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

Answer:

the reading on the scale is 158.5 mm.

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"

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

Therefore, the reading on the scale is 158.5 mm.