CHARLES’S LAW: THE VOLUME–TEMPERATURE
RELATIONSHIP; THE ABSOLUTE TEMPERATURE SCALEIn his pressure–volume studies on gases, Robert Boyle noticed that heating a sample of
gas caused some volume change, but he did not follow up on this observation. About 1800,
two French scientists—Jacques Charles (1746–1823) and Joseph Gay-Lussac (1778–
1850), pioneer balloonists at the time—began studying the expansion of gases with
increasing temperature. Their studies showed that the rate of expansion with increased
temperature was constant and was the same for all the gases they studied as long as the
pressure remained constant. The implications of their discovery were not fully recognized
until nearly a century later. Then scientists used this behavior of gases as the basis of a
new temperature scale, the absolute temperature scale.
The change of volume with temperature, at constant pressure, is illustrated in Figure
12-5. From the table of typical data in Figure 12-5b, we see that volume (V, mL) increases
as temperature (t,°C) increases, but the quantitative relationship is not yet obvious. These
data are plotted in Figure 12-5c (line A), together with similar data for the same gas sample
at different pressures (lines B and C).
Lord Kelvin, a British physicist, noticed that an extension of the different temperature–
volume lines back to zero volume (dashed line) yields a common intercept at 273.15°C
on the temperature axis. Kelvin named this temperature absolute zero.The degrees are
the same size over the entire scale, so 0°C becomes 273.15 degrees above absolute zero.
In honor of Lord Kelvin’s work, this scale is called the Kelvin temperature scale. As pointed
out in Section 1-12, the relationship between the Celsius and Kelvin temperature scales
is K°C273.15°.
If we convert temperatures (°C) to absolute temperatures (K), the green scale in Figure
12-5c, the volume–temperature relationship becomes obvious. This relationship is known
as Charles’s Law.At constant pressure, the volume occupied by a definite mass of a gas is directly
proportional to its absolute temperature.12-5
An artist’s representation of Jacques
Charles’s first ascent in a hydrogen
balloon at the Tuileries, Paris,
December 1, 1783.
Lord Kelvin (1824–1907) was born
William Thompson. At the age
of ten he was admitted to Glasgow
University. Because its new appliance
was based on Kelvin’s theories, a
refrigerator company named its
product the Kelvinator.
Recall that temperatures on the Kelvin
scale are expressed in kelvins (not
degrees Kelvin) and represented by K,
not °K.
Absolute zero may be thought of as
the limit of thermal contraction for an
ideal gas.
444 CHAPTER 12: Gases and the Kinetic–Molecular Theory
Problem-Solving Tip:Use What You Can Predict About the AnswerIn Example 12-1 the calculated volume decrease is consistent with the increase in pres-
sure. We can use this reasoning in another method for solving that problem, that is, by
setting up a “Boyle’s Law factor” to change the volume in the direction required by the
pressure change. We reason that the pressure increases from 1.2 atm to 2.4 atm, so the
volume decreasesby the factor (1.2 atm/2.4 atm). The solution then becomes_?_L12 L(Boyle’s Law factor that would decrease the volume)12 L6.0 L
Now solve Example 12-2 using a Boyle’s Law factor.1.2 atm
2.4 atm