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EP015 Lecture 14L

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EP015 Lecture 14L

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

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