CHARLES’ LAW

12.5. CHARLES’ LAW

If a given quantity of gas is heated at constant pressure in a container that has a movable wall, such as a piston (Fig. 12-4), the volume of the gas will increase. If a given quantity of gas is heated in a container that has a fixed volume (Fig. 12-5), its pressure will increase. Conversely, cooling a gas at constant pressure causes

a decrease in its volume, while cooling it at constant volume causes a decrease in its pressure.

Constant-volume bomb

Constant pressure of the atmosphere

Fig. 12-4. Piston Fig. 12-5. Bomb J. A. C. Charles (1746–1823) observed, and J. L. Gay-Lussac (1778–1850) confirmed, that when a given

C for every degree Celsius that it is cooled. Conversely, when the sample of gas is heated at constant pressure, it expands by 1 273 times its volume at 0 ◦

sample of gas is cooled at constant pressure, it shrinks by 1 273 times its volume at 0 ◦

C for every degree Celsius that it is heated. The changes in volume with temperature of two different-sized samples of a gas are shown in Fig. 12-6. The chemical identity of the gas has no influence on the volume changes as long as the gas does not liquefy in the range of temperatures studied. It is seen in Fig. 12-6 that for each sample, the volume of the C for every degree Celsius that it is heated. The changes in volume with temperature of two different-sized samples of a gas are shown in Fig. 12-6. The chemical identity of the gas has no influence on the volume changes as long as the gas does not liquefy in the range of temperatures studied. It is seen in Fig. 12-6 that for each sample, the volume of the

T (K) Fig. 12-6. Two samples of gas

gas changes linearly with temperature. A straight line can be drawn through all the points. If it were assumed that the gas does not liquefy at very low temperatures, each sample would have zero volume at −273 ◦

C. Of course, any real gas could never have zero volume. (Gases liquefy before this very cold temperature is reached.) Nevertheless, −273 ◦

C is the temperature at which a sample of gas would theoretically have zero volume. This type of graph can be plotted for any sample of any gas, and in every case the observed volume will change with temperature at such a rate that at −273 ◦

C the volume would be zero. Therefore, the temperature −273 ◦

C can

be regarded as the absolute zero of temperature. Since there cannot be less than zero volume, there can be no colder temperature than −273 ◦

C. The temperature scale that has been devised using this fact is called the Kelvin, or absolute, temperature scale (Sec. 2.7). A comparison of the Kelvin scale and the Celsius scale is shown in Fig. 12-7. It is seen that any temperature in degrees Celsius (t, ◦

C) may be converted to kelvins (T , K) by adding 273 ◦ . It is customary to use capital T to represent Kelvin temperatures and small t to represent Celsius temperatures. No degree sign ( ◦ ) is used with Kelvin temperatures, and the units are called kelvins.

T=t+ 273 ◦

In Fig. 12-6, the volume can be seen to be directly proportional to the Kelvin temperature, since the lines go through the zero-volume point at 0 K.

Normal boiling point of water

Freezing point of water

°C

Fig. 12-7. Comparison of Kelvin and Celsius temperature scales

EXAMPLE 12.6. What are the freezing point of water and the normal boiling point of water on the Kelvin scale? Ans.

Freezing point of water = 0 ◦

C + 273 ◦ = 273 K

Normal boiling point of water = 100 ◦

C + 273 ◦ = 373 K

The fact that the volume of a gas varies linearly with temperature is combined with the concept of absolute temperature to give a statement of Charles’ law:

At constant pressure, the volume of a given sample of gas is directly proportional to its absolute temperature .

Expressed mathematically,

V = kT

( at constant pressure)

This equation can be rearranged to give

Since V/T is a constant, this ratio for a given sample of gas at one volume and temperature is equal to the same ratio at any other volumes and temperatures. See Table 12-3. That is, for a given sample at constant pressure,

( at constant pressure)

One can see from the data of Table 12-3 that absolute temperatures must be used.

Table 12-3 Volumes and Temperatures of a Given Sample of Gas Volume V

V /t (L)

Temperature T