# Boyle’s law, Charles’s law, Gay-Lussac’s law

**Boyle’s law**

Robert Boyle (1627-1691) conducted experiments to investigate the quantitative relationship between gas pressure and volume. This experiment is carried out by inserting a certain amount of gas into a closed container. Until a pretty good approach, he found that if the gas temperature was kept constant, then when the gas pressure increased, the gas volume was reduced. Likewise, when the gas pressure decreases, the gas volume increases. Gas pressure is inversely proportional to gas volume. This relationship is known as Boyle’s Law. Mathematically:

Boyle’s law can also be written:

P V = constant → equation 1

P_{1 }V_{1} = P_{2 }V_{2} → equation 2

The meaning of equation 1 is at a constant temperature (T) if the pressure (P) of the gas changes then the volume (V) of the gas also changes so that the results of the multiplication between pressure and volume are always constant. If the gas pressure increases, the gas volume decreases or vice versa if the gas pressure decreases, the gas volume increases, so the multiplication between pressure and volume is always constant.

The graph that states the relationship between volume and pressure looks like in the picture below. Based on the results of the experiment, Robert Boyle found that the volume of gas changes irregularly so that the lines in the graph appear curved. The pressure depicted on the graph is absolute pressure.

**Charles’s law**

One hundred years after Robert Boyle discovered the relationship between volume and pressure, a French scientist named Jacques Charles (1746-1823) investigated the relationship between temperature and gas volume. Based on the results of the experiment, he found that when the gas pressure is always constant, then when the gas temperature increases, the gas volume also increases. Conversely, when the gas temperature decreases, the gas volume also decreases.

Changes in gas volume due to changes in temperature occur regularly so that the lines on this graph appear straight. If the lines on the graph are depicted until the temperature is lower, then the line will cut the axis around -273 ^{o}C.

Based on many experiments that have been conducted, it was found that although the magnitude of the change in volume of each gas varies, when the lines on the V-T chart are drawn to a lower temperature, the line always cuts the axis around -273 ^{o}C. We can say that if the gas is cooled to -273 ^{o}C then the volume of gas = 0. If the gas is cooled again until the temperature is below -273 ^{o}C then the gas volume will be negative, something that is impossible.

So -273 ^{o}C is the lowest temperature that can be achieved. Because the line intersects the axis around -273 ^{o}C according to the agreement, it is determined that the lowest temperature that can be achieved is -273.15 ^{o}C. -273.15 ^{o}C is called the absolute zero temperature and is used as an absolute scale reference, aka the Kelvin scale. Kelvin is the name of Lord Kelvin (1824-1907), British physicist. On this scale, the temperature is expressed in Kelvin (K), not the Kelvin (^{o}K) degree. The distance between degrees is the same as in the centigrade scale. 0 K = -273.15 ^{o}C and 273.15 K = 0 ^{o}C.

The temperature in the Celsius scale can be converted to a Kelvin scale by adding 273.15, the temperature on the Kelvin scale can be converted to a Celsius scale by reducing 273.15. Mathematically:

T (K) = T (^{o}C) + 273.15

T (^{o}C) = T (K) – 273.15

T = Temperature

K = Kelvin

C = Celsius

If the temperature is expressed on a Kelvin scale, the chart above will look like the picture below.

Based on this graph it can be concluded that at a fixed pressure, the volume of gas is always directly proportional to the absolute temperature of the gas. If the absolute temperature of the gas increases, the gas volume also increases, on the contrary, if the absolute temperature of the gas decreases, the gas volume also decreases. This relationship is known as Charles’s law. Mathematically :

Volume α Temperature → Constant pressure

V α T → P constant

The meaning of equation 1 is at constant pressure (P) if the absolute temperature (T) changes then the volume (V) of the gas also turns so that the ratio between absolute temperature and volume is always constant. If the absolute temperature of the gas increases, the volume of gas also increases or vice versa if the absolute temperature of the gas decreases, the volume of the gas also decreases, so the ratio between temperature and volume is always constant. The absolute temperature of the gas is the temperature of the gas which is stated on the Kelvin scale. If the temperature is still in the Celsius scale, then change it first to the Kelvin scale.

**Gay-Lussac’s law**

Joseph Gay-Lussac (1778-1850) experimented and found that if the gas volume is set constant, when gas pressure increases, the absolute temperature of the gas increases. Likewise, when the gas pressure decreases, the absolute temperature of the gas decreases. At constant volume, the gas pressure is directly proportional to the absolute temperature of the gas. This relationship is called Gay-Lussac Law. Mathematically:

Pressure α Temperature → Constant volume

P α T → V is constant

The meaning of equation 1 is that at constant volume (V) if the pressure (P) of the gas changes, the absolute temperature (T) of the gas also changes so that the ratio between the pressure and absolute temperature is constant. In other words, if the gas pressure increases, the absolute temperature of the gas also increases or vice versa if the gas pressure decreases, the absolute temperature of the gas also decreases, so that the ratio between pressure and temperature is always constant.

The absolute temperature of the gas is the temperature of the gas which is stated on the Kelvin scale. If the temperature is still in the Celsius scale, then change it first to the Kelvin scale.

Please note that Boyle’s law, Charles’s law, and Gay-Lussac’s law provide accurate results when the pressure and density of the gas are not too significant. Also, the three laws also apply only to the gas whose temperature is not near the boiling point.

Based on this fact, it can be concluded that Boyle’s law, Charles’s law, and Gay-Lussac’s law cannot be applied to all gas conditions. Because it cannot refer to all real gas conditions, we need the Ideal Gas concept. This ideal gas does not exist in everyday life. The ideal gas is just an ideal model, similar to the ideal rigid and fluid concept. So we assume the three gas laws above apply in all ideal gas conditions.

In solving gas law problems, the temperature must be stated on a Kelvin scale. If the gas pressure is still in the form of measuring pressure, change it first to absolute pressure. Absolute pressure = atmospheric pressure + measuring pressure