12.1

Common Temperature Scales

To measure temperature we use a thermometer. Many thermometers make use of the fact that materials usually expand with increasing temperature. For example, Figure 12-1 shows the common mercury-in-glass thermometer, which consists of a mercury-filled glass bulb connected to a capillary tube. When the mercury is heated, it expands into the capillary tube, the amount of expansion being proportional to the change in temperature. The outside of the glass is marked with an appropriate scale for reading the temperature.

Figure 12-1 The Celsius and Fahrenheit temperature scales.

A number of different temperature scales have been devised, two popular choices being the Celsius (formerly, centigrade) and Fahrenheit scales. Figure 12-1 illustrates these scales. Historically,* both scales were defined by assigning two temperature points on the scale and then dividing the distance between them into a number of equally spaced intervals. One point was chosen to be the temperature at which ice melts under one atmosphere of pressure (the “ice point”), and the other was the temperature at which water boils under one atmosphere of pressure (the “steam point”). On the Celsius scale, an ice point of 0 °C (0 degrees Celsius) and a steam point of 100 °C were selected. On the Fahrenheit scale, an ice point of 32 °F (32 degrees Fahrenheit) and a steam point of 212 °F were chosen. The Celsius scale is used worldwide, while the Fahrenheit scale is used mostly in the United States, often in home medical thermometers.
There is a subtle difference in the way the temperature of an object is reported, as compared to a change in its temperature. For example, the temperature of the human body is about 37 °C, where the symbol °C stands for “degrees Celsius.” However, the change between two temperatures is specified in “Celsius degrees” (C°)—not in “degrees Celsius.” Thus, if the body temperature rises to 39 °C, the change in temperature is 2 Celsius degrees or 2 C°, not 2 °C.
As Figure 12-1 indicates, the separation between the ice and steam points on the Celsius scale is divided into 100 Celsius degrees, while on the Fahrenheit scale the separation is divided into 180 Fahrenheit degrees. Therefore, the size of the Celsius degree is larger than that of the Fahrenheit degree by a factor of , or . Examples 1 and 2 and Examples 1 and 2 illustrate how to convert between the Celsius and Fahrenheit scales using this factor.

| Example 1 | | | Converting from a Fahrenheit to a Celsius Temperature

A healthy person has an oral temperature of 98.6 °F. What would this reading be on the Celsius scale? Reasoning and Solution A temperature of 98.6 °F is 66.6 Fahrenheit degrees above the ice point of 32.0 °F. Since , the difference of 66.6 F° is equivalent to

Thus, the person’s temperature is 37.0 Celsius degrees above the ice point. Adding 37.0 Celsius degrees to the ice point of 0 °C on the Celsius scale gives a Celsius temperature of .

| Example 2 | | | Converting from a Celsius to a Fahrenheit Temperature

A time and temperature sign on a bank indicates that the outdoor temperature is −20.0 °C. Find the corresponding temperature on the Fahrenheit scale. Reasoning and Solution The temperature of −20.0 °C is 20.0 Celsius degrees below the ice point of 0 °C. This number of Celsius degrees corresponds to

The temperature, then, is 36.0 Fahrenheit degrees below the ice point. Subtracting 36.0 Fahrenheit degrees from the ice point of 32.0 °F on the Fahrenheit scale gives a Fahrenheit temperature of .

The reasoning strategy used in Examples 1 and 2 and Examples 1 and 2 for converting between the Celsius and Fahrenheit scales is summarized below.

| Reasoning Strategy

Converting Between Different Temperature Scales
1. | Determine the magnitude of the difference between the stated temperature and the ice point on the initial scale.
2. | Convert this number of degrees from one scale to the other scale by using the fact that .
3. | Add or subtract the number of degrees on the new scale to or from the ice point on the new scale.

Check Your Understanding 1

On a new temperature scale the steam point is 348 °X, and the ice point is 112 °X. What is the temperature on this scale that corresponds to 28.0 °C? (The answer is given at the end of the book.) Background: The reasoning strategy for converting between different temperature scales applies here.
For similar questions (including conceptual counterparts), consult Self-Assessment Test 12.1. This test is described at the end of Section 12.5.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.