# The ideal gas laws contradict each other

## Gas laws in science - general gas equation

The gas laws are interdisciplinary in chemistry and physics and serve to describe the behavior of gases in the event of pressure or temperature changes. The gas laws describe the state of the (ideal) gas in terms of the state variables pressure p, volume V, temperature T and amount of substance and thus establish a relationship between these variables.

The gas laws (e.g. Boyle-Mariotte's gas law) derive the ideal gas law or the real gas law, with the help of which all essential properties of a gas can be determined in physics and chemistry. The ideal gas equation (for ideal gases) and the gas equation for real gases are always used when the pressure, temperature or amount of substance of a gas is to be determined.

### The gas laws

The gas laws (Gay-Lussac gas law, Boyle-Mariotte gas law and Amontons gas law) essentially serve to derive the ideal gas equation. Each of the scientists mentioned has investigated the dependency of a gas in relation to two state variables (e.g. temperature and volume) and the ideal gas law can be derived from the laws derived from these.

Gay-Lussac Gas Act

Gay-Lussac was one of the scientists who studied the temperature-volume behavior of gases. Gay-Lussic investigated the change in volume of a gas when a gas was heated or cooled (the pressure of the gas was always constant). In this way he recognized the relationship between the volume of a gas at different temperatures.

During the experiments, Gay-Lussac observed that volume is proportional to temperature and vice versa. For example, if the temperature of the gas is doubled, the volume of the gas also doubles.

The Gay-Lussac gas law is derived from this:

Gay-Lussac's gas law states that the quotient of volume and temperature of a certain amount of a gas (at constant pressure) is constant. This is why this law is also known as the volume-temperature law.

More on the Gay-Lussac gas law

Boyle-Mariotte gas law

Other scientists who had studied the behavior of gases were Boyle and Mariotte. They investigated the change in pressure of a gas when the volume in which the gas is located (e.g. in a flask) is changed. For example, they investigated the change in pressure when the gas in a filled cylinder is compressed by a piston.

As expected, Boyle and Mariotte observed that the volume of gas in the cylinder decreased (as soon as they pushed the piston into the gas-filled cylinder) while the pressure of the gas increased (indirectly) proportionally.

The Boyle-Mariotte gas law is derived from this:

Gay-Lussac's gas law states that the quotient of volume and temperature of a certain amount of a gas (at constant pressure) is constant. Therefore this law is also called the pressure-volume law.

Law of Amontons

With the help of the gas laws of Gay-Lussac and Boyle-Mariotte we have a connection between temperature and volume or pressure and volume. If one now had a relationship between temperature and pressure, one could connect all three parameters of a gas.

This is exactly what the scientist Amontons, who examined the temperature and pressure behavior of a gas, was concerned with. Amontons found out that (with a constant volume of a gas) temperature and pressure are proportional to each other.

p1: T1 = p2: T2

The Amontons gas law is derived from this:

The gas law of Amontons states that the quotient of pressure and temperature of a certain amount of a gas (at constant volume) is constant. This is why this law is also known as the pressure-temperature law - the ideal gas law

The ideal gas law can be derived from these three gas laws. If you put these three gas laws in relation, then the following applies for a gas (with a certain quantity) in a closed system:

If you change a state variable pressure or volume in a closed system, the other state variables also change, which can then be calculated using the above-mentioned relationship, which means that the product of pressure and volume divided by temperature is constant (i.e. always the same value Has)

The general or ideal gas equation is derived from this physical relationship

### General gas equation

With

• p = pressure of the gas
• V = volume of the gas
• n = amount of substance of the gas
• R = 8.31448 J · K-1 · Mol-1
• T = absolute temperature in Kelvin