Question

A temperature scale has an upper fixed point of 260mm and the lower fixed point of 50mm.what will be the reading on this scale when the thermometer read 125°F​

Answer 1

the reading on the scale is 158.5 mm.

Step-by-step explanation:

Given;

upper fixed point of the temperature scale, x₁ = 260 mm

lower fixed point of the temperature scale, x₂ = 50 mm

upper temperature scale, T₁ = 212 °F

lower temperature scale, T₂ = 32 °F

thermometer reading, t = 125 °F, let the reading on the scale = x

Interpolate as follows to determine the value of "x"

`(X_1 - X)/(X_1-X_2) = (T_1-t)/(T_1-T_2) \\\\(260-X)/(260-50) = (212-125)/(212-32) \\\\(260 -X)/(210) =(87)/(180) \\\\180(260-X) = 87(210)\\\\46800 -180 X = 18270 \\\\180X = 46800-18270\\\\180X = 28530\\\\X = (28530)/(180) \\\\X = 158.5 \ mm`

Therefore, the reading on the scale is 158.5 mm.