Ch 9Kinetic Theory of Gases — Class 11 Physics, concept-first.

Thermodynamics, the subject of the previous unit, is fundamentally a macroscopic science: it describes a gas only through bulk, measurable parameters such as its pressure, temperature, and volume, wit…

When a gas is enclosed inside a container, it exerts an outward push on every wall it touches -- this is the pressure that can be measured with a simple gauge.

Setting up the problem. Consider a monatomic gas of identical molecules, each of mass , enclosed in a cubical container of side (Figure 9.1(a)).

Comparing with the ideal gas equation. Equation (9.6) can be rewritten as (9.7). Comparing this directly with the macroscopic ideal gas equation (where is Boltzmann's constant) gives Multiplying both…

Pressure in terms of internal energy. From the internal energy result (9.11), , and since the ideal gas equation gives , this can be written , or rearranged as where is the internal energy per unit vo…

Boyle's law. From equation (9.12), . The internal energy of an ideal gas also equals times the average kinetic energy of a single molecule, .

Definition. The root mean square speed, , is defined as the square root of the mean of the squared speeds of every molecule in the gas: .

Definition. The mean (or average) speed, , is simply the arithmetic average of the individual speeds of all molecules in the gas: if the speeds are , then .

Definition. The most probable speed, , is the single speed value shared by the largest number of molecules in the gas -- it is the speed at which the Maxwell speed-distribution curve (Section 9.2.8) r…

Why a distribution function is needed. Even though macroscopic quantities like temperature and pressure are fixed for a gas sample, individual molecules are constantly colliding and exchanging speed w…

So far every molecule has been treated as if it can only translate -- move bodily from one point to another.

Definition. The degree of freedom of a system is the minimum number of independent coordinates needed to completely specify the position and configuration of that system in space.

A monatomic molecule -- one made of a single atom, treated as a structureless point mass -- has no internal bonds to rotate about and nothing to vibrate against, so the only way it can store energy is…

A diatomic molecule -- two atoms bound together by an interatomic force, physically modelled as two point masses connected by a massless elastic spring lying along the molecular axis -- behaves differ…

Molecules built from three atoms come in two structurally distinct shapes -- linear, where all three atoms lie on one straight line, and non-linear (bent), where the three atoms form a triangle -- and…

Building the law from a single direction of motion. Section 9.2.2 showed that the average kinetic energy associated with motion along the x-direction alone is .

Meyer's relation. For one mole of an ideal gas, the molar specific heat at constant pressure and at constant volume are always related by Meyer's relation, .

Why molecules take so long to travel across a room. The average speed of gas molecules is typically several hundred metres per second, even at ordinary room temperature -- yet the smell from an open p…

The discovery. In 1827, the Scottish botanist Robert Brown reported that tiny grains of pollen suspended in water moved about randomly, in an unpredictable zig-zag path, with no apparent cause -- a ph…

- Kinetic theory explains the microscopic origin of macroscopic parameters like temperature and pressure, starting from the idea that a gas is an enormous collection of tiny, randomly moving, elastica…

This unit's concept map is rooted at 'Kinetic theory of gases' and branches out to show how every result in the chapter connects back to the same molecular picture.

This closing exercise set brings together every idea developed in the unit -- the microscopic origin of pressure and temperature, the three characteristic molecular speeds and the Maxwell-Boltzmann di…

Sample papers and previous-year board questions for this subject.