The** ideal gas model** is used to predict the behavior of gases and is one of the most useful and commonly used substance models ever developed. I was found, that if we confine **1 mol samples** of **various gases** in **identical volume** and hold the gases at the **same temperature**, then their measured **pressures are almost the same**. Moreover when we confine gases at lower densities the differences tend to disappear.

Any equation that relates the pressure, temperature, and specific volume of a substance is called an **equation of state**. The simplest and **best-known** equation of state for substances in the gas phase is the **Ideal Gas equation** of state. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle’s law, Charles’ law and Avogadro’s Law. This equation predicts the **p-v-T behavior** of a gas quite accurately for dilute or low-pressure gases. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with** temperature **and **quantity**, and inversely with **volume**.

*pV = nRT*

where:

** p** is the

**absolute pressure**of the gas

** n** is the

**amount**of substance

** T** is the

**absolute temperature**

** V **is the

**volume**

** R **is the ideal, or universal,

**gas constant**, equal to the product of the

**Boltzmann constant**and the

**Avogadro constant.**The power of the

**ideal gas law**is in its simplicity. When any two of the thermodynamic variables, p, v, and T are given, the third can easily be found.

The** ideal gas model** is based on following assumptions:

- The pressure, volume, and temperature of an ideal gas obey the
**ideal gas law**. - The
**specific internal energy**is only a function of the temperature:*u = u(T)* - The molar mass of an ideal gas is identical with the molar mass of the real substance
- The
**specific heats**—and*c*_{p}— are independent of temperature which means that they are constants.*c*_{v}

From microscopic point of view it is based on these assumptions:

- The molecules of the gas are
**small, hard spheres**. - The only forces between the gas molecules are those that determine the
**point-like collisions**. - All collisions are
**elastic**and all motion is**frictionless**. - The average distance between molecules is much larger than the size of the molecules.
- The molecules are moving in random directions.
- There are no other attractive or repulsive force between these molecules.

## Gas Laws

In general, the **gas laws** are** first equations of state**, that correlate densities of gases and liquids to temperatures and pressures. The** gas laws** were completely developed at the end of the 18th century. These laws or statements **preceded**the **ideal gas law**, since individually these laws are considered as special cases of the ideal gas equation, with one or more of the variables held constant. Since they have been almost completely replaced by the ideal gas equation, it is not usual for students to learn these laws in detail. The **ideal gas equation** was first stated by Émile Clapeyron in 1834 as a combination of these laws: