# Can we compress ideal gas

### The ideal gas law

In order to be able to consider the behavior of gases, we first have to introduce the term state variable. A state variable is a variable that characterizes a substance, e.g. pressure, volume and temperature. For gases there is a simple relationship between these state variables and the amount of substance n. It reads:

This is Boyle-Mariotte's law which follows from the ideal gas law if we keep the amount of substance n and the temperature T constant.

Fig. 2978 Pressure-volume dependence of an ideal gas according to Boyle-Mariotte (SVG)

With this law, if we know the volume at a pressure, we can calculate the volume at any pressure. Let us consider a gas which has a volume of 2 L at a pressure of 200 Pa. Now we want to compress this gas to a pressure of 500 Pa and ask ourselves how big the volume will be. To do this, we are converting Boyle-Mariotte's law:

Gay-Lussac's law

In 1802 Joseph Gay-Lussac studied gases at constant pressures. He found that a 1 ° C increase in temperature caused an expansion of 1/273 the volume at 0 ° C. If we measure the temperature in Kelvin, the volume is directly proportional to the temperature.

In 1802 Joseph Gay-Lussac studied gases at constant pressures. He found that a 1 ° C increase in temperature caused an expansion of 1/273 the volume at 0 ° C. If we measure the temperature in Kelvin, the volume is directly proportional to the temperature.

Fig. 2966 T-V diagram for an ideal gas (SVG)

At constant volume, it behaves identically to pressure. A temperature increase of 1 ° C causes a pressure increase of 1/273 of the pressure that prevails at 0 ° C. These two discoveries are known as Gay-Lussac's laws. Mathematically we express them as follows:

With these laws we can calculate what its volume of gas or pressure is after we have heated or cooled it. Let us consider a gas that takes up a volume of 150 mL at 60 ° C. We want to cool this gas to a room temperature of 25 ° C while keeping the pressure constant. To determine the volume at 25 ° C, we first have to convert the temperature values into the unit Kelvin.

Then we reproduce the corresponding Gay-Lussac law around and use:

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