Charles’s Law
Ck12 Science
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Printed: August 18, 2016
AUTHOR
Ck12 Science
www.ck12.org
C HAPTER
Chapter 1. Charles’s Law
1
Charles’s Law
• State Charles’ Law.
• Use this law to perform calculations involving volume-temperature relationships.
How do you bake bread?
Everybody enjoys the smell and taste of freshly-baked bread. It is light and fluffy as a result of the action of yeast
on sugar. The yeast converts the sugar to carbon dioxide, which at high temperatures causes the dough to expand.
The end-result is an enjoyable treat, especially when covered with melted butter.
Charles’s Law
French physicist Jacques Charles (1746-1823) studied the effect of temperature on the volume of a gas at constant
pressure. Charles’s law states that the volume of a given mass of gas varies directly with the absolute temperature
of the gas when pressure is kept constant. The absolute temperature is temperature measured with the Kelvin scale.
The Kelvin scale must be used because zero on the Kelvin scale corresponds to a complete stoppage of molecular
motion.
Mathematically, the direct relationship of Charles’s law can be represented by the following equation:
V
=k
T
As with Boyle’s law, k is constant only for a given gas sample. Table 1.1 shows temperature and volume data for a
set amount of gas at a constant pressure. The third column is the constant for this particular data set and is always
equal to the volume divided by the Kelvin temperature.
1
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FIGURE 1.1
As a container of confined gas is heated,
its molecules increase in kinetic energy
and push the movable piston outward,
resulting in an increase in volume.
TABLE 1.1: Temperature-Volume Data
Temperature (K)
50
100
150
200
300
500
1000
Volume (mL)
20
40
60
80
120
200
400
V
T
=k
0.40
0.40
0.40
0.40
0.40
0.40
0.40
mL
K
When this data is graphed, the result is a straight line, indicative of a direct relationship, shown in Figure 1.2.
FIGURE 1.2
The volume of a gas increases as the
Kelvin temperature increases.
2
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Chapter 1. Charles’s Law
Step 1: List the known quantities and plan the problem.
Known
• V1 = 2.20 L
• T1 = 22◦ C = 295 K
• T2 = 71◦ C = 344 K
Unknown
• V2 =? L
Use Charles’s law to solve for the unknown volume (V2 ). The temperatures have first been converted to Kelvin.
Step 2: Solve.
First, rearrange the equation algebraically to solve for V2 .
V2 =
V1 × T2
T1
Now substitute the known quantities into the equation and solve.
V2 =
2.20 L × 344 K
= 2.57 L
295 K
Step 3: Think about your result.
The volume increases as the temperature increases. The result has three significant figures.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/185115
Summary
• Increasing the temperature of a gas at constant pressure will produce and increase in the volume.
Review
1. Explain Charles’s Law in terms of the kinetic molecular theory.
2. Why does the temperature need to be in Kelvin?
3. Does Charles’s law hold when the gas becomes a liquid?
• Charles’s law: The volume of a given mass of gas varies directly with the absolute temperature of the gas
when pressure is kept constant.
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References
1. Courtesy of Petty Officer 3rd Class Charles Oki, US Navy. http://commons.wikimedia.org/wiki/File:Navy_
baking_bread.jpg .
2. CK-12 Foundation - Christopher Auyeung. .
3. CK-12 Foundation - Wade Baxter. CK-12 Foundation .
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