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**The Ideal Gas **

In the foregoing discussions we have pointed out that a thermodynamic system typically encloses a fluid (pure gas, liquid or solid or a mixture) within its boundary. The simplest of the intensive variables that can be used to define its state are temperature, pressure and molar volume (or density), and composition (in case of mixtures). Let us consider for example a pure gas in a vessel. As mentioned above, by phase rule the system has two degrees of freedom. It is an experimentally observed phenomenon that in an equilibrium state the intensive variables such as pressure, temperature and volume obey a definitive inter-relationship, which in its simplest form is expressed mathematically by the Boyle’s and Charles’s laws. These laws are compositely expressed in the form of the following equation that is said to represent a behaviour termed as Ideal Gas Law:

PV = RT

Where, P = system pressure (say, Pa = N/m^{2}), T = system temperature (in 0K), V = gas molar volume (mol/m^{3}) and, R = universal gas constant (= 8.314 J / mol^{0} K ). The above relation is said to represent an equation of state, and may alternately be written as:

PV^{t} = nRT ..(1.13)

Where, V^{t }= total system volume; n = total moles of gas in the system. Units of typical thermodynamic variables and that of the gas constant .

The equations (1.10) and (1.11) are also termed Equations of State (EOS) as they relate the variables that represent the thermodynamic state of a system in the simplest possible manner. It is obvious that the EOS indicates that if one fixes temperature and pressure the molar volume is automatically fixed as well, i.e., the latter is not an independent property in such a case. The ideal gas law is a limiting law in the sense that it is valid primarily for gaseous systems at low pressure, strictly speaking at pressure far below the atmospheric. However, for practical purposes it is observed to remain valid at atmospheric pressures as well. As we shall see later, the ideal gas law serves as a very useful approximation as well as a datum for estimation of both the volumetric as well as all other real fluid thermodynamic properties of practical interest.

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