Question #8f60c

1 Answer
May 18, 2017

Answer:

Thermometer Y shows a temperature of 24 °Y.

Explanation:

To help us work through this problem, I adapted an image of two common thermometer scales.

Ignore the markings on the thermometers and look at the markings outside them.

Thermometers X and Y
(Adapted from www.tf.uni-kiel.de)

On Thermometer X,

#T_text(boil) - T_text(freeze) = "220 ° - 20 ° = 200 °"#

On Thermometer Y,

#T_text(boil) - T_text(freeze) = "120 ° - (-40 °) = 160 °"#

#"200 X° = 160 Y °"#

A temperature of 100 °X is 80 X° above the freezing point of water.

#80 color(red)(cancel(color(black)("X°"))) × "160 Y°"/(200 color(red)(cancel(color(black)("X°")))) = "64 Y°"#

The temperature is 64 Y° above the freezing point of water.

∴ On Thermometer Y,

#T = "-40 ° + 64 ° = 24 °"#

Hence, #"100 °X = 24 °Y"#