The drawing shows two thermometers, A and B, whose
temperatures are measured in °A and °B. The ice and boiling
points of water are also indicated.
(a) Using the data in the drawing, determine the number of B
degrees on the B scale that correspond to 1 A° on the A scale.
(b) If the temperature of a substance reads +40.0°A on the A
scale, what would that temperature read on the B scale?
(Cutnell 354)

a) 1 A° corresponds to 1.22 B°

b)

Explanation:

a)

The image of the problem is missing: find it in attachment.

Here we have two temperature scales:

- In scale A, the freezing point is at , while the boiling point is at a temperature of

- In scale B, the freezing point is at , while the boiling point is at a temperature of

The freezing point and the boiling point must be at the same absolute temperature on the two scales: this means that the interval

(boiling point - freezing point)

must be the same in the two scales.

For scale A, this interval is equal to:

For scale B, this interval is equal to:

Therefore, 1 degree on the A scale corresponds to:

So, 1 A° corresponds to 1.22 B°.

b)

The temperature of the substance on the A scale is

This means that the difference of its temperature relative to the freezing point on the A scale is

In part A, we stated that 1 degree on the A scale corresponds to 1.22 degrees on the B scale, so this temperature interval on the B scale is

And therefore, the temperature of the substance on the B-scale is equal to the freezing point (on the B scale) plus this interval:

1.