Question #8175

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.

Expert's answer

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.

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.

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