[Chemistry Class Notes] on Perfect Gas Pdf for Exam

In the entire universe, there is no such gas that possesses the properties of a perfect gas. An ideal gas law states the relationship between the pressure applied by a gas, the amount of gaseous substance, the absolute temperature of the gas, and the volume occupied by the gas. A gas that perfectly obeys the law of ideal gas is known as a perfect gas or general gas law. 

The ideal gas law, despite its limitations, is a good approximation of the behavior of many gasses in several conditions. The ideal gas law, developed by Benoit Paul Émile Clapeyron in 1834 stated that it’s a combination of the below laws:

• Empirical Charles’s law

• Boyle’s law

• Avogadro’s law

• Gay Lussac’s law

In short, the ideal gas law states that the product of one gram molecule’s pressure and volume is equal to the product of the gas’s absolute temperature and the universal gas constant.

Equation: PV=nRT

where,

Ideal Gas Equation Units

When using the gas constant R = 8.31 J/K.mol, we must enter the pressure P in pascals Pa, volume in m3, and temperature T in kelvin K.

When using the gas constant R = 0.082 L.atm/K.mol, pressure should be measured in atmospheres atm, volume measured in litres L, and temperature measured in Kelvin K.

The ideal gas law is based on Robert Boyle’s, Gay- Lussac’s, and Amedeo Avogadro’s observations. We arrive at the Ideal gas equation, which describes all of the relationships simultaneously, by combining their observations into a single formula.

The following are the three distinct expressions:

Boyle’s Law

Charle’s Law

Avagadro’s Law

When these 3 are combined it gives:

Volume is proportional to the number of moles and temperature, but inversely proportional to pressure, as shown by the equation above.

The following is a rewrite of this expression:

To get clear of the fraction, multiply both sides of the equation by P.

The ideal gas equation is depicted in the above equation.

Perfect Gas Law

The general perfect gas law is derived from the kinetic theory of gases. Its assumptions state that

• The volume of molecules is very small as compared to the volume that has been occupied by the gas

• The gas contains many molecules that move in random motion and obey Newton’s law of motion.

• Except during the elastic collision, there are no forces that act on the molecules.

No gas has only these properties. The behavior of the real gasses is closely studied by the perfect gas law at a very high temperature and low pressure when a maximum distance between the molecules and their high speeds moves ahead of this interaction. Gas will not obey the equation when the situation is such that the gas gets liquefied near its condensation point.

Types of a Perfect Gas

A perfect gas is simplified into two to more general perfect gases which are as follows:

1. Calorically Perfect Gas

Calorically perfect gas is the most restricted gas model that still gives accurate and reasonable calculations. For instance, if a compression stage of one model of the axial compressor is made having a variable, Cp and constant, Cv to compare the simplifications, then the derivation is found at a small order of magnitude. This gives a major impact on the final result Cp.

The expression of a calorically perfect gas is generalized as follows:

2. Thermally Perfect Gas

Thermally perfect gas is present in thermodynamics equilibrium. It does not react chemically. The functions of temperature are only applied in this case that are enthalpy, specific heat, and internal energy. This type of gas is generally used for modelling. For instance, if an axial compressor with limited temperature for fluctuations does not cause any significant deviations, then the heat capacity is still liable to vary only through temperature and the molecules are not allowed to disassociate.

e = e(T)h = h(T)de = CvdTdh = CpdT