# How can Avogadros Law be applied

## General gas equation (thermal equation of state of ideal gases)

The **thermal equation of state of ideal gases**, often simplified and trivial as **general gas equation** describes the relationship between the thermal state variables of an ideal gas.

It combines the individual experimental results and the gas laws derived from them to form a general equation of state.

Many researchers and scientists have dealt with gases and their behavior and provided partial results for the general gas equation that we use. All parts of the works brought together are combined in the formula

Boyle-Mariotte's Law

The **Boyle-Mariotte's Law** (also Boyle-Mariotte's Law, Boyle-Mariotte's Law or Boyle's Law) states

that the **Pressure of ideal gases** at **constant temperature** (isothermal change of state) and **constant amount of substance****inversely proportional to the volume** is.

Or to put it more simply:

**If the pressure on gas is increased, the volume is reduced by the increased pressure. If you reduce the pressure, it expands**.

This law was discovered independently by two physicists, the Irishman **Robert Boyle **(1662) and the **French Edme Mariotte **(1676).

For *T* = constant and *n* = constant applies:

### Gay-Lussac's law

The **Gay-Lussac's law ** (also 1st Law of Gay-Lussac, Gay-Lussac's Law, Charles's Law or Charles's Law) states,

that this **Volume of ideal gases** at **constant pressure** (isobaric change of state) and** constant amount of substance****directly proportional to temperature** is.

Or to put it more simply:

**A gas expands when it is heated and contracts when it is cooled.**

This connection was made in 1787 by **Jacques Charles **and 1802 by **Joseph Louis Gay-Lussac **recognized.

For *p* = const and *n* = const applies:

The actual law of Gay-Lussac (the above is just the part that is mostly referred to as the *Charles' law* but is:

Here is *T*_{0} the temperature at the zero point of the Celsius scale, i.e. 273.15 K or 0 ° C. Against it is *T* the temperature you are looking for. Is analog *V.* the volume at *T*, *V.*_{0} the volume at *T*_{0} and *γ*_{0} the volume expansion coefficient at *T*_{0}, where for ideal gases in general *γ* = 1/*T* applies.

From this equation one can also conclude that there must be an absolute temperature zero, since the equation for this predicts a volume of zero and the volume cannot become negative. Their empirical basis is therefore also the basis for the absolute Kelvin temperature scale, since the temperature zero point could be determined by extrapolation.

Law of Amontons

The **Law of Amontons**, (also the 2nd law of Gay-Lussac) states,

that the **Pressure of ideal gases** at **constant volume** (isochoric change of state) and **constant amount of substance **is directly proportional to temperature.

Or again simply said:

**When the gas is heated, the pressure increases and when the gas cools, it decreases.**

This connection was made by **Guillaume Amontons** discovered.

For *V.* = const and *n* = const applies:

Analogous to the *Gay-Lussac's law* also applies here:

Law of Uniformity

The law of homogeneity says

the existence **ideal gas** through and through **homogeneous,** that is, uniform, is that it is so everywhere **same density** Has.

If in a large container with a homogeneous substance, for example with a gas, a partial amount in one place *V.*_{1} is included, it contains the same amount of substance as a subset with the same volume *V.*_{1} elsewhere. If you divide the total amount of substance into two equal volumes, they contain the same amount of substance, namely half of the original. It follows:

The **volume** is at **constant pressure** and **constant temperature****proportional to the amount of substance**.

For *T* = const and *p* = const applies:

These laws apply to all homogeneous substances as long as temperature and pressure remain unchanged, and also to ideal gases.

Law of Avogadro

The law of Avogadro says

that two **equally large gas volumes**that under **same pressure** stand and the **same temperature** to have, **also the same number of particles** lock in.

This is true even if the volumes contain different gases.

It goes without saying that it also applies in the event that the composition is the same in the two volumes; therefore the relationship follows from Avogadro's law *V.* ~ *n* For *T* = const and *p* = const. In addition, it also means that a gas also has a certain number of particles in a certain volume, which is independent of the type of substance. However, there are certain exceptions, for example if there are fewer or too many particles in a gas packet.

The law of Avogadro was passed in 1811 **Amedeo Avogadro** discovered.

It can also be formulated like this:

The molar volume is identical for all ideal gases at a certain temperature and pressure.

Measurements have shown that one mole of an ideal gas at 0 ° C = 273.15 K and 1013.25 hPa pressure takes up a volume of around 22.4 dm³.

A major consequence of this law is: **The gas constant is identical for all ideal gases**.

The thermal equation of state

The equation describes the state of the ideal gas in terms of the state variables pressure *p*, Volume *V.*, Temperature *T* and amount of substance *n* or number of particles *N* or mass *m*. It can be represented in different forms that are equivalent to one another, whereby all these forms describe the state of the system under consideration in the same way and clearly.

Your first formulation comes from **Émile Clapeyron **in 1834.

Extensive forms:

Intense forms:

The individual symbols stand for the following quantities:

*k*_{B.}- Boltzmann constant*m*- Dimensions*M.*- Molar mass*N*- number of particles*n*- Amount of substance*p*- Print*R.*- universal or molar gas constant_{m}*R.*- individual or special gas constant_{s}*ρ*- density*T*- absolute temperature*v*- molar volume_{m}*v*- specific volume*V.*- Volume

The equation represents the limiting case of all thermal equations of state for vanishing density that means for vanishing pressure at a sufficiently high temperature. In this case, the intrinsic volume of the gas molecules and the cohesion - the attractive force between the molecules - can be neglected. The equation is a good approximation for many gases such as air that is not saturated with water vapor, even under normal conditions.

Expanded in 1873 **Johannes Diderik van der Waals** the gas law for the Van der Waals equation, which takes into account the intrinsic volume of the gas particles and the attraction between them in contrast to the general gas equation and can therefore also be used as an approximation for clearly real gases. Another approximate solution for real gases is the series expansion of the virial equations, whereby the general gas equation is identical to a break in the series expansion after the first term.

In general, the general gas equation is suitable as an approximate solution for weakly real gases with low intermolecular interactions, low pressures and high temperatures (large molar volumes). In particular, ideal gases here have no Joule-Thomson effect.

### Special cases

There are various special cases of the general gas law that establish a relationship between two quantities while all other quantities are kept constant.

These relationships between the state variables of a gas are explained and not only empirically derived through its particle character, i.e. through the kinetic gas theory.

*The smallest movement is important for all of nature!*

Blaise Pascal

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