Why are gases important?

The gaseous state of matter behaves differently from solids and liquids. It is neither limited in volume nor in compressibility. A gas fills entire volume of the container it is kept in, and distributes itself uniformly. This property makes them very useful and interesting because we can change its physical properties (volume, temperature, pressure etc.) to a large extent. These properties are not independent of each other and any of them can be manipulated by changing other variables. We can derive “work” from gases and thus gases were studied extensively in the early days of thermodynamics(e.g. for designing steam engines). On the other hand, physical states of solids and liquids don’t change that much and there is little to be studied unless you transform them into another state (e.g. melting a solid or freezing a liquid).

The Ideal Gas

Traditionally, the study of Thermodynamics begins with the properties of an Ideal gas. By ideal, we mean that the gas molecules behave totally independently of each other and are point particles. The behaviour overall is governed by simple laws and is easy to understand. Under certain conditions, Real gases behave very much like an ideal gas. We will discuss what these conditions are below.

The main properties of an ideal gas are twofold:

  1. Each molecule behaves like a point particle and has no volume of its own.
  2. There are no intermolecular interactions except collisions among themselves or with the walls of the container.

At high temperature, real gas molecules have enough kinetic energy to “jiggle around” with high speeds. Under low pressure, the gas is diluted enough so that no two molecules get very close to each other(thus avoiding attractive intermolecular forces). With the two conditions combined, the molecules are all running around with high speeds, interacting only through collisions. Hence, we can see that:

At high temperatures and low pressures, behaviour of real gases can be approximated to the ideal gas behaviour.

Properties of an Ideal Gas

The most important properties of an ideal gas are its Pressure(P), Volume(V), Temperature(T) and number of molecules(or moles, n). These are not independent, however. The relationships between these properties were first discovered empirically by various scientists and later shown to be derivable from Newton’s laws of Motion (studied in the domain of Kinetic Theory of Gases).

These laws are as follows:

Boyle’s Law  

    \[P \propto\frac{1}{V}\]

Charles’ Law

    \[V \propto T\]

Gay-Lussac’s Law  

    \[P \propto T\]

The above relations can be combined in a single equation, known as the ideal gas law:

    \[PV \propto T\]

or, 

    \[PV = nRT\]

where R = gas constant = 8.31441 J K-1 mol-1

    \[n = \frac{N}{N_{A}}\]

where n = No. of moles, N = No. of molecules and NA = Avogadro’s number = 6.022 x 1023 

The ideal gas law can also be expressed as

    \[PV = Nk_{B}T\]

where kB = Boltzmann constant = 1.38064852 × 10-23 mkg s-2 K-1

 

Thermodynamics: Ideal Gas
Tagged on:             

Leave a Reply

Your email address will not be published. Required fields are marked *