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Last updated date: 15th Sep 2023

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The chapter kinetic theory of gases starts with the basic revision of all the concepts we studied in our lower grades to build the connection between the advanced parts of the kinetic theory of gases. In the kinetic theory of gases we have discussed the molecular nature of matter, behaviour of gases, kinetic theory of an ideal gas, law of equipartition of energy, specific heat capacity, mean free path etc.

The chapter Kinetic theory of gases deals with macroscopic to microscopic properties of gas which includes quantities like temperature, pressure,speed and kinetic energy.

Moving further we got introduced to a few more important concepts like the law of equipartition of energy,degrees of freedom and Maxwell’s distribution of molecular speeds.

Now, let us move on to the important concepts and formulae related to NEET and NEET mains exams along with a few solved examples.

Behaviour of Gas Molecules

Ideal Gas Equation

Kinetic Theory of an Ideal Gas

Kinetic Interpretation of temperature

Degree of Freedom

Law of Equipartition of Energy

Calculate the rms speed of nitrogen at STP(pressure =1atm and temperature = $0^{\circ}$ C. The density of nitrogen in these conditions is 1.25kg/m3.

Sol:

Given,

At STP the pressure is $1 \times 10^{5}$ N/m2

hence the rms speed is $v_{rms} = 1.73\sqrt{\dfrac{p}{⍴} }$

where p is the pressure of gas and ⍴ is the density

So $v_{rms}$ = $1.73\sqrt{\dfrac{10^{5}}{1.25}}}$ = 490m/s

Key point: Here only the formula of $v_{rms}$ should be remembered by the student.

Calculate the number of molecules in each cubic metre of a gas at 1atm and $27^{\circ}$ C.

Sol:

From the ideal gas equation PV=nRT

Where P is the pressure of gas

R= gas constant

V = volume of gas

T= temperature of gas and n = no. of molecules

Hence n = $\dfrac{PV}{RT}$

=$\dfrac{10^{5}}{300\times 1.38\times 10^{-23 }}$

Hence n = $2.4\times 10^{5}$

Key point: Here only the formula of ideal gas equation should be remembered by the student

Previous Year Questions

A gas mixture consists of 2 moles of $O_{2}$ and 4 moles of Ar at temperature T. Neglecting all the vibrational modes, the total internal energy of the system is:- (NEET 2017)

Sol:

Here oxygen being a diatomic molecule will have no vibrational mode

So U(oxygen) = $2\times\dfrac{5}{2}RT$= 5RT

Similarly argon being monoatomic gas having only translational mode has 4 moles

So U(Ar) = $4\times\dfrac{3}{2}RT$ = 6RT

Hence total internal energy of system = U(oxygen)+ U(Ar) = 11RT

Trick: Here only the concept of degrees of freedom should be remembered by the student with the formula $U = \dfrac{U}{2RT}$

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas? (NEET 2016)

Sol:

From ideal gas equation

PV= nRT

And n = $\dfrac{PV}{RT}$

Also we know that k = $\dfrac{R}{N_{a}}$

$\dfrac{nN_{a}}{V}$ = $\dfrac{P}{kT}$

Multiplying both sides with m and after calculations we have

Density = $\dfrac{mP}{kT}$

Trick: Here only the formula of the ideal gas equation should be remembered by the student.

The translational kinetic energy of molecules of one mole of monatomic gas is U=$\dfrac{3NKT}{2}$. The value of atomic specific heat of gas under constant pressure will be: (Ans:- $\dfrac{5}{2}R$)

A gas is at zero degree celsius. Upto what temp the gas has to be heated so that the root mean square velocity of its molecules be doubled? (Ans:- 819 degree celsius)

In this article we have provided important information regarding the chapter kinetic theory of gases such as important concepts, formulae, etc.. Students should work on more solved examples and kinetic theory of ideal gas examples for securing good grades in the NEET exams.

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FAQ

1. What is the weightage of the Kinetic Theory of gases in NEET?

Nearly 1-2 questions arise in the exam from this chapter covering about 10 marks which makes about 1 % of the total marks.

2. What are the key points that need to be practiced for solving questions from Kinetic Theory of gases?

Students should practice the numericals and learn the formulas mainly for solving the questions from the Kinetic Theory of gases.

3. Are previous year questions enough for JEE Mains?

To score 600+ in NEET, NCERT (both 11th and 12th) and previous year NEET papers are sufficient. Solving previous 10-year NEET examinations offers us a tremendous advantage because 2-3 questions with the identical alternatives are guaranteed to be repeated every year.

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