### Charles law graph?

### The relationship between volume and temperature (Charles’ Law)

The **law of Charles** describes the relationship between the volume and temperature of a gas. It stipulates that, at constant pressure, the volume occupied by a certain quantity of gas is directly proportional to its absolute temperature.

The French physicist Jacques Charles (1746-1823) demonstrated that there is a relationship between the volume and temperature of a gas. He has established that, at constant pressure and for a given number of moles, the volume of a gas varies according to its temperature. Thus, as the temperature of the gas increases, so will its volume. The opposite is also true: if the temperature of the gas decreases, its volume will decrease. This relationship is called Charles’s law.

In the animation below, the gas pressure and the amount of gas, represented by the black dots, remain constant. It can be seen that when the gas is heated and its temperature increases, it expands. As a result, the volume must increase so that the pressure can remain constant.

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The volume of a gas increases when its temperature in degrees Celsius increases. This variation can be explained by the kinetic theory of gases . According to this theory, an increase in temperature results in an increase in the kinetic energy of the particles. The risk of collisions is therefore more likely, which causes a pressure change. In order to keep the pressure constant, the volume must increase. However, this relation is not directly proportional since the obtained line does not go through the origin. If the line passes through the origin, this would indicate that no gas exists at a temperature of 0 ° C, which is fortunately not the case.

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The extrapolation of the line shows a volume that seems to be zero at a temperature of **-273.15** ° C. This observation is repeated regardless of the nature of the gas considered. This temperature would therefore be the absolute zero, that is, the temperature beyond which matter would no longer exist. There would then be no movement of the particles of matter and zero kinetic energy.

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Trapped by this mathematical evidence where the lowest temperature corresponds to a negative value (absence of kinetic energy ), Lord Kelvin (1824-1907) proposed a new temperature scale , that of absolute degrees. According to this new scale, the absolute zero corresponds to – 273.15 ° C. In order to transform degrees Celsius (ºC) into kelvins (K) or absolute degrees, the following mathematical relationships must be used:

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Using the Kelvin scale rather than the Celsius scale, the relationship between volume and absolute temperature becomes directly proportional since the line then goes to zero. This means that if the temperature increases, the volume increases by an equal factor and vice versa. Mathematically, we can write this relation as follows:

Since the division of the volume by the temperature is equal to one constant, two situations can be compared for the same gas, as long as the quantity of gas and the pressure do not vary. This results in the following relation:

Charles’s law is sometimes called Gay-Lussac’s law. In fact, the relationship between volume and temperature at constant pressure was discovered by Jacques Charles in 1787. However, Louis Joseph Gay-Lussac publicly stated it for the first time in 1802. However, to avoid any confusion We will reserve the name of Charles’ law for the relation between volume and temperature, and Gay-Lussac’s law for the relation between pressure and temperature.

The law of Charles allows to understand the operation of a balloon. In order to make it fly, we heat the air contained in the envelope of the balloon. The volume of heated air increases because the space between the gas particles increases by increasing their kinetic energy. The hot air bubble allows the balloon to rise because its density is lower.

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