sem5 thermal nota v1 dr wan

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Thermal & Statistical Physics

Introduction

Thermodynamics

Definition

-Thermodynamics: is the study of the macroscopic

behaviour of physical systems under the influence of

exchange of work and heat with other systems or their

environment

Thermodynamics can be defined as the science of energy.

Energy can be viewed as the ability to cause changes.

Classical thermodynamics

-thermodynamic states and properties

-energy, work, and heat

-with the laws of thermodynamics

- PV = k, a constant --- R Boyle

The 1st and 2nd laws of thermodynamics

-simultaneously in the 1850s

-W Rankine, R Clausius, and W Thomson (Lord Kelvin).

Statistical thermodynamics

-Late 19th century -- molecular interpretation of thermodynamics

-bridge between macroscopic and microscopic properties of

systems.

-The statistical approach is to derive all macroscopic properties

(T, V, P, E, S, etc.) from the properties of moving constituent

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particles and the interactions between them (including quantum

phenomena)

Note:

-The number of the elements can be very large --- impossible to

keep track of the behaviour of each element.

-A statistical property is a single measurement which gives a

physical picture of what is occurring in all the individual parts.

Chemical thermodynamics

-Is the study of the interrelation of heat with chemical reactions or

with a physical change of state within the confines of the laws of

thermodynamics.

Thermodynamic systems

STATISTICAL

MECHANICS

QUANTUM MECHANICS OF

ATOMS & MOLECULES

MARCOSCOPIC PROPERTIES:

Large number of molecules

TIME

DEPENDENT

BEHAVIOUR:

Chemical

Kinetics

EQUILIBRIUM

PROPERTIES:

Thermodynamics

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-System is the region of the universe under study.

-Surroundings - everything in the universe except the system.

-Boundary -separates the system with the remainder of the

universe.

-fixed, moveable, real, and imaginary

There are five dominant classes of systems:

1. Isolated Systems matter and energy may not cross the boundary.

2. Adiabatic Systems heat must not cross the boundary. 3. Diathermic Systems - heat may cross boundary. 4. Closed Systems matter may not cross the boundary. 5. Open Systems heat, work, and matter may cross the

boundary

Thermodynamic parameters

Energy transfers between thermodynamic systems as the result of

a generalized force causing a generalized displacement conjugate

variables.

SYSTEM

SURROUNDINGS

BOUNDARY

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The most common are

Pressure-volume (mechanical parameters)

Temperature-entropy (thermal parameters)

Chemical potential-particle number (material parameters)

Thermodynamic instruments

Two types: the meter and the reservoir.

A thermodynamic meter is any device which measures any

parameter of a thermodynamic system.

-The zeroth law --it is possible to measure temperature.

-An idealized thermometer--ideal gas at constant pressure.

-a barometer-constructed from a sample of an ideal gas held

at a constant temperature.

-a calorimeter is a device which is used to measure and

define the internal energy of a system.

A thermodynamic reservoir is a very large system does not alter

its state parameters when brought into contact with the test

system.

The earth's atmosphere is an example of heat reservoir.

Thermodynamic states

State - a system is at equilibrium under a given set of conditions

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The state of the system can be described by a number of intensive

and extensive variables.

The properties of the system can be described by an equation of

state which specifies the relationship between these variables.

Thermodynamic processes

-the energetic evolution of a thermodynamic system proceeding

from an initial state to a final state.

The seven most common thermodynamic processes are;

1. An isobaris process occurs at constant pressure. 2. An isochoric process, or isometric/isovolumetric process,

occurs at constant volume.

3. An isothermal process occurs at a constant temperature. 4. An adiabatic process occurs without loss or gain of heat. 5. An isentropic process (reversible adiabatic process) occurs at

constant entropy.

6. An isenthalpic process occurs at a constant enthalpy. Also known as a throttling process.

7. A steady state process occurs without a change in the internal energy of a system.

The laws of thermodynamics

Classical thermodynamics is based on the four laws of

thermodynamics:

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Zeroth law of thermodynamics, stating that thermodynamic

equilibrium is an equivalence relation about temperature

and temperature scale.

First law of thermodynamics is about the conservation of

energy -- deals with macroscopic properties, work, energy,

enthalpy, etc

Second law of thermodynamics is about entropy

Third law of thermodynamics is about absolute zero

temperature --the determination of entropy.

Thermodynamic potentials

-the quantitative measure of the stored energy in the system.

The five most well known potentials are:

Internal energy U

Helmholtz free energy A + U TS

Enthalpy H = U + PV

Gibbs free energy G = U + PV TS

Grand potential

Potentials are used to measure energy changes in systems as they

evolve from an initial state to a final state.

Note: the term thermodynamic free energy is a measure of the

amount of mechanical (or other) work that can be extracted from

a system.

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The Kinetic Theory of Gases

Kinetic theory or kinetic theory of gases -- explain macroscopic

properties of gases, such as P, T, or V, by considering their

molecular composition and motion.

Ideal gases kinetic theory of -modeling the gases as molecules (or atoms) in constant motion in

space

-A mathematical explanation of the behaviour of gases

-the KE depending on the temperature of the gas

The kinetc theory makes seven assumptions:

The volume occupied by the

gas molecules themselves is

negligible compared with the

volume of space between them

All the particles that

make up the gas are

identical

The distribution of

energy amoung

particles is random

There are sufficent

numbers of molecules for

the statistical average to

be meaningful.

Collisions are

all perfectly

elastic.

The molecules

travel in straight

lines between

collisions

Newtonian

mechanics can be

applied to molecule interactions

Assumptions

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The kinetic theory of gases -- deduced equations that related the

easily observable properties such as P, , V and T to properties not easily or directly observable -such as the sizes and speeds of

molecules.

Pressure

The pressure of a gas is caused by collisions of the molecules

of the gas with the walls of the container.

The magnitude of the pressure is related to how hard and how

often the molecules strike the wall

Absolute Temperature

The absolute temperature of a gas is a measure of the average

kinetic energy of its' molecules

If two different gases are at the same temperature, their

molecules have the same average kinetic energy

If the temperature of a gas is doubled, the average kinetic

energy of its molecules is doubled

Favg

m vx

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Molecular Speed

All the molecules average kinetic energy (and therefore an average speed)

the individual molecules move at various speeds, exhibit a DISTRIBUTION of speeds

Collisions can change individual molecular speeds but the

distribution of speeds remains the same.

At the same temperature, lighter gases move on average

faster than heavier gases.

The average kinetic energy, , is related to the root mean square (rms) speed u

2mu2

1 =

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Statistical mechanics

Statistical mechanics is the application of probability theory to the

field of mechanics, which is concerned with the motion of

particles or objects when subjected to a force.

-relating the microscopic properties of individual atoms and

molecules to the macroscopic or bulk properties of materials that

can be observed in everyday life

-it can be used to calculate the thermodynamic properties of bulk

materials from the spectroscopic data of individual molecules.

The fundamental postulate in statistical mechanics:

Given an isolated system in equilibrium, it is found with

equal probability in each of its accessiblemicrostates.

This postulate is necessary because it allows one to conclude that

for a system at equilibrium, the thermodynamic state (macrostate)

which