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it has a direct relationship with a third scale to be described
shortly, the Kelvin scale. Both scales have arbitrarily assigned EXAMPLE 4.2
reference points and an arbitrary number line that indicates A bank temperature display indicates 20°C (room temperature). What
relative temperature changes. Zero is simply one of the points is the equivalent temperature on the Fahrenheit scale? (Answer: 68°F)
on each number line and does not mean that there is no tem-
perature. Likewise, since the numbers are relative measures
of temperature change, 2° is not twice as hot as a temperature
of 1° and 10° is not twice as hot as a temperature of 5°. Th e There is a temperature scale that does not have arbitrarily

numbers simply mean some measure of temperature rela- assigned reference points, and zero does mean nothing. Th is is
tive to the freezing and boiling points of water under normal not a relative scale but an absolute temperature scale called the
conditions. Kelvin scale. The Kelvin scale was proposed in 1848 by William

You can convert from one temperature to the other by Thompson (1824–1907), who became Lord Kelvin in 1892. Th e

considering two differences in the scales: (1) the diff erence zero point on the Kelvin scale is thought to be the lowest limit

in the degree size between the freezing and boiling points on of temperature. Absolute zero is the lowest temperature possible,
the two scales and (2) the difference in the values of the lower occurring when all random motion of molecules was histori-

reference points. cally projected to cease. Absolute zero is written as 0 K. A degree

The Fahrenheit scale has 180° between the boiling and symbol is not used, and the K stands for the SI standard scale
freezing points (212°F – 32°F), and the Celsius scale has 100° unit, Kelvin. The Kelvin scale uses the same degree size as the

between the same two points. Therefore, each Celsius degree Celsius scale, and –273°C = 0 K. Note in Figure 4.7 that 273 K

is 180/100, or 9/5, as large as a Fahrenheit degree. Each Fahr- is the freezing point of water, and 373 K is the boiling point. You
enheit degree is 100/180, or 5/9, of a Celsius degree. You know could think of the Kelvin scale as a Celsius scale with the zero
that this is correct because there are more Fahrenheit degrees point shifted by 273°. Thus, the relationship between the Kelvin

than Celsius degrees between freezing and boiling. Th e rela- and Celsius scales is
tionship between the degree sizes is 1°C = 9/5°F and 1°F =
5/9°C. In addition, considering the difference in the values of T K = T C + 273

the lower reference points (0°C and 32°F) gives the equations equation 4.3
for temperature conversion. (For a review of the sequence
of mathematical operations used with equations, refer to the A temperature of absolute zero has never been reached, but
“Working with Equations” section in the Mathematical Review scientists have cooled a sample of sodium to 700 nanokelvins,
of appendix A.) or 700 billionths of a kelvin above absolute zero.
9 _
T F = T C + 32°

5
EXAMPLE 4.3
equation 4.1
A science article refers to a temperature of 300.0 K. (a) What is
5 _ the equivalent Celsius temperature? (b) Th e equivalent Fahrenheit

C 9
T = ( T F – 32°) temperature?
equation 4.2
SOLUTION
(a) The relationship between the Kelvin scale and Celsius scale is
EXAMPLE 4.1 found in equation 4.3, T K = T C + 273. Solving this equation for

The average human body temperature is 98.6°F. What is the equivalent Celsius yields T C = T K – 273.
temperature on the Celsius scale?
T C = T K – 273
= 300.0 – 273
SOLUTION = 27°C
9 _
5 _ T F = T + 32°

T = ( T F – 32°) (b) 5 C
C
9
5 _ 9 _

= (98.6° – 32°) = 27.0° + 32°
9 5
243°
_
5 _ = + 32°

= (66.6°)

9 5
333°
_ = 48.6° + 32°
=
9 = 81°F
= 37°C
4-7 CHAPTER 4 Heat and Temperature 91