## Ideal Gas Model

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. It was found, such gases tend to obey the following relation, which is known as the **ideal gas law**:

*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.

## Validity of Ideal Gas Law

Since **ideal gas** is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces, there is no such thing in nature as a truly ideal gas. On the other hand, all real gases approach the ideal state **at low pressures (densities)**. At low pressures molecules are far enough apart that they do not interact with one another.

In other words, the **Ideal Gas Law** is accurate only **at relatively low pressures** (relative to the critical pressure p_{cr}) and **high temperatures** (relative to the critical temperature T_{cr}). At these parameters, the **compressibility factor, Z = pv / RT**, is

**approximately 1**. The compressibility factor is used to account for deviation from the ideal situation. This correction factor is dependent on pressure and temperature for each gas considered.

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