# Perfect Gas

## Perfect Gas Definition

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.

As the perfect gas obeys the ideal gas law, so it will also obey Avogadro's law, Charlie's law, and Boyle's law. Avogadro’s law provides a relationship between the amount of gaseous substance and the volume that has been occupied by the gas.

### Perfect Gas Equation

The perfect gas equation states that for a given quantity of gas, the pressure (p) and volume (v) of the gas is directly proportional to its absolute temperature (t).

pv = kt

Here, k = perfect gas constant

P denotes pressure in N/m2

v is the molar volume in M3/mole

R = 8314 joule/ mole K

Or,

8314kJ/mole K

T denotes absolute temperature K

This relation is also known as the equation that is sufficient to show the behaviour of a perfect gas.

pv = RT

If both the sides are divided by M that is the molar mass of a given gas then the equation will be

pv = RT

From the perfect gas equation and the equation of thermodynamics differentials

(du/dv)t = -p + T(dp/dt)v

If du/dv = zero, that is the internal energy does not depend on the volume of the perfect gas, then this will become an independent property of a perfect gas.

So, for real gas if p = 0

$(\frac{dh}{dp})t=B-T(\frac{dB}{dT})$

Which is non zero and therefore,

For a real gas, the functions are equal to the perfect gas where p → zero

According to Avogadro's law, the universal gas constant specifies the quantity of gas that is expressed in terms of the total number of molecules of gas. This is possible by using the mass unit that is the molecular weight expressed in grams. The equation of the state of a perfect gas can be written as

Pv/t = nR

Where R is known as the universal gas constant, which is equal to 8.314 472 joules per mole Kelvin.

### 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 contained 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 behaviour of the real gases 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

e = CvTh = CpT

### 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

1. What is the Difference Between Perfect Gas and Ideal Gas?

Ans: Perfect gas is the one where the intermolecular forces are not considered. Most of the gases present in the universe behave as perfect gases at a very high temperature and low pressures. A perfect gas obeys the ideal gas law and its heat constants.

Here, CP and CV are constant values.

For example if a perfect gas has Cp is equal to 1.005kJ/kg.K and Cv = 0.718kJ/kg.K

Then the internal energy present in the perfect gas can be calculated from

du = Cv.dT

And , dh= Cp.dT

2. What are Boyle’s Law and Charles's Law?

Ans: A gas that follows Boyle’s law and Charle’s law in all the given temperatures is called a perfect gas. Boyle’s law states that for a given gas, the pressure of the gas is inversely proportional to its volume at a constant temperature. Whereas, for a given gas, when the volume of the gas is directly proportional to the absolute temperature at a constant pressure it is called Charle’s law.