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## NCERT Class 11 Physics Textbook Chapter 13 With Answer PDF Free Download

### Chapter 13: Kinetic Theory

Boyle discovered the law named after him in 1661. Boyle, Newton, and several others tried to explain the behavior of gases by considering that gases are made up of tiny atomic particles.

The actual atomic theory got established more than 150 years later. Kinetic theory explains the behavior of gases based on the idea that gas consists of rapidly moving atoms or molecules.

This is possible as the inter-atomic forces, which are short-range forces that are important for solids and liquids, can be neglected for gases.

The kinetic theory was developed in the nineteenth century by Maxwell, Boltzmann, and others.

It has been remarkably successful. It gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis.

It correctly explains the specific heat capacities of many gases.

It also relates measurable properties of gases such as viscosity, conduction, and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.

This chapter gives an introduction to kinetic theory.

#### 13.2 Molecular Nature of Matter

Richard Feynman, one of the great physicists of the 20th century considers the discovery that “Matter is made up of atoms” to be a very significant one.

Humanity may suffer annihilation (due to nuclear catastrophe) or extinction (due to environmental disasters) if we do not act wisely.

If that happens, and all scientific knowledge were to be destroyed then Feynman would like the ‘Atomic Hypothesis’ to be communicated to the next generation of creatures in the universe.

Atomic Hypothesis: All things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.

Speculation that matter may not be continuous, existed in many places and cultures.

Kanada in India and Democritus in Greece had suggested that matter may consist of indivisible constituents. The scientific ‘Atomic Theory’ is usually credited to John Dalton.

He proposed the atomic theory to explain the laws of definite and multiple proportions obeyed by

elements when they combine into compounds.

The first law says that any given compound has, a fixed proportion by mass of its constituents.

The second law says that when two elements form more than one compound, for a fixed mass of one element, the masses of the other elements are in the ratio of small integers.

### NCERT Solutions Class 11 Physics Chapter 13 Kinetic Theory

**1. 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 3 Å.**

**Solution:**

Diameter of an oxygen molecule, d = 3 Å

Radius, r = d / 2

r = 3 / 2 = 1.5 Å = 1.5 x 10^{ -8 }cm

Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm^{3}

Molecular volume of oxygen gas, V = 4 / 3 πr^{3}. N

Where, N is Avogadro’s number = 6.023 x 10^{23} molecules/ mole

Hence,

V = 4 / 3 x 3.14 x (1.5 x 10^{-8})^{3} x 6.023 x 10^{23}

We get,

V = 8.51 cm^{3}

Therefore, ratio of the molecular volume to the actual volume of oxygen = 8.51/ 22400 = 3. 8 x 10^{-4}

**2. Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 liters**

**Solution:**

The ideal gas equation relating pressure (P), volume (V), and absolute temperature (T) is given as:

PV = nRT

Where, R is the universal gas constant = 8.314 J mol^{-1}K^{-1}

n = Number of moles = 1

T = Standard temperature = 273 K

P = Standard pressure = 1 atm = 1.013 x 10^{5}Nm^{-2}

Hence,

V = nRT / P

= 1 x 8.314 x 273 / 1.013 x 10^{5}

= 0.0224 m^{3}

= 22.4 litres

Therefore, the molar volume of a gas at STP is 22.4 liters

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