Physics · Class 11 Science
Ch 12Kinetic Theory — Class 11 Physics, concept-first.
The story of kinetic theory begins with a puzzle: what is a gas, really? In 1661, Robert Boyle discovered the law that bears his name, describing how the pressure and volume of a gas are related.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Molecular Volume Fraction
Kinetic theory begins with a bold assumption: gas molecules are so small compared to the space they roam in that we can treat them as point particles with essentially zero volume.
Most relevant Q&A
- The density of water is $1000\ \text{kg m}^{-3}$. The density of water vapour at $100\ ^\circ\text{C}$ and $1\ \text{atm}$ pressure is $0.6\…Preview
- Estimate the volume of a water molecule using the data in Example 12.1.Preview
- Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be…Free
- Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 Å and 2 Å. The gases may be considered…Preview
- We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm kept at NTP. The gas in the chamber is compressed keeping the temperature const…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
The story of kinetic theory begins with a puzzle: what is a gas, really? In 1661, Robert Boyle discovered the law that bears his name, describing how the pressure and volume of a gas are related.
Molecular Nature of Matter
The idea that matter is not continuous but made of tiny, discrete particles is one of the most profound in science.
Behaviour of Gases
4 QSection 12.2 introduced the ideal gas law, , as a macroscopic fact about gases — a relation between pressure, volume, temperature and the amount of substance that every real gas obeys, to a very good…
+−Worked Examplesi1 question
+−Worked Examplesi1 question
+−Worked Examplesi1 question
Kinetic Theory of an Ideal Gas
The kinetic theory of gases connects the macroscopic behaviour of a gas — its pressure, temperature, and volume — to the microscopic motion of its molecules.
Pressure of an Ideal Gas
The kinetic theory of gases aims to connect the macroscopic property we call pressure to the microscopic behaviour of molecules.
Kinetic Interpretation of Temperature
3 QThe kinetic theory of gases gives us a powerful insight: temperature is not a separate, mysterious quantity. It is a direct measure of the average kinetic energy of the molecules in a gas.
+−Worked Examplesi1 question
+−Worked Examplesi1 question
Law of Equipartition of Energy
The kinetic theory gives us a microscopic picture of a gas: a huge number of molecules in ceaseless, random motion.
Specific Heat Capacity
When you heat a substance, its temperature rises. The amount of heat required to raise the temperature of a unit mass of the substance by one degree (1 °C or 1 K) is called its specific heat capacity.…
Monatomic Gases
The specific heat capacity of a gas is not a single fixed number — it depends on whether the gas is heated at constant volume or constant pressure.
Diatomic Gases
The kinetic theory of gases, when applied to diatomic molecules, reveals a richer story than for monatomic gases. A diatomic molecule is not a point particle; it can rotate and vibrate.
Polyatomic Gases
The kinetic theory we have applied so far assumed molecules are point masses with only translational motion. That works well for monatomic gases like helium or argon.
Specific Heat Capacity of Solids
The kinetic theory of gases gives us a molecular picture of heat capacity, but the same ideas can be extended — with important modifications — to solids.
Mean Free Path
In a gas, molecules are in constant, random motion, colliding with one another. Between two successive collisions, a molecule travels freely in a straight line.
Summary
- Ideal gas equation (from the kinetic theory): , where is mass of one molecule, is number of molecules, and is mean square speed. This leads to (the macroscopic ideal gas law).
Points to Ponder
1. Pressure is not a surface-only phenomenon. It exists at every point inside a fluid. A thin layer of gas anywhere inside a container is in equilibrium because the pressure on both sides of that laye…
Exercises
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- 12.1Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be…Free
- 12.2Molar volume is the volume occupied by $1\ \text{mol}$ of any (ideal) gas at standard temperature and pressure (STP: $1$ atmospheric pressur…Free
- 12.3Figure 12.8 shows plot of $PV/T$ versus $P$ for $1.00\times10^{-3}$ kg of oxygen gas at two different temperatures.  in a room of capacity $25.0\…Preview
- 12.7Estimate the average thermal energy of a helium atom at (i) room temperature ($27\ ^\circ\text{C}$), (ii) the temperature on the surface of…Preview
- 12.8Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second cont…Preview
- 12.9At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at $-20\ ^…Preview
- 12.10Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at $2.0\ \text{atm}$ and temper…Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
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- Q1A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a…Free
- Q2One mole of an ideal gas at 300 K is contained in a cubical vessel of volume $V$ whose eight corners are labelled A, B, C, D, E, F, G, H, so…Free
- Q3Boyle's law is applicable for an (a) adiabatic process. (b) isothermal process. (c) isobaric process. (d) isochoric process.Free
- Q4A vertical cylinder contains an ideal gas and is closed at the top by a piston of mass $M$ that can slide up or down without friction. The g…Preview
- Q5For a fixed mass of an ideal gas, its volume $V$ (vertical axis, in litres) is plotted against its absolute temperature $T$ (horizontal axis…Preview
- Q61 mole of H$_2$ gas is contained in a box of volume $V$ = 1.00 m$^3$ at $T$ = 300K. The gas is heated to a temperature of $T$ = 3000K and th…Preview
- Q7A vessel of volume $V$ contains a mixture of 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let $f_1(v)dv$, denote the…Preview
- Q8An inflated rubber balloon contains one mole of an ideal gas, has a pressure $p$, volume $V$ and temperature $T$. If the temperature rises t…Preview
- Q9A hollow cube with corners labelled A, B, C, D, E, F, G, H is made of an insulating material. One face of the cube, ABCD, carries a positive…Preview
- Q10Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory $…Preview
- Q11In a diatomic molecule, the rotational energy at a given temperature (Note: more than one of the given options may be correct.) (a) obeys Ma…Preview
- Q12Four pressure–volume–temperature graphs for a fixed mass of gas are given, and you must decide which of them correctly depict ideal-gas beha…Preview
- Q13When an ideal gas is compressed adiabatically, its temperature rises: the molecules on the average have more kinetic energy than before. The…Preview
- Q14Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197 g mole$^{-1}$.Preview
- Q15The volume of a given mass of a gas at 27°C, 1 atm is 100 cc. What will be its volume at 327°C?Preview
- Q16The molecules of a given mass of a gas have root mean square speeds of $100\ \text{m s}^{-1}$ at 27°C and 1.00 atmospheric pressure. What wi…Preview
- Q17Two molecules of a gas have speeds of $9 \times 10^{6}\ \text{m s}^{-1}$ and $1 \times 10^{6}\ \text{m s}^{-1}$, respectively. What is the r…Preview
- Q18A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the tota…Preview
- Q19Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 Å and 2 Å. The gases may be considered…Preview
- Q20A rigid, thermally isolated container is divided into two chambers by a partition. The left chamber has volume $V_1 = 2.0$ litre and contain…Preview
- Q21A gas mixture consists of molecules of types A, B and C with masses $m_A > m_B > m_C$. Rank the three types of molecules in decreasing order…Preview
- Q22We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm kept at NTP. The gas in the chamber is compressed keeping the temperature const…Preview
- Q23When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle's law in this case?Preview
- Q24A ballon has 5.0 g mole of helium at 7°C. Calculate (a) the number of atoms of helium in the balloon, (b) the total internal energy of the s…Preview
- Q25Calculate the number of degrees of freedom of molecules of hydrogen in 1 cc of hydrogen gas at NTP.Preview
- Q26An insulated container containing monoatomic gas of molar mass $m$ is moving with a velocity $v_o$. If the container is suddenly stopped, fi…Preview
- Q27Explain why (a) there is no atmosphere on moon. (b) there is fall in temperature with altitude.Preview
- Q28Consider an ideal gas with following distribution of speeds. Speed (m/s) | % of molecules 200 | 10 400 | 20 600 | 40 800 | 20 1000 | 10 (i)…Preview
- Q29Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 × 20 × 1.5 km$^3$ in volume. You are in one…Preview
- Q30A box of 1.00m$^3$ is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm$^2$. How much time is required for th…Preview
- Q31Consider a rectangular block of wood moving with a velocity $v_0$ in a gas at temperature $T$ and mass density $\rho$. Assume the velocity i…Preview