Physics

Problem

A linear thermometer X is designed such that it reads

20^{\circ}\!\text{X}

at the melting point of ice and

120^{\circ}\!\text{X}

at the boiling point of water, both at standard atmospheric pressure. a. (i) Derive an expression that relates a temperature

\theta^{\circ}\!\text{X}

on this thermometer to the corresponding temperature

t^{\circ}\!\text{C}

on the Celsius scale. b. (ii) Using the result of part (i), find the reading on thermometer X when the temperature is

350\,\text{K}

. c. (iii) When thermometer X reads

68^{\circ}\!\text{X}

, determine the corresponding temperature on the Fahrenheit scale.