EP015 Lecture 14L

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