Chapter 14

14.1 Ideal Gas Equations.

14.2 Kinetic Theory of Gases.

14.3 Molecular Kinetic Energy & Internal Energy.

14.4 Molar Specific Heats

CONCEPTUAL MAP : Kinetic Theory of Gases

14.0 INTRODUCTION

14.0 INTRODUCTION

Gas is one of three classical

states of matter. A pure gas may

be made up of individual atoms,

molecules, or compounds.

What distinguishes a gas from

liquids and solids is the vast

separation of the individual gas

particles. This separation usually

makes a colorless gas invisible to

the human observer.

14.0 INTRODUCTION

One of the basic methods

used to describe gases is the

kinetic theory of ideal gas.

An ideal gas is a theoretical

gas composed of a set of

randomly-moving, negligible

volume, elastic non-

interacting point (individual)

particles.

LEARNING OUTCOMES : Heat Conduction & Thermal Expansion

14.1 IDEAL GAS EQUATIONS

A gas has 3 physical quantities which determine its

state : pressure, volume and temperature (p,V,T).

In order to investigate the relationship between any 2

quantities, the 3rd quantity is kept at constant. The

derivation of gas equation is based on three law :

• Boyle’s Law.

• Charles’ Law.

• Pressure Law.

14.1 IDEAL GAS EQUATIONS

Boyle’s law states that :

“At constant temperature, the

pressure of a gas is inversely

proportional to its volume.”

14.1 IDEAL GAS EQUATIONS

Charles’ law states that :

“At constant pressure, the

volume of a gas is directly

proportional to its

temperature.”

14.1 IDEAL GAS EQUATIONS

Pressure law states that :

“At constant volume, the

pressure of a gas is directly

proportional to its temperature.”

14.1 IDEAL GAS EQUATIONS

Combination of all the equations produce the ideal

gas equation, i.e. :

where nR = constant.

n = number of mole.

R = molar gas constant = 8.31 J mol-1 K-1

or

LEARNING OUTCOMES : Heat Conduction & Thermal Expansion

14.2 KINETIC THEORY OF GASES

Ideal gas are always undergoing

random non-stop translation (linear)

motion which is related closely to

temperature.

The average of molecular

translational kinetic energy

(average of kinetic energy of every

gas molecule) is represented as

follow :

14.2 KINETIC THEORY OF GASES

The root mean square of the

speed :

The speed is closely related to

temperature. Based on the

general :

14.2 KINETIC THEORY OF GASES

Therefore, the relationship

between root mean square

speed and temperature is as

follow:

or

M = mass of 1 mole gas (with unit of kg mol-1)

14.2 KINETIC THEORY OF GASES

LEARNING OUTCOMES : Heat Conduction & Thermal Expansion

14.3 MOLECULAR KINETIC ENERGY & INTERNAL ENERGY

The total molecular translational

kinetic energy (average of kinetic

energy of gas) is represented as :

or

14.3 MOLECULAR KINETIC ENERGY & INTERNAL ENERGY

Degree of freedom, f :

= the number of independent ways by which a

molecule can process energy.

It refers to the number of independent variables

required to determine the specific location and spatial

orientation of a body.

14.3 MOLECULAR KINETIC ENERGY & INTERNAL ENERGY

14.3 MOLECULAR KINETIC ENERGY & INTERNAL ENERGY

The principle of Equipartition of Energy states that :

“When a certain amount of energy is supplied to a

system, each of the possible degrees of freedom will

receive an equal share of the total energy supplied.”

The kinetic energy for each translational and rotational

degree of freedom of a molecule is ½ kT.

14.3 MOLECULAR KINETIC ENERGY & INTERNAL ENERGY

The internal energy of an ideal gas :

= the kinetic energy of the thermal motion of its

molecules.

The total energy (internal energy) in a gas :

or

LEARNING OUTCOMES : Heat Conduction & Thermal Expansion