Question

Suppose you have designed a new thermometer called the x thermometer. on the x scale the boiling point of water is 129 ∘x and the freezing point of water is 12 ∘x. part a at what temperature are the readings on the fahrenheit and x thermometers the same? express your answer using two significant figures.

Answer 1

For any temperature scale the ratio of difference of temperature will be same

so we can write

$\frac{T^ox - 12^ox}{129^ox - 12^ox} = \frac{T^of - 32^of}{212^of - 32^of}$

now given that in both scales the temperature must be same

$\frac{T^ox - 12^ox}{117^ox} = \frac{T^of - 32^of}{180^of}$

$T - 12 = 0.65 (T - 32)$

$0.35T = -8.8$

$T = -25.14 ^ox$

so at above temperature both scales will have same temperature