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)
Since I can not see the drawing it is hard to say.
To determine the number of B degrees on the B scale that correspond to 1 A° on the A scale, we need to find the temperature interval on the B scale that corresponds to the same temperature interval on the A scale.
(a) By observing the drawing, we notice that on the A scale, the temperature interval between the ice point and boiling point of water is divided into 100 equal intervals, indicated by 100 A degrees. On the B scale, the same temperature interval is divided into 180 equal intervals, indicated by 180 B degrees.
Since we want to determine the number of B degrees that correspond to 1 A°, we divide the temperature interval on the B scale (180 B degrees) by the number of temperature intervals on the A scale (100 A degrees):
180 B degrees ÷ 100 A degrees = 1.8 B degrees per A°.
Therefore, 1 A° on the A scale is equivalent to 1.8 B degrees on the B scale.
(b) If the temperature of a substance reads +40.0°A on the A scale, we can now use the ratio we found in part (a) to convert it to the B scale.
Multiply the temperature in A degrees by the conversion factor:
40.0°A × 1.8 B degrees per A° = 72.0°B.
So, a temperature of +40.0°A on the A scale would read +72.0°B on the B scale.