Question

The ice and steam points on a thermometer correspond to X and 50mm respectively. A temperature of 60 degree Celsius corresponds to 52mm on the thermometer. Calculate the value of X.

Answer 1

Let's find out the relation between termometer height and temperature. We assume that height changes linearly with respect to temperature, i.e.
H = αT + C.
We know that
52 = 60α + C ==> C = 52 - 60α.
Also, the ice and the steam points corresponds to 0°C and 100°C respectively, so
50 = 100α + C ==> C = 50 - 100α
and
X = 0α + C ==> X = C.
At last, X = C = 52 - 60α = 50 - 100α ==> 52 - 60α = 50 - 100α ==> 2 = -40α ==> α = -0.05
and X = C = 52 - 60α = 52 - 60*(-0.05) = 55mm.