Contents for this page | Related topics | |
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1. Influence of temperature gas on gas volume 2. The kinetic theory explains Charles' law 3. The Kelvin temperature scale 4. Additional questions |
General properties of gases Boyle's law The generalised gas law Dalton's law of partial pressures |
Data Glossary |

Learning Outcomes | ||

After studying this section, you will (a) know the relationship between the volume of an ideal gas at constant pressure and its temperature, and (b), be able to apply the Kelvin temperature scale and the concept of standard temperature and pressure (STP). |

1. Influence of temperature on gas volume

At *CONSTANT PRESSURE*, the volume of a given sample of gas decreases as the temperature decreases. The diagram shows the results of an experiment where a sample of pure hydrogen gas was kept at a pressure of 100 kPa while its volume was measured at different temperatures:

If we extend the straight line to the point where it meets the temperature axis (the mathematical term for this is *EXTRAPOLATION*), we can read the temperature at which, theoretically, the sample of gas will have zero-volume. This occurs at a temperature of -273.2 ºC.

If we had plotted the change in pressure of a sample of gas maintained at a constant volume as the temperature changed, we would have observed the same results.

*CHARLES' LAW* (known in France as Gay-Lussac's law) may be stated as:

Charles' law |
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"The volume of a given mass of a gas kept at constant pressure increases 1/273 of its volume at 0 ºC for each degree rise in temperature." |

2. The kinetic theory explains Charles' law

The kinetic theory explains why the volume of a gas increases when the temperature increases at constant pressure.

- The increased temperature results in an increase in the mean speed of the gas molecules, thus increasing the momentum of individual molecules.
- This results in a greater force exerted by the molecules on the walls of the vessel.
- In order to keep this force (and thereby the pressure) constant , the number of collisions in unit time must be reduced.
- This is achieved by increasing the path travelled by the molecules before they collide with the walls.
- This occurs when the volume occupied by the gas increases.

The kinetic theory also explains why the pressure of a gas increases when the temperature increases at constant volume.

- The increased temperature results in an increase in the mean speed of the gas molecules, thus increasing the momentum of individual molecules.
- This results in more frequent collisions with the walls of the vessel.
- Both these effects result in a greater force, and hence a greater pressure, exerted by the molecules on the walls of the vessel.

3. The Kelvin temperature scale

We can introduce a new temperature scale, by adding 273.2 to the values of the temperature on the Celsius scale. This scale is called the *KELVIN SCALE* (after its originator, Lord Kelvin), and temperatures on this scale are expressed in K.

**Example**: What is the Kelvin temperature of a sample of gas at 25.0 ºC?

Kelvin temperature = Celsius temperature + 273.2 = 25.0 + 273.2 = 295.2 K.

**Example** : What is the Kelvin temperature corresponding to -273.2 ºC?

Kelvin temperature = Celsius temperature + 273.2 = -273.2 + 273.2 = 0 K

The temperature 0 K is very significant and is known as the *ABSOLUTE ZERO*. It is the lowest temperature that can be attained.

A second point on the Kelvin scale needs to be defined. It is the *TRIPLE POINT OF WATER*, the temperature and pressure at which water, ice and water vapour are in simultaneous equilibrium with each other. This occurs at 273.15 K and a pressure of 0.6 kPa. The temperature of 273.15 K is known as the *STANDARD TEMPERATURE*.

For all practical purposes, the triple point of water can be taken as the melting point of pure ice at atmospheric pressure, the difference being 0.01 ºC.

Since the volume of a given amount of gas varies with both the pressure and the temperature, gas volumes are often converted to *STANDARD TEMPERATURE AND PRESSURE (STP)*.

*STANDARD PRESSURE* is defined as 1 atmosphere, which is 101.3 kPa, and is equal to the pressure exerted by a column of mercury 759.8 mm in height.

4. Additional questions