Physics · Class 11 Science
Ch 12Kinetic Theory — Class 11 Physics, concept-first.
Thermodynamics, studied in the previous chapter, treats a gas purely as a bulk substance -- it tells us how pressure, volume, temperature and heat relate to one another through empirical laws, but it never asks what a gas actually IS at the smallest scale, or why those relations should hold at all.
Key concepts
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Assumptions of Kinetic Theory of Gases
Kinetic theory models a gas as an enormous number of identical molecules in ceaseless, random motion, treated as point masses (negligible volume compared to the container), exerting no force on one another except during…
Most relevant Q&A
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Thermodynamics, studied in the previous chapter, treats a gas purely as a bulk substance -- it tells us how pressure, volume, temperature and heat relate to one another through empirical laws, but it…
Assumptions of the Kinetic Theory of Gases
Kinetic theory does not attempt to track the exact motion of every individual molecule in a gas -- with roughly molecules in even a small sample, this would be both impossible and pointless.
Pressure of a Gas: Kinetic Interpretation
Consider an ideal gas of identical molecules, each of mass , confined inside a cubical container of side (so volume ), and focus on one wall of the cube, of area , taken perpendicular to the -axis.
RMS Speed of Gas Molecules
The pressure derivation of Section 9.3 involves , the MEAN of the squared molecular speeds, rather than the simple average speed -- and this is not an arbitrary choice: since a molecule's kinetic ener…
Kinetic Interpretation of Temperature
Rearranging the result found while deriving in Section 9.4, , and recognising that is precisely the average translational kinetic energy of a single molecule, gives, for one mole (, so ):
Gas Laws in the Light of Kinetic Theory
Kinetic theory's real power is that it does not merely describe pressure and temperature separately -- it shows that the THREE gas laws found empirically, decades earlier, by Boyle, Charles and Avogad…
Degrees of Freedom
So far, a gas molecule has been treated as a structureless point mass, free to move only through simple translation in three-dimensional space -- along the , and directions.
Law of Equipartition of Energy and Specific Heats of Gases
The law of equipartition of energy -- taken here as a STATED result, without proof, exactly as WB's own syllabus specifies -- asserts that when a gas is in thermal equilibrium at absolute temperature…
Mean Free Path
Between one collision and the next, a gas molecule travels in a straight line at essentially constant velocity (Section 9.2's assumption 3) -- but because the gas is full of other molecules to collide…
Avogadro's Number
Avogadro's number, , is defined as the number of elementary entities (atoms, molecules, ions, or any other specified particle) contained in exactly one mole of a substance -- historically fixed so tha…
Summary
This chapter built up WBCHSE Unit 9's kinetic theory of gases in the order the syllabus lists it. Assumptions (Section 9.2): molecules are point-like, in ceaseless random motion, exert no force on eac…
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
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- Q1The perfect gas equation for 4 g of hydrogen gas is (a) PV = RT (b) PV = 2RT (c) PV = (1/2)RT (d) PV = 4RTPreview
- Q2From the relation P = (1/3) mn C²rms, show that the mean kinetic energy of a molecule is the same for all types of gases. **OR** Write down…Preview
- Q3Define degrees of freedom. Write down the principle of equipartition of energy. Find the value of γ (= Cp/Cv) of a diatomic gas. **OR** Show…Preview
More questions
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- Example 1State the basic assumptions of the kinetic theory of gases as applied to an ideal gas.Free
- Example 2Estimate the RMS speed of oxygen ($O_2$, molar mass $32\ \text{g/mol}$) molecules at $300\ \text{K}$. Take $R = 8.31\ \text{J/(mol\,K)}$.Free
- Example 3A sample of nitrogen gas is at temperature $T_1 = 300\ \text{K}$. At what temperature $T_2$ would the RMS speed of its molecules be double t…Free
- Example 4$2.0\ \text{mol}$ of an ideal monatomic gas is confined in a cubical box of side $0.30\ \text{m}$ at $300\ \text{K}$. Using the kinetic theo…Preview
- Example 5Using the kinetic theory relation between pressure and mean square speed, show that Boyle's law ($PV = \text{constant}$ at fixed temperature…Preview
- Example 6Calculate the total translational kinetic energy of $1\ \text{mol}$ of an ideal gas at $27\,^\circ\text{C}$. Take $k_B = 1.38 \times 10^{-23…Preview
- Example 7Find the total number of degrees of freedom of (a) a monatomic gas molecule, (b) a rigid diatomic gas molecule at moderate temperature (igno…Preview
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- Q8List the basic assumptions of the kinetic theory of gases. Which of these assumptions is directly responsible for a gas exerting pressure on…Free
- Q9Derive the expression $P = \tfrac{1}{3}\rho\overline{v^2}$ for the pressure exerted by an ideal gas, where $\rho$ is the density of the gas…Free
- Q10Starting from the kinetic theory expression for pressure, derive the ideal gas equation $PV = nRT$ and show how the kinetic interpretation o…Free
- Q11Using kinetic theory, show how (a) Charles's law ($V \propto T$ at constant $P$) and (b) Avogadro's law (equal volumes of different gases at…Preview
- Q12What is meant by a 'degree of freedom'? State the number of degrees of freedom for a monatomic gas, a rigid diatomic gas, and a non-linear t…Preview
- Q13State the law of equipartition of energy. Use it to explain why the molar specific heat at constant volume of a diatomic gas ($\tfrac{5}{2}R…Preview
- Q14Derive the relation $C_p - C_v = R$ (Mayer's relation) for an ideal gas, starting from the first law of thermodynamics.Preview
- Q15Define mean free path. Derive the expression $\lambda = \dfrac{1}{\sqrt{2}\,\pi d^2 n}$ for the mean free path of a gas molecule, explaining…Preview
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- Q16Find the RMS speed of hydrogen ($H_2$, molar mass $2\ \text{g/mol}$) molecules at $27\,^\circ\text{C}$. Take $R = 8.31\ \text{J/(mol\,K)}$.Free
- Q17At what temperature will the RMS speed of nitrogen ($N_2$, molar mass $28\ \text{g/mol}$) molecules equal $500\ \text{m/s}$?Free
- Q18Find the average translational kinetic energy of a single gas molecule at $400\ \text{K}$. Take $k_B = 1.38 \times 10^{-23}\ \text{J/K}$.Free
- Q19A vessel contains $0.5\ \text{mol}$ of helium (monatomic) gas at $27\,^\circ\text{C}$. Find the total internal energy of the gas, using $U =…Preview
- Q20For nitrogen gas (treated as a rigid diatomic molecule), find $C_v$, $C_p$, and $\gamma = C_p/C_v$ using the law of equipartition of energy.Preview
- Q21The mean free path of a gas molecule is $2.0 \times 10^{-7}\ \text{m}$ at a certain pressure and temperature. If the pressure is halved whil…Preview
- Q22Given that $1\ \text{mol}$ of an ideal gas occupies $22.4$ litres at STP and Avogadro's number is $6.022 \times 10^{23}\ \text{mol}^{-1}$, f…Preview