Dhristi JEE 2022-24

About Perfect Gas

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,

  • P is the pressure

  • V is the volume

  • n is the amount of substance

  • R is the ideal gas constant


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

  • V ∝ 1/P


Charle’s Law

  • V ∝ T


Avagadro’s Law

  • V ∝ n


When these 3 are combined it gives:

  • V ∝ nT/P


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:

  • V = RnT/P = nRT/P


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

  • PV = nRT


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:

  • 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

FAQs on Perfect Gas

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

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?

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.

3. What do you understand about the term Ideal Gas?

Gasses are difficult to understand. They're teaming with billions upon billions of energetic gas molecules that might collide and interact. Because it's difficult to precisely characterize a real gas, the concept of an ideal gas was developed as a rough approximation that may be used to simulate and forecast the behavior of real gasses. An ideal gas is a hypothetical gas made composed of molecules that follow certain rules:

  • Gas molecules in ideal conditions are neither attracted nor repulsive to one another.

  • The molecules of an ideal gas take up no space.

4. What are the limitations of an Ideal Gas Law?

The ideal gas law makes various gas assumptions that aren't always correct. The ideal gas law, as a result, has some limits. Explanation: The ideal gas law, for example, assumes that gas particles have no volume and aren't attracted to one another. Here's why the concept of the gas law is limited.


Because the volume occupied by the gas is quite tiny at low temperature and high pressure, the ideal gas law fails because the intermolecular distance between the molecules shrinks. As a result, an enticing force might be noticed.

5.What are the assumptions for a gas to be ideal?

Four controlling assumptions must be met for a gas to be considered "ideal":

  • The gas particles have a small volume in comparison to the surrounding air.

  • All of the gas particles are of the same size and do not interact with one another through intermolecular forces (such as attraction or repulsion).

  • Newton's Laws of Motion apply to the motion of the gas particles, which means that they move randomly.

  • The collisions between the gas particles are perfectly elastic, with no energy loss.

6. Is there any issue of concern with Ideal Gas Law?

The fundamental issue with the Ideal Gas Law is that it is not always correct because no actual ideal gasses exist. The Ideal Gas Law's controlling assumptions are theoretical and ignore numerous elements of real gasses. 


The Ideal Gas Law, for example, does not account for chemical processes in the gaseous phase that could modify the system's pressure, volume, or temperature. This is a major worry since the pressure in gaseous processes can quickly rise and become a safety hazard.

7. Does Ideal gas exist in nature and is considered inaccurate?

A theoretical gas made up of numerous randomly moving and non-interacting particles is known as an ideal gas. It isn't found in nature. Real gasses, on the other hand, can behave like ideal gasses under certain situations, such as when intermolecular interactions are low.


The ideal gas law is incorrect because it provides for no or minimal molecule interaction, whereas real gasses do have molecular interaction under certain circumstances.

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