.811.$

Therefore, $T=1.013F -0.811.$