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10 Name: VIPPER 2016-12-09 02:44

Quoted by: >>13

This

two-year

course

in

physics

is

presented

from

the

point

of

view

that

you,

the

reader,

are

going

to

be

a

physicist.

This

is

not

necessarily

the

case

of

course,

but

that

is

what

every

professor

in

every

subject

assumes!

If

you

are

going

to

be

a

physicist,

you

will

have

a

lot

to

study:

two

hundred

years

of

the

most

rapidly

developing

field

of

knowledge

that

there

is.

So

much

knowledge,

in

fact,

that

you

might

think

that

you

cannot

learn

all

of

it

in

four

years,

and

truly

you

cannot;

you

will

have

to

go

to

graduate

school

too!

Surprisingly

enough,

in

spite

of

the

tremendous

amount

of

work

that

has

been

done

for

all

this

time

it

is

possible

to

condense

the

enormous

mass

of

results

to

a

large

extent—that

is,

to

find

laws

which

summarize

all

our

knowledge.

Even

so,

the

laws

are

so

hard

to

grasp

that

it

is

unfair

to

you

to

start

exploring

this

tremendous

subject

without

some

kind

of

map

or

outline

of

the

relationship

of

one

part

of

the

subject

of

science

to

another.

Following

these

preliminary

remarks,

the

first

three

chapters

will

therefore

outline

the

relation

of

physics

to

the

rest

of

the

sciences,

the

relations

of

the

sciences

to

each

other,

and

the

meaning

of

science,

to

help

us

develop

a

“feel”

for

the

subject.

You

might

ask

why

we

cannot

teach

physics

by

just

giving

the

basic

laws

on

page

one

and

then

showing

how

they

work

in

all

possible

circumstances,

as

we

do

in

Euclidean

geometry,

where

we

state

the

axioms

and

then

make

all

sorts

of

deductions.

(So,

not

satisfied

to

learn

physics

in

four

years,

you

want

to

learn

it

in

four

minutes?

)

We

cannot

do

it

in

this

way

for

two

reasons.

First,

we

do

not

yet

know

all

the

basic

laws:

there

is

an

expanding

frontier

of

ignorance.

Second,

the

correct

statement

of

the

laws

of

physics

involves

some

very

unfamiliar

ideas

which

require

advanced

mathematics

for

their

description.

Therefore,

one

needs

a

considerable

amount

of

preparatory

training

even

to

learn

what

the

words

mean.

No,

it

is

not

possible

to

do

it

that

way.

We

can

only

do

it

piece

by

piece.

Each

piece,

or

part,

of

the

whole

of

nature

is

always

merely

an

approximation

to

the

complete

truth,

or

the

complete

truth

so

far

as

we

know

it.

In

fact,

everything

we

know

is

only

some

kind

of

approximation,

because

we

know

that

we

do

not

know

all

the

laws

as

yet.

Therefore,

things

must

be

learned

only

to

be

unlearned

again

or,

more

likely,

to

be

corrected.

The

principle

of

science,

the

definition,

almost,

is

the

following:

The

test

of

all

knowledge

is

experiment.

Experiment

is

the

sole

judge

of

scientific

“truth.

”

But

what

is

the

source

of

knowledge?

Where

do

the

laws

that

are

to

be

tested

come

from?

Experiment,

itself,

helps

to

produce

these

laws,

in

the

sense

that

it

gives

us

hints.

But

also

needed

is

imagination

to

create

from

these

hints

the

great

generalizations—to

guess

at

the

wonderful,

simple,

but

very

strange

patterns

beneath

them

all,

and

then

to

experiment

to

check

again

whether

we

have

made

the

right

guess.

This

imagining

process

is

so

difficult

that

there

is

a

division

of

labor

in

physics:

there

are

theoretical

physicists

who

imagine,

deduce,

and

guess

at

new

laws,

but

do

not

experiment;

and

then

there

are

experimental

physicists

who

experiment,

imagine,

deduce,

and

guess.

We

said

that

the

laws

of

nature

are

approximate:

that

we

first

find

the

“wrong”

ones,

and

then

we

find

the

“right”

ones.

Now,

how

can

an

experiment

be

“wrong”?

First,

in

a

trivial

way:

if

something

is

wrong

with

the

apparatus

that

you

did

not

notice.

But

these

things

are

easily

fixed,

and

checked

back

and

forth.

So

without

snatching

at

such

minor

things,

how

can

the

results

of

an

experiment

be

wrong?

Only

by

being

inaccurate.

For

example,

the

mass

of

an

object

never

seems

to

change:

a

spinning

top

has

the

same

weight

as

a

still

one.

So

a

“law”

was

invented:

mass

is

constant,

independent

of

speed.

That

“law”

is

now

found

to

be

incorrect.

Mass

is

found

to

increase

with

velocity,

but

appreciable

increases

require

velocities

near

that

of

light.

A

true

law

is:

if

an

object

moves

with

a

speed

of

less

than

one

hundred

miles

a

second

the

mass

is

constant

to

within

one

part

in

a

million.

In

some

such

approximate

form

this

is

a

correct

law.

So

in

practice

one

might

think

that

the

new

law

makes

no

significant

difference.

Well,

yes

and

no.

For

ordinary

speeds

we

can

certainly

forget

it

and

use

the

simple

constant-mass

law

as

a

good

approximation.

But

for

high

speeds

we

are

wrong,

and

the

higher

the

speed,

the

more

wrong

we

are.

Finally,

and

most

interesting,

philosophically

we

are

completely

wrong

with

the

approximate

law.

Our

entire

picture

of

the

world

has

to

be

altered

even

though

the

mass

changes

only

by

a

little

bit.

This

is

a

very

peculiar

thing

about

the

philosophy,

or

the

ideas,

behind

the

laws.

Even

a

very

small

effect

sometimes

requires

profound

changes

in

our

ideas.

Now,

what

should

we

teach

first?

Should

we

teach

the

correct

but

unfamiliar

law

with

its

strange

and

difficult

conceptual

ideas,

for

example

the

theory

of

relativity,

four-dimensional

space-time,

and

so

on?

Or

should

we

first

teach

the

simple

“constant-mass”

law,

which

is

only

approximate,

but

does

not

involve

such

difficult

ideas?

The

first

is

more

exciting,

more

wonderful,

and

more

fun,

but

the

second

is

easier

to

get

at

first,

and

is

a

first

step

to

a

real

understanding

of

the

first

idea.

This

point

arises

again

and

again

in

teaching

physics.

At

different

times

we

shall

have

to

resolve

it

in

different

ways,

but

at

each

stage

it

is

worth

learning

what

is

now

known,

how

accurate

it

is,

how

it

fits

into

everything

else,

and

how

it

may

be

changed

when

we

learn

more.

Let

us

now

proceed

with

our

outline,

or

general

map,

of

our

understanding

of

science

today

(in

particular,

physics,

but

also

of

other

sciences

on

the

periphery),

so

that

when

we

later

concentrate

on

some

particular

point

we

will

have

some

idea

of

the

background,

why

that

particular

point

is

interesting,

and

how

it

fits

into

the

big

structure.

So,

what

is

our

over-all

picture

of

the

world?

1–2Matter

is

made

of

atoms

If,

in

some

cataclysm,

all

of

scientific

knowledge

were

to

be

destroyed,

and

only

one

sentence

passed

on

to

the

next

generations

of

creatures,

what

statement

would

contain

the

most

information

in

the

fewest

words?

I

believe

it

is

the

atomic

hypothesis

(or

the

atomic

fact,

or

whatever

you

wish

to

call

it)

that

all

things

are

made

of

atoms—little

particles

that

move

around

in

perpetual

motion,

attracting

each

other

when

they

are

a

little

distance

apart,

but

repelling

upon

being

squeezed

into

one

another.

In

that

one

sentence,

you

will

see,

there

is

an

enormous

amount

of

information

about

the

world,

if

just

a

little

imagination

and

thinking

are

applied.

Figure

1–1

To

illustrate

the

power

of

the

atomic

idea,

suppose

that

we

have

a

drop

of

water

a

quarter

of

an

inch

on

the

side.

If

we

look

at

it

very

closely

we

see

nothing

but

water—smooth,

continuous

water.

Even

if

we

magnify

it

with

the

best

optical

microscope

available—roughly

two

thousand

times—then

the

water

drop

will

be

roughly

forty

feet

across,

about

as

big

as

a

large

room,

and

if

we

looked

rather

closely,

we

would

still

see

relatively

smooth

water—but

here

and

there

small

football-shaped

things

swimming

back

and

forth.

Very

interesting.

These

are

paramecia.

You

may

stop

at

this

point

and

get

so

curious

about

the

paramecia

with

their

wiggling

cilia

and

twisting

bodies

that

you

go

no

further,

except

perhaps

to

magnify

the

paramecia

still

more

and

see

inside.

This,

of

course,

is

a

subject

for

biology,

but

for

the

present

we

pass

on

and

look

still

more

closely

at

the

water

material

itself,

magnifying

it

two

thousand

times

again.

Now

the

drop

of

water

extends

about

fifteen

miles

across,

and

if

we

look

very

closely

at

it

we

see

a

kind

of

teeming,

something

which

no

longer

has

a

smooth

appearance—it

looks

something

like

a

crowd

at

a

football

game

as

seen

from

a

very

great

distance.

In

order

to

see

what

this

teeming

is

about,

we

will

magnify

it

another

two

hundred

and

fifty

times

and

we

will

see

something

similar

to

what

is

shown

in

Fig.

1–1.

This

is

a

picture

of

water

magnified

a

billion

times,

but

idealized

in

several

ways.

In

the

first

place,

the

particles

are

drawn

in

a

simple

manner

with

sharp

edges,

which

is

inaccurate.

Secondly,

for

simplicity,

they

are

sketched

almost

schematically

in

a

two-dimensional

arrangement,

but

of

course

they

are

moving

around

in

three

dimensions.

Notice

that

there

are

two

kinds

of

“blobs”

or

circles

to

represent

the

atoms

of

oxygen

(black)

and

hydrogen

(white),

and

that

each

oxygen

has

two

hydrogens

tied

to

it.

(Each

little

group

of

an

oxygen

with

its

two

hydrogens

is

called

a

molecule.

)

The

picture

is

idealized

further

in

that

the

real

particles

in

nature

are

continually

jiggling

and

bouncing,

turning

and

twisting

around

one

another.

You

will

have

to

imagine

this

as

a

dynamic

rather

than

a

static

picture.

Another

thing

that

cannot

be

illustrated

in

a

drawing

is

the

fact

that

the

particles

are

“stuck

together”—that

they

attract

each

other,

this

one

pulled

by

that

one,

etc.

The

whole

group

is

“glued

together,”

so

to

speak.

On

the

other

hand,

the

particles

do

not

squeeze

through

each

other.

If

you

try

to

squeeze

two

of

them

too

close

together,

they

repel.

The

atoms

are

1

or

2×10−8

cm

in

radius.

Now

10−8

cm

is

called

an

angstrom

(just

as

another

name),

so

we

say

they

are

1

or

2

angstroms

(Å)

in

radius.

Another

way

to

remember

their

size

is

this:

if

an

apple

is

magnified

to

the

size

of

the

earth,

then

the

atoms

in

the

apple

are

approximately

the

size

of

the

original

apple.

Now

imagine

this

great

drop

of

water

with

all

of

these

jiggling

particles

stuck

together

and

tagging

along

with

each

other.

The

water

keeps

its

volume;

it

does

not

fall

apart,

because

of

the

attraction

of

the

molecules

for

each

other.

If

the

drop

is

on

a

slope,

where

it

can

move

from

one

place

to

another,

the

water

will

flow,

but

it

does

not

just

disappear—things

do

not

just

fly

apart—because

of

the

molecular

attraction.

Now

the

jiggling

motion

is

what

we

represent

as

heat:

when

we

increase

the

temperature,

we

increase

the

motion.

If

we

heat

the

water,

the

jiggling

increases

and

the

volume

between

the

atoms

increases,

and

if

the

heating

continues

there

comes

a

time

when

the

pull

between

the

molecules

is

not

enough

to

hold

them

together

and

they

do

fly

apart

and

become

separated

from

one

another.

Of

course,

this

is

how

we

manufacture

steam

out

of

water—by

increasing

the

temperature;

the

particles

fly

apart

because

of

the

increased

motion.

Figure

1–2

In

Fig.

1–2

we

have

a

picture

of

steam.

This

picture

of

steam

fails

in

one

respect:

at

ordinary

atmospheric

pressure

there

certainly

would

not

be

as

many

as

three

water

molecules

in

this

figure.

Most

squares

this

size

would

contain

none—but

we

accidentally

have

two

and

a

half

or

three

in

the

picture

(just

so

it

would

not

be

completely

blank).

Now

in

the

case

of

steam

we

see

the

characteristic

molecules

more

clearly

than

in

the

case

of

water.

For

simplicity,

the

molecules

are

drawn

so

that

there

is

a

120∘

angle

between

the

hydrogen

atoms.

In

actual

fact

the

angle

is

105∘3′,

and

the

distance

between

the

center

of

a

hydrogen

and

the

center

of

the

oxygen

is

0.

957

Å,

so

we

know

this

molecule

very

well.

Let

us

see

what

some

of

the

properties

of

steam

vapor

or

any

other

gas

are.

The

molecules,

being

separated

from

one

another,

will

bounce

against

the

walls.

Imagine

a

room

with

a

number

of

tennis

balls

(a

hundred

or

so)

bouncing

around

in

perpetual

motion.

When

they

bombard

the

wall,

this

pushes

the

wall

away.

(Of

course

we

would

have

to

push

the

wall

back.

)

This

means

that

the

gas

exerts

a

jittery

force

which

our

coarse

senses

(not

being

ourselves

magnified

a

billion

times)

feel

only

as

an

average

push.

In

order

to

confine

a

gas

we

must

apply

a

pressure.

Figure

1–3

shows

a

standard

vessel

for

holding

gases

(used

in

all

textbooks),

a

cylinder

with

a

piston

in

it.

Now,

it

makes

no

difference

what

the

shapes

of

water

molecules

are,

so

for

simplicity

we

shall

draw

them

as

tennis

balls

or

little

dots.

These

things

are

in

perpetual

motion

in

all

directions.

So

many

of

them

are

hitting

the

top

piston

all

the

time

that

to

keep

it

from

being

patiently

knocked

out

of

the

tank

by

this

continuous

banging,

we

shall

have

to

hold

the

piston

down

by

a

certain

force,

which

we

call

the

pressure

(really,

the

pressure

times

the

area

is

the

force).

Clearly,

the

force

is

proportional

to

the

area,

for

if

we

increase

the

area

but

keep

the

number

of

molecules

per

cubic

centimeter

the

same,

we

increase

the

number

of

collisions

with

the

piston

in

the

same

proportion

as

the

area

was

increased.

Figure

1–3

Now

let

us

put

twice

as

many

molecules

in

this

tank,

so

as

to

double

the

density,

and

let

them

have

the

same

speed,

i.

e.

,

the

same

temperature.

Then,

to

a

close

approximation,

the

number

of

collisions

will

be

doubled,

and

since

each

will

be

just

as

“energetic”

as

before,

the

pressure

is

proportional

to

the

density.

If

we

consider

the

true

nature

of

the

forces

between

the

atoms,

we

would

expect

a

slight

decrease

in

pressure

because

of

the

attraction

between

the

atoms,

and

a

slight

increase

because

of

the

finite

volume

they

occupy.

Nevertheless,

to

an

excellent

approximation,

if

the

density

is

low

enough

that

there

are

not

many

atoms,

the

pressure

is

proportional

to

the

density.

We

can

also

see

something

else:

If

we

increase

the

temperature

without

changing

the

density

of

the

gas,

i.

e.

,

if

we

increase

the

speed

of

the

atoms,

what

is

going

to

happen

to

the

pressure?

Well,

the

atoms

hit

harder

because

they

are

moving

faster,

and

in

addition

they

hit

more

often,

so

the

pressure

increases.

You

see

how

simple

the

ideas

of

atomic

theory

are.

Let

us

consider

another

situation.

Suppose

that

the

piston

moves

inward,

so

that

the

atoms

are

slowly

compressed

into

a

smaller

space.

What

happens

when

an

atom

hits

the

moving

piston?

Evidently

it

picks

up

speed

from

the

collision.

You

can

try

it

by

bouncing

a

ping-pong

ball

from

a

forward-moving

paddle,

for

example,

and

you

will

find

that

it

comes

off

with

more

speed

than

that

with

which

it

struck.

(Special

example:

if

an

atom

happens

to

be

standing

still

and

the

piston

hits

it,

it

will

certainly

move.

)

So

the

atoms

are

“hotter”

when

they

come

away

from

the

piston

than

they

were

before

they

struck

it.

Therefore

all

the

atoms

which

are

in

the

vessel

will

have

picked

up

speed.

This

means

that

when

we

compress

a

gas

slowly,

the

temperature

of

the

gas

increases.

So,

under

slow

compression,

a

gas

will

increase

in

temperature,

and

under

slow

expansion

it

will

decrease

in

temperature.

Figure

1–4

We

now

return

to

our

drop

of

water

and

look

in

another

direction.

Suppose

that

we

decrease

the

temperature

of

our

drop

of

water.

Suppose

that

the

jiggling

of

the

molecules

of

the

atoms

in

the

water

is

steadily

decreasing.

We

know

that

there

are

forces

of

attraction

between

the

atoms,

so

that

after

a

while

they

will

not

be

able

to

jiggle

so

well.

What

will

happen

at

very

low

temperatures

is

indicated

in

Fig.

1–4:

the

molecules

lock

into

a

new

pattern

which

is

ice.

This

particular

schematic

diagram

of

ice

is

wrong

because

it

is

in

two

dimensions,

but

it

is

right

qualitatively.

The

interesting

point

is

that

the

material

has

a

definite

place

for

every

atom,

and

you

can

easily

appreciate

that

if

somehow

or

other

we

were

to

hold

all

the

atoms

at

one

end

of

the

drop

in

a

certain

arrangement,

each

atom

in

a

certain

place,

then

because

of

the

structure

of

interconnections,

which

is

rigid,

the

other

end

miles

away

(at

our

magnified

scale)

will

have

a

definite

location.

So

if

we

hold

a

needle

of

ice

at

one

end,

the

other

end

resists

our

pushing

it

aside,

unlike

the

case

of

water,

in

which

the

structure

is

broken

down

because

of

the

increased

jiggling

so

that

the

atoms

all

move

around

in

different

ways.

The

difference

between

solids

and

liquids

is,

then,

that

in

a

solid

the

atoms

are

arranged

in

some

kind

of

an

array,

called

a

crystalline

array,

and

they

do

not

have

a

random

position

at

long

distances;

the

position

of

the

atoms

on

one

side

of

the

crystal

is

determined

by

that

of

other

atoms

millions

of

atoms

away

on

the

other

side

of

the

crystal.

Figure

1–4

is

an

invented

arrangement

for

ice,

and

although

it

contains

many

of

the

correct

features

of

ice,

it

is

not

the

true

arrangement.

One

of

the

correct

features

is

that

there

is

a

part

of

the

symmetry

that

is

hexagonal.

You

can

see

that

if

we

turn

the

picture

around

an

axis

by

60∘,

the

picture

returns

to

itself.

So

there

is

a

symmetry

in

the

ice

which

accounts

for

the

six-sided

appearance

of

snowflakes.

Another

thing

we

can

see

from

Fig.

1–4

is

why

ice

shrinks

when

it

melts.

The

particular

crystal

pattern

of

ice

shown

here

has

many

“holes”

in

it,

as

does

the

true

ice

structure.

When

the

organization

breaks

down,

these

holes

can

be

occupied

by

molecules.

Most

simple

substances,

with

the

exception

of

water

and

type

metal,

expand

upon

melting,

because

the

atoms

are

closely

packed

in

the

solid

crystal

and

upon

melting

need

more

room

to

jiggle

around,

but

an

open

structure

collapses,

as

in

the

case

of

water.

Now

although

ice

has

a

“rigid”

crystalline

form,

its

temperature

can

change—ice

has

heat.

If

we

wish,

we

can

change

the

amount

of

heat.

What

is

the

heat

in

the

case

of

ice?

The

atoms

are

not

standing

still.

They

are

jiggling

and

vibrating.

So

even

though

there

is

a

definite

order

to

the

crystal—a

definite

structure—all

of

the

atoms

are

vibrating

“in

place.

”

As

we

increase

the

temperature,

they

vibrate

with

greater

and

greater

amplitude,

until

they

shake

themselves

out

of

place.

We

call

this

melting.

As

we

decrease

the

temperature,

the

vibration

decreases

and

decreases

until,

at

absolute

zero,

there

is

a

minimum

amount

of

vibration

that

the

atoms

can

have,

but

not

zero.

This

minimum

amount

of

motion

that

atoms

can

have

is

not

enough

to

melt

a

substance,

with

one

exception:

helium.

Helium

merely

decreases

the

atomic

motions

as

much

as

it

can,

but

even

at

absolute

zero

there

is

still

enough

motion

to

keep

it

from

freezing.

Helium,

even

at

absolute

zero,

does

not

freeze,

unless

the

pressure

is

made

so

great

as

to

make

the

atoms

squash

together.

If

we

increase

the

pressure,

we

can

make

it

solidify.

1–3Atomic

processes

Figure

1–5

So

much

for

the

description

of

solids,

liquids,

and

gases

from

the

atomic

point

of

view.

However,

the

atomic

hypothesis

also

describes

processes,

and

so

we

shall

now

look

at

a

number

of

processes

from

an

atomic

standpoint.

The

first

process

that

we

shall

look

at

is

associated

with

the

surface

of

the

water.

What

happens

at

the

surface

of

the

water?

We

shall

now

make

the

picture

more

complicated—and

more

realistic—by

imagining

that

the

surface

is

in

air.

Figure

1–5

shows

the

surface

of

water

in

air.

We

see

the

water

molecules

as

before,

forming

a

body

of

liquid

water,

but

now

we

also

see

the

surface

of

the

water.

Above

the

surface

we

find

a

number

of

things:

First

of

all

there

are

water

molecules,

as

in

steam.

This

is

water

vapor,

which

is

always

found

above

liquid

water.

(There

is

an

equilibrium

between

the

steam

vapor

and

the

water

which

will

be

described

later.

)

In

addition

we

find

some

other

molecules—here

two

oxygen

atoms

stuck

together

by

themselves,

forming

an

oxygen

molecule,

there

two

nitrogen

atoms

also

stuck

together

to

make

a

nitrogen

molecule.

Air

consists

almost

entirely

of

nitrogen,

oxygen,

some

water

vapor,

and

lesser

amounts

of

carbon

dioxide,

argon,

and

other

things.

So

above

the

water

surface

is

the

air,

a

gas,

containing

some

water

vapor.

Now

what

is

happening

in

this

picture?

The

molecules

in

the

water

are

always

jiggling

around.

From

time

to

time,

one

on

the

surface

happens

to

be

hit

a

little

harder

than

usual,

and

gets

knocked

away.

It

is

hard

to

see

that

happening

in

the

picture

because

it

is

a

still

picture.

But

we

can

imagine

that

one

molecule

near

the

surface

has

just

been

hit

and

is

flying

out,

or

perhaps

another

one

has

been

hit

and

is

flying

out.

Thus,

molecule

by

molecule,

the

water

disappears—it

evaporates.

But

if

we

close

the

vessel

above,

after

a

while

we

shall

find

a

large

number

of

molecules

of

water

amongst

the

air

molecules.

From

time

to

time,

one

of

these

vapor

molecules

comes

flying

down

to

the

water

and

gets

stuck

again.

So

we

see

that

what

looks

like

a

dead,

uninteresting

thing—a

glass

of

water

with

a

cover,

that

has

been

sitting

there

for

perhaps

twenty

years—really

contains

a

dynamic

and

interesting

phenomenon

which

is

going

on

all

the

time.

To

our

eyes,

our

crude

eyes,

nothing

is

changing,

but

if

we

could

see

it

a

billion

times

magnified,

we

would

see

that

from

its

own

point

of

view

it

is

always

changing:

molecules

are

leaving

the

surface,

molecules

are

coming

back.

Why

do

we

see

no

change?

Because

just

as

many

molecules

are

leaving

as

are

coming

back!

In

the

long

run

“nothing

happens.

”

If

we

then

take

the

top

of

the

vessel

off

and

blow

the

moist

air

away,

replacing

it

with

dry

air,

then

the

number

of

molecules

leaving

is

just

the

same

as

it

was

before,

because

this

depends

on

the

jiggling

of

the

water,

but

the

number

coming

back

is

greatly

reduced

because

there

are

so

many

fewer

water

molecules

above

the

water.

Therefore

there

are

more

going

out

than

coming

in,

and

the

water

evaporates.

Hence,

if

you

wish

to

evaporate

water

turn

on

the

fan!

Here

is

something

else:

Which

molecules

leave?

When

a

molecule

leaves

it

is

due

to

an

accidental,

extra

accumulation

of

a

little

bit

more

than

ordinary

energy,

which

it

needs

if

it

is

to

break

away

from

the

attractions

of

its

neighbors.

Therefore,

since

those

that

leave

have

more

energy

than

the

average,

the

ones

that

are

left

have

less

average

motion

than

they

had

before.

So

the

liquid

gradually

cools

if

it

evaporates.

Of

course,

when

a

molecule

of

vapor

comes

from

the

air

to

the

water

below

there

is

a

sudden

great

attraction

as

the

molecule

approaches

the

surface.

This

speeds

up

the

incoming

molecule

and

results

in

generation

of

heat.

So

when

they

leave

they

take

away

heat;

when

they

come

back

they

generate

heat.

Of

course

when

there

is

no

net

evaporation

the

result

is

nothing—the

water

is

not

changing

temperature.

If

we

blow

on

the

water

so

as

to

maintain

a

continuous

preponderance

in

the

number

evaporating,

then

the

water

is

cooled.

Hence,

blow

on

soup

to

cool

it!

Of

course

you

should

realize

that

the

processes

just

described

are

more

complicated

than

we

have

indicated.

Not

only

does

the

water

go

into

the

air,

but

also,

from

time

to

time,

one

of

the

oxygen

or

nitrogen

molecules

will

come

in

and

“get

lost”

in

the

mass

of

water

molecules,

and

work

its

way

into

the

water.

Thus

the

air

dissolves

in

the

water;

oxygen

and

nitrogen

molecules

will

work

their

way

into

the

water

and

the

water

will

contain

air.

If

we

suddenly

take

the

air

away

from

the

vessel,

then

the

air

molecules

will

leave

more

rapidly

than

they

come

in,

and

in

doing

so

will

make

bubbles.

This

is

very

bad

for

divers,

as

you

may

know.

Figure

1–6

Figure

1–7

Now

we

go

on

to

another

process.

In

Fig.

1–6

we

see,

from

an

atomic

point

of

view,

a

solid

dissolving

in

water.

If

we

put

a

crystal

of

salt

in

the

water,

what

will

happen?

Salt

is

a

solid,

a

crystal,

an

organized

arrangement

of

“salt

atoms.

”

Figure

1–7

is

an

illustration

of

the

three-dimensional

structure

of

common

salt,

sodium

chloride.

Strictly

speaking,

the

crystal

is

not

made

of

atoms,

but

of

what

we

call

ions.

An

ion

is

an

atom

which

either

has

a

few

extra

electrons

or

has

lost

a

few

electrons.

In

a

salt

crystal

we

find

chlorine

ions

(chlorine

atoms

with

an

extra

electron)

and

sodium

ions

(sodium

atoms

with

one

electron

missing).

The

ions

all

stick

together

by

electrical

attraction

in

the

solid

salt,

but

when

we

put

them

in

the

water

we

find,

because

of

the

attractions

of

the

negative

oxygen

and

positive

hydrogen

for

the

ions,

that

some

of

the

ions

jiggle

loose.

In

Fig.

1–6

we

see

a

chlorine

ion

getting

loose,

and

other

atoms

floating

in

the

water

in

the

form

of

ions.

This

picture

was

made

with

some

care.

Notice,

for

example,

that

the

hydrogen

ends

of

the

water

molecules

are

more

likely

to

be

near

the

chlorine

ion,

while

near

the

sodium

ion

we

are

more

likely

to

find

the

oxygen

end,

because

the

sodium

is

positive

and

the

oxygen

end

of

the

water

is

negative,

and

they

attract

electrically.

Can

we

tell

from

this

picture

whether

the

salt

is

dissolving

in

water

or

crystallizing

out

of

water?

Of

course

we

cannot

tell,

because

while

some

of

the

atoms

are

leaving

the

crystal

other

atoms

are

rejoining

it.

The

process

is

a

dynamic

one,

just

as

in

the

case

of

evaporation,

and

it

depends

on

whether

there

is

more

or

less

salt

in

the

water

than

the

amount

needed

for

equilibrium.

By

equilibrium

we

mean

that

situation

in

which

the

rate

at

which

atoms

are

leaving

just

matches

the

rate

at

which

they

are

coming

back.

If

there

is

almost

no

salt

in

the

water,

more

atoms

leave

than

return,

and

the

salt

dissolves.

If,

on

the

other

hand,

there

are

too

many

“salt

atoms,”

more

return

than

leave,

and

the

salt

is

crystallizing.

In

passing,

we

mention

that

the

concept

of

a

molecule

of

a

substance

is

only

approximate

and

exists

only

for

a

certain

class

of

substances.

It

is

clear

in

the

case

of

water

that

the

three

atoms

are

actually

stuck

together.

It

is

not

so

clear

in

the

case

of

sodium

chloride

in

the

solid.

There

is

just

an

arrangement

of

sodium

and

chlorine

ions

in

a

cubic

pattern.

There

is

no

natural

way

to

group

them

as

“molecules

of

salt.

”

Returning

to

our

discussion

of

solution

and

precipitation,

if

we

increase

the

temperature

of

the

salt

solution,

then

the

rate

at

which

atoms

are

taken

away

is

increased,

and

so

is

the

rate

at

which

atoms

are

brought

back.

It

turns

out

to

be

very

difficult,

in

general,

to

predict

which

way

it

is

going

to

go,

whether

more

or

less

of

the

solid

will

dissolve.

Most

substances

dissolve

more,

but

some

substances

dissolve

less,

as

the

temperature

increases.

1–4Chemical

reactions

In

all

of

the

processes

which

have

been

described

so

far,

the

atoms

and

the

ions

have

not

changed

partners,

but

of

course

there

are

circumstances

in

which

the

atoms

do

change

combinations,

forming

new

molecules.

This

is

illustrated

in

Fig.

1–8.

A

process

in

which

the

rearrangement

of

the

atomic

partners

occurs

is

what

we

call

a

chemical

reaction.

The

other

processes

so

far

described

are

called

physical

processes,

but

there

is

no

sharp

distinction

between

the

two.

(Nature

does

not

care

what

we

call

it,

she

just

keeps

on

doing

it.

)

This

figure

is

supposed

to

represent

carbon

burning

in

oxygen.

In

the

case

of

oxygen,

two

oxygen

atoms

stick

together

very

strongly.

(Why

do

not

three

or

even

four

stick

together?

That

is

one

of

the

very

peculiar

characteristics

of

such

atomic

processes.

Atoms

are

very

special:

they

like

certain

particular

partners,

certain

particular

directions,

and

so

on.

It

is

the

job

of

physics

to

analyze

why

each

one

wants

what

it

wants.

At

any

rate,

two

oxygen

atoms

form,

saturated

and

happy,

a

molecule.

)

Figure

1–8

The

carbon

atoms

are

supposed

to

be

11 Name: VIPPER 2016-12-09 02:56

generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to
m(_ _m) It's finally here

12 Name: VIPPER 2016-12-09 03:14

homose.cx to be a real website

13 Name: VIPPER 2016-12-09 03:25

Quoted by: >>15

>>10 why

14 Name: VIPPER 2016-12-09 03:28

I want Bleen to save Kwanzaa

15 Name: VIPPER 2016-12-09 03:39

>>13
Some monoliths got to learn you men.

16 Name: VIPPER 2016-12-09 03:56

Quoted by: >>17

This monkey ain't worshipping that shit

17 Name: VIPPER 2016-12-09 04:03

>>16
(ノjДj)ノ You killed it!

18 Name: VIPPER 2016-12-09 04:05

Oh wait! I found another one.

This

two-year

course

in

physics

is

presented

from

the

point

of

view

that

you,

the

reader,

are

going

to

be

a

physicist.

This

is

not

necessarily

the

case

of

course,

but

that

is

what

every

professor

in

every

subject

assumes!

If

you

are

going

to

be

a

physicist,

you

will

have

a

lot

to

study:

two

hundred

years

of

the

most

rapidly

developing

field

of

knowledge

that

there

is.

So

much

knowledge,

in

fact,

that

you

might

think

that

you

cannot

learn

all

of

it

in

four

years,

and

truly

you

cannot;

you

will

have

to

go

to

graduate

school

too!

Surprisingly

enough,

in

spite

of

the

tremendous

amount

of

work

that

has

been

done

for

all

this

time

it

is

possible

to

condense

the

enormous

mass

of

results

to

a

large

extent—that

is,

to

find

laws

which

summarize

all

our

knowledge.

Even

so,

the

laws

are

so

hard

to

grasp

that

it

is

unfair

to

you

to

start

exploring

this

tremendous

subject

without

some

kind

of

map

or

outline

of

the

relationship

of

one

part

of

the

subject

of

science

to

another.

Following

these

preliminary

remarks,

the

first

three

chapters

will

therefore

outline

the

relation

of

physics

to

the

rest

of

the

sciences,

the

relations

of

the

sciences

to

each

other,

and

the

meaning

of

science,

to

help

us

develop

a

“feel”

for

the

subject.

You

might

ask

why

we

cannot

teach

physics

by

just

giving

the

basic

laws

on

page

one

and

then

showing

how

they

work

in

all

possible

circumstances,

as

we

do

in

Euclidean

geometry,

where

we

state

the

axioms

and

then

make

all

sorts

of

deductions.

(So,

not

satisfied

to

learn

physics

in

four

years,

you

want

to

learn

it

in

four

minutes?

)

We

cannot

do

it

in

this

way

for

two

reasons.

First,

we

do

not

yet

know

all

the

basic

laws:

there

is

an

expanding

frontier

of

ignorance.

Second,

the

correct

statement

of

the

laws

of

physics

involves

some

very

unfamiliar

ideas

which

require

advanced

mathematics

for

their

description.

Therefore,

one

needs

a

considerable

amount

of

preparatory

training

even

to

learn

what

the

words

mean.

No,

it

is

not

possible

to

do

it

that

way.

We

can

only

do

it

piece

by

piece.

Each

piece,

or

part,

of

the

whole

of

nature

is

always

merely

an

approximation

to

the

complete

truth,

or

the

complete

truth

so

far

as

we

know

it.

In

fact,

everything

we

know

is

only

some

kind

of

approximation,

because

we

know

that

we

do

not

know

all

the

laws

as

yet.

Therefore,

things

must

be

learned

only

to

be

unlearned

again

or,

more

likely,

to

be

corrected.

The

principle

of

science,

the

definition,

almost,

is

the

following:

The

test

of

all

knowledge

is

experiment.

Experiment

is

the

sole

judge

of

scientific

“truth.

”

But

what

is

the

source

of

knowledge?

Where

do

the

laws

that

are

to

be

tested

come

from?

Experiment,

itself,

helps

to

produce

these

laws,

in

the

sense

that

it

gives

us

hints.

But

also

needed

is

imagination

to

create

from

these

hints

the

great

generalizations—to

guess

at

the

wonderful,

simple,

but

very

strange

patterns

beneath

them

all,

and

then

to

experiment

to

check

again

whether

we

have

made

the

right

guess.

This

imagining

process

is

so

difficult

that

there

is

a

division

of

labor

in

physics:

there

are

theoretical

physicists

who

imagine,

deduce,

and

guess

at

new

laws,

but

do

not

experiment;

and

then

there

are

experimental

physicists

who

experiment,

imagine,

deduce,

and

guess.

We

said

that

the

laws

of

nature

are

approximate:

that

we

first

find

the

“wrong”

ones,

and

then

we

find

the

“right”

ones.

Now,

how

can

an

experiment

be

“wrong”?

First,

in

a

trivial

way:

if

something

is

wrong

with

the

apparatus

that

you

did

not

notice.

But

these

things

are

easily

fixed,

and

checked

back

and

forth.

So

without

snatching

at

such

minor

things,

how

can

the

results

of

an

experiment

be

wrong?

Only

by

being

inaccurate.

For

example,

the

mass

of

an

object

never

seems

to

change:

a

spinning

top

has

the

same

weight

as

a

still

one.

So

a

“law”

was

invented:

mass

is

constant,

independent

of

speed.

That

“law”

is

now

found

to

be

incorrect.

Mass

is

found

to

increase

with

velocity,

but

appreciable

increases

require

velocities

near

that

of

light.

A

true

law

is:

if

an

object

moves

with

a

speed

of

less

than

one

hundred

miles

a

second

the

mass

is

constant

to

within

one

part

in

a

million.

In

some

such

approximate

form

this

is

a

correct

law.

So

in

practice

one

might

think

that

the

new

law

makes

no

significant

difference.

Well,

yes

and

no.

For

ordinary

speeds

we

can

certainly

forget

it

and

use

the

simple

constant-mass

law

as

a

good

approximation.

But

for

high

speeds

we

are

wrong,

and

the

higher

the

speed,

the

more

wrong

we

are.

Finally,

and

most

interesting,

philosophically

we

are

completely

wrong

with

the

approximate

law.

Our

entire

picture

of

the

world

has

to

be

altered

even

though

the

mass

changes

only

by

a

little

bit.

This

is

a

very

peculiar

thing

about

the

philosophy,

or

the

ideas,

behind

the

laws.

Even

a

very

small

effect

sometimes

requires

profound

changes

in

our

ideas.

Now,

what

should

we

teach

first?

Should

we

teach

the

correct

but

unfamiliar

law

with

its

strange

and

difficult

conceptual

ideas,

for

example

the

theory

of

relativity,

four-dimensional

space-time,

and

so

on?

Or

should

we

first

teach

the

simple

“constant-mass”

law,

which

is

only

approximate,

but

does

not

involve

such

difficult

ideas?

The

first

is

more

exciting,

more

wonderful,

and

more

fun,

but

the

second

is

easier

to

get

at

first,

and

is

a

first

step

to

a

real

understanding

of

the

first

idea.

This

point

arises

again

and

again

in

teaching

physics.

At

different

times

we

shall

have

to

resolve

it

in

different

ways,

but

at

each

stage

it

is

worth

learning

what

is

now

known,

how

accurate

it

is,

how

it

fits

into

everything

else,

and

how

it

may

be

changed

when

we

learn

more.

Let

us

now

proceed

with

our

outline,

or

general

map,

of

our

understanding

of

science

today

(in

particular,

physics,

but

also

of

other

sciences

on

the

periphery),

so

that

when

we

later

concentrate

on

some

particular

point

we

will

have

some

idea

of

the

background,

why

that

particular

point

is

interesting,

and

how

it

fits

into

the

big

structure.

So,

what

is

our

over-all

picture

of

the

world?

1–2Matter

is

made

of

atoms

If,

in

some

cataclysm,

all

of

scientific

knowledge

were

to

be

destroyed,

and

only

one

sentence

passed

on

to

the

next

generations

of

creatures,

what

statement

would

contain

the

most

information

in

the

fewest

words?

I

believe

it

is

the

atomic

hypothesis

(or

the

atomic

fact,

or

whatever

you

wish

to

call

it)

that

all

things

are

made

of

atoms—little

particles

that

move

around

in

perpetual

motion,

attracting

each

other

when

they

are

a

little

distance

apart,

but

repelling

upon

being

squeezed

into

one

another.

In

that

one

sentence,

you

will

see,

there

is

an

enormous

amount

of

information

about

the

world,

if

just

a

little

imagination

and

thinking

are

applied.

Figure

1–1

To

illustrate

the

power

of

the

atomic

idea,

suppose

that

we

have

a

drop

of

water

a

quarter

of

an

inch

on

the

side.

If

we

look

at

it

very

closely

we

see

nothing

but

water—smooth,

continuous

water.

Even

if

we

magnify

it

with

the

best

optical

microscope

available—roughly

two

thousand

times—then

the

water

drop

will

be

roughly

forty

feet

across,

about

as

big

as

a

large

room,

and

if

we

looked

rather

closely,

we

would

still

see

relatively

smooth

water—but

here

and

there

small

football-shaped

things

swimming

back

and

forth.

Very

interesting.

These

are

paramecia.

You

may

stop

at

this

point

and

get

so

curious

about

the

paramecia

with

their

wiggling

cilia

and

twisting

bodies

that

you

go

no

further,

except

perhaps

to

magnify

the

paramecia

still

more

and

see

inside.

This,

of

course,

is

a

subject

for

biology,

but

for

the

present

we

pass

on

and

look

still

more

closely

at

the

water

material

itself,

magnifying

it

two

thousand

times

again.

Now

the

drop

of

water

extends

about

fifteen

miles

across,

and

if

we

look

very

closely

at

it

we

see

a

kind

of

teeming,

something

which

no

longer

has

a

smooth

appearance—it

looks

something

like

a

crowd

at

a

football

game

as

seen

from

a

very

great

distance.

In

order

to

see

what

this

teeming

is

about,

we

will

magnify

it

another

two

hundred

and

fifty

times

and

we

will

see

something

similar

to

what

is

shown

in

Fig.

1–1.

This

is

a

picture

of

water

magnified

a

billion

times,

but

idealized

in

several

ways.

In

the

first

place,

the

particles

are

drawn

in

a

simple

manner

with

sharp

edges,

which

is

inaccurate.

Secondly,

for

simplicity,

they

are

sketched

almost

schematically

in

a

two-dimensional

arrangement,

but

of

course

they

are

moving

around

in

three

dimensions.

Notice

that

there

are

two

kinds

of

“blobs”

or

circles

to

represent

the

atoms

of

oxygen

(black)

and

hydrogen

(white),

and

that

each

oxygen

has

two

hydrogens

tied

to

it.

(Each

little

group

of

an

oxygen

with

its

two

hydrogens

is

called

a

molecule.

)

The

picture

is

idealized

further

in

that

the

real

particles

in

nature

are

continually

jiggling

and

bouncing,

turning

and

twisting

around

one

another.

You

will

have

to

imagine

this

as

a

dynamic

rather

than

a

static

picture.

Another

thing

that

cannot

be

illustrated

in

a

drawing

is

the

fact

that

the

particles

are

“stuck

together”—that

they

attract

each

other,

this

one

pulled

by

that

one,

etc.

The

whole

group

is

“glued

together,”

so

to

speak.

On

the

other

hand,

the

particles

do

not

squeeze

through

each

other.

If

you

try

to

squeeze

two

of

them

too

close

together,

they

repel.

The

atoms

are

1

or

2×10−8

cm

in

radius.

Now

10−8

cm

is

called

an

angstrom

(just

as

another

name),

so

we

say

they

are

1

or

2

angstroms

(Å)

in

radius.

Another

way

to

remember

their

size

is

this:

if

an

apple

is

magnified

to

the

size

of

the

earth,

then

the

atoms

in

the

apple

are

approximately

the

size

of

the

original

apple.

Now

imagine

this

great

drop

of

water

with

all

of

these

jiggling

particles

stuck

together

and

tagging

along

with

each

other.

The

water

keeps

its

volume;

it

does

not

fall

apart,

because

of

the

attraction

of

the

molecules

for

each

other.

If

the

drop

is

on

a

slope,

where

it

can

move

from

one

place

to

another,

the

water

will

flow,

but

it

does

not

just

disappear—things

do

not

just

fly

apart—because

of

the

molecular

attraction.

Now

the

jiggling

motion

is

what

we

represent

as

heat:

when

we

increase

the

temperature,

we

increase

the

motion.

If

we

heat

the

water,

the

jiggling

increases

and

the

volume

between

the

atoms

increases,

and

if

the

heating

continues

there

comes

a

time

when

the

pull

between

the

molecules

is

not

enough

to

hold

them

together

and

they

do

fly

apart

and

become

separated

from

one

another.

Of

course,

this

is

how

we

manufacture

steam

out

of

water—by

increasing

the

temperature;

the

particles

fly

apart

because

of

the

increased

motion.

Figure

1–2

In

Fig.

1–2

we

have

a

picture

of

steam.

This

picture

of

steam

fails

in

one

respect:

at

ordinary

atmospheric

pressure

there

certainly

would

not

be

as

many

as

three

water

molecules

in

this

figure.

Most

squares

this

size

would

contain

none—but

we

accidentally

have

two

and

a

half

or

three

in

the

picture

(just

so

it

would

not

be

completely

blank).

Now

in

the

case

of

steam

we

see

the

characteristic

molecules

more

clearly

than

in

the

case

of

water.

For

simplicity,

the

molecules

are

drawn

so

that

there

is

a

120∘

angle

between

the

hydrogen

atoms.

In

actual

fact

the

angle

is

105∘3′,

and

the

distance

between

the

center

of

a

hydrogen

and

the

center

of

the

oxygen

is

0.

957

Å,

so

we

know

this

molecule

very

well.

Let

us

see

what

some

of

the

properties

of

steam

vapor

or

any

other

gas

are.

The

molecules,

being

separated

from

one

another,

will

bounce

against

the

walls.

Imagine

a

room

with

a

number

of

tennis

balls

(a

hundred

or

so)

bouncing

around

in

perpetual

motion.

When

they

bombard

the

wall,

this

pushes

the

wall

away.

(Of

course

we

would

have

to

push

the

wall

back.

)

This

means

that

the

gas

exerts

a

jittery

force

which

our

coarse

senses

(not

being

ourselves

magnified

a

billion

times)

feel

only

as

an

average

push.

In

order

to

confine

a

gas

we

must

apply

a

pressure.

Figure

1–3

shows

a

standard

vessel

for

holding

gases

(used

in

all

textbooks),

a

cylinder

with

a

piston

in

it.

Now,

it

makes

no

difference

what

the

shapes

of

water

molecules

are,

so

for

simplicity

we

shall

draw

them

as

tennis

balls

or

little

dots.

These

things

are

in

perpetual

motion

in

all

directions.

So

many

of

them

are

hitting

the

top

piston

all

the

time

that

to

keep

it

from

being

patiently

knocked

out

of

the

tank

by

this

continuous

banging,

we

shall

have

to

hold

the

piston

down

by

a

certain

force,

which

we

call

the

pressure

(really,

the

pressure

times

the

area

is

the

force).

Clearly,

the

force

is

proportional

to

the

area,

for

if

we

increase

the

area

but

keep

the

number

of

molecules

per

cubic

centimeter

the

same,

we

increase

the

number

of

collisions

with

the

piston

in

the

same

proportion

as

the

area

was

increased.

Figure

1–3

Now

let

us

put

twice

as

many

molecules

in

this

tank,

so

as

to

double

the

density,

and

let

them

have

the

same

speed,

i.

e.

,

the

same

temperature.

Then,

to

a

close

approximation,

the

number

of

collisions

will

be

doubled,

and

since

each

will

be

just

as

“energetic”

as

before,

the

pressure

is

proportional

to

the

density.

If

we

consider

the

true

nature

of

the

forces

between

the

atoms,

we

would

expect

a

slight

decrease

in

pressure

because

of

the

attraction

between

the

atoms,

and

a

slight

increase

because

of

the

finite

volume

they

occupy.

Nevertheless,

to

an

excellent

approximation,

if

the

density

is

low

enough

that

there

are

not

many

atoms,

the

pressure

is

proportional

to

the

density.

We

can

also

see

something

else:

If

we

increase

the

temperature

without

changing

the

density

of

the

gas,

i.

e.

,

if

we

increase

the

speed

of

the

atoms,

what

is

going

to

happen

to

the

pressure?

Well,

the

atoms

hit

harder

because

they

are

moving

faster,

and

in

addition

they

hit

more

often,

so

the

pressure

increases.

You

see

how

simple

the

ideas

of

atomic

theory

are.

Let

us

consider

another

situation.

Suppose

that

the

piston

moves

inward,

so

that

the

atoms

are

slowly

compressed

into

a

smaller

space.

What

happens

when

an

atom

hits

the

moving

piston?

Evidently

it

picks

up

speed

from

the

collision.

You

can

try

it

by

bouncing

a

ping-pong

ball

from

a

forward-moving

paddle,

for

example,

and

you

will

find

that

it

comes

off

with

more

speed

than

that

with

which

it

struck.

(Special

example:

if

an

atom

happens

to

be

standing

still

and

the

piston

hits

it,

it

will

certainly

move.

)

So

the

atoms

are

“hotter”

when

they

come

away

from

the

piston

than

they

were

before

they

struck

it.

Therefore

all

the

atoms

which

are

in

the

vessel

will

have

picked

up

speed.

This

means

that

when

we

compress

a

gas

slowly,

the

temperature

of

the

gas

increases.

So,

under

slow

compression,

a

gas

will

increase

in

temperature,

and

under

slow

expansion

it

will

decrease

in

temperature.

Figure

1–4

We

now

return

to

our

drop

of

water

and

look

in

another

direction.

Suppose

that

we

decrease

the

temperature

of

our

drop

of

water.

Suppose

that

the

jiggling

of

the

molecules

of

the

atoms

in

the

water

is

steadily

decreasing.

We

know

that

there

are

forces

of

attraction

between

the

atoms,

so

that

after

a

while

they

will

not

be

able

to

jiggle

so

well.

What

will

happen

at

very

low

temperatures

is

indicated

in

Fig.

1–4:

the

molecules

lock

into

a

new

pattern

which

is

ice.

This

particular

schematic

diagram

of

ice

is

wrong

because

it

is

in

two

dimensions,

but

it

is

right

qualitatively.

The

interesting

point

is

that

the

material

has

a

definite

place

for

every

atom,

and

you

can

easily

appreciate

that

if

somehow

or

other

we

were

to

hold

all

the

atoms

at

one

end

of

the

drop

in

a

certain

arrangement,

each

atom

in

a

certain

place,

then

because

of

the

structure

of

interconnections,

which

is

rigid,

the

other

end

miles

away

(at

our

magnified

scale)

will

have

a

definite

location.

So

if

we

hold

a

needle

of

ice

at

one

end,

the

other

end

resists

our

pushing

it

aside,

unlike

the

case

of

water,

in

which

the

structure

is

broken

down

because

of

the

increased

jiggling

so

that

the

atoms

all

move

around

in

different

ways.

The

difference

between

solids

and

liquids

is,

then,

that

in

a

solid

the

atoms

are

arranged

in

some

kind

of

an

array,

called

a

crystalline

array,

and

they

do

not

have

a

random

position

at

long

distances;

the

position

of

the

atoms

on

one

side

of

the

crystal

is

determined

by

that

of

other

atoms

millions

of

atoms

away

on

the

other

side

of

the

crystal.

Figure

1–4

is

an

invented

arrangement

for

ice,

and

although

it

contains

many

of

the

correct

features

of

ice,

it

is

not

the

true

arrangement.

One

of

the

correct

features

is

that

there

is

a

part

of

the

symmetry

that

is

hexagonal.

You

can

see

that

if

we

turn

the

picture

around

an

axis

by

60∘,

the

picture

returns

to

itself.

So

there

is

a

symmetry

in

the

ice

which

accounts

for

the

six-sided

appearance

of

snowflakes.

Another

thing

we

can

see

from

Fig.

1–4

is

why

ice

shrinks

when

it

melts.

The

particular

crystal

pattern

of

ice

shown

here

has

many

“holes”

in

it,

as

does

the

true

ice

structure.

When

the

organization

breaks

down,

these

holes

can

be

occupied

by

molecules.

Most

simple

substances,

with

the

exception

of

water

and

type

metal,

expand

upon

melting,

because

the

atoms

are

closely

packed

in

the

solid

crystal

and

upon

melting

need

more

room

to

jiggle

around,

but

an

open

structure

collapses,

as

in

the

case

of

water.

Now

although

ice

has

a

“rigid”

crystalline

form,

its

temperature

can

change—ice

has

heat.

If

we

wish,

we

can

change

the

amount

of

heat.

What

is

the

heat

in

the

case

of

ice?

The

atoms

are

not

standing

still.

They

are

jiggling

and

vibrating.

So

even

though

there

is

a

definite

order

to

the

crystal—a

definite

structure—all

of

the

atoms

are

vibrating

“in

place.

”

As

we

increase

the

temperature,

they

vibrate

with

greater

and

greater

amplitude,

until

they

shake

themselves

out

of

place.

We

call

this

melting.

As

we

decrease

the

temperature,

the

vibration

decreases

and

decreases

until,

at

absolute

zero,

there

is

a

minimum

amount

of

vibration

that

the

atoms

can

have,

but

not

zero.

This

minimum

amount

of

motion

that

atoms

can

have

is

not

enough

to

melt

a

substance,

with

one

exception:

helium.

Helium

merely

decreases

the

atomic

motions

as

much

as

it

can,

but

even

at

absolute

zero

there

is

still

enough

motion

to

keep

it

from

freezing.

Helium,

even

at

absolute

zero,

does

not

freeze,

unless

the

pressure

is

made

so

great

as

to

make

the

atoms

squash

together.

If

we

increase

the

pressure,

we

can

make

it

solidify.

1–3Atomic

processes

Figure

1–5

So

much

for

the

description

of

solids,

liquids,

and

gases

from

the

atomic

point

of

view.

However,

the

atomic

hypothesis

also

describes

processes,

and

so

we

shall

now

look

at

a

number

of

processes

from

an

atomic

standpoint.

The

first

process

that

we

shall

look

at

is

associated

with

the

surface

of

the

water.

What

happens

at

the

surface

of

the

water?

We

shall

now

make

the

picture

more

complicated—and

more

realistic—by

imagining

that

the

surface

is

in

air.

Figure

1–5

shows

the

surface

of

water

in

air.

We

see

the

water

molecules

as

before,

forming

a

body

of

liquid

water,

but

now

we

also

see

the

surface

of

the

water.

Above

the

surface

we

find

a

number

of

things:

First

of

all

there

are

water

molecules,

as

in

steam.

This

is

water

vapor,

which

is

always

found

above

liquid

water.

(There

is

an

equilibrium

between

the

steam

vapor

and

the

water

which

will

be

described

later.

)

In

addition

we

find

some

other

molecules—here

two

oxygen

atoms

stuck

together

by

themselves,

forming

an

oxygen

molecule,

there

two

nitrogen

atoms

also

stuck

together

to

make

a

nitrogen

molecule.

Air

consists

almost

entirely

of

nitrogen,

oxygen,

some

water

vapor,

and

lesser

amounts

of

carbon

dioxide,

argon,

and

other

things.

So

above

the

water

surface

is

the

air,

a

gas,

containing

some

water

vapor.

Now

what

is

happening

in

this

picture?

The

molecules

in

the

water

are

always

jiggling

around.

From

time

to

time,

one

on

the

surface

happens

to

be

hit

a

little

harder

than

usual,

and

gets

knocked

away.

It

is

hard

to

see

that

happening

in

the

picture

because

it

is

a

still

picture.

But

we

can

imagine

that

one

molecule

near

the

surface

has

just

been

hit

and

is

flying

out,

or

perhaps

another

one

has

been

hit

and

is

flying

out.

Thus,

molecule

by

molecule,

the

water

disappears—it

evaporates.

But

if

we

close

the

vessel

above,

after

a

while

we

shall

find

a

large

number

of

molecules

of

water

amongst

the

air

molecules.

From

time

to

time,

one

of

these

vapor

molecules

comes

flying

down

to

the

water

and

gets

stuck

again.

So

we

see

that

what

looks

like

a

dead,

uninteresting

thing—a

glass

of

water

with

a

cover,

that

has

been

sitting

there

for

perhaps

twenty

years—really

contains

a

dynamic

and

interesting

phenomenon

which

is

going

on

all

the

time.

To

our

eyes,

our

crude

eyes,

nothing

is

changing,

but

if

we

could

see

it

a

billion

times

magnified,

we

would

see

that

from

its

own

point

of

view

it

is

always

changing:

molecules

are

leaving

the

surface,

molecules

are

coming

back.

Why

do

we

see

no

change?

Because

just

as

many

molecules

are

leaving

as

are

coming

back!

In

the

long

run

“nothing

happens.

”

If

we

then

take

the

top

of

the

vessel

off

and

blow

the

moist

air

away,

replacing

it

with

dry

air,

then

the

number

of

molecules

leaving

is

just

the

same

as

it

was

before,

because

this

depends

on

the

jiggling

of

the

water,

but

the

number

coming

back

is

greatly

reduced

because

there

are

so

many

fewer

water

molecules

above

the

water.

Therefore

there

are

more

going

out

than

coming

in,

and

the

water

evaporates.

Hence,

if

you

wish

to

evaporate

water

turn

on

the

fan!

Here

is

something

else:

Which

molecules

leave?

When

a

molecule

leaves

it

is

due

to

an

accidental,

extra

accumulation

of

a

little

bit

more

than

ordinary

energy,

which

it

needs

if

it

is

to

break

away

from

the

attractions

of

its

neighbors.

Therefore,

since

those

that

leave

have

more

energy

than

the

average,

the

ones

that

are

left

have

less

average

motion

than

they

had

before.

So

the

liquid

gradually

cools

if

it

evaporates.

Of

course,

when

a

molecule

of

vapor

comes

from

the

air

to

the

water

below

there

is

a

sudden

great

attraction

as

the

molecule

approaches

the

surface.

This

speeds

up

the

incoming

molecule

and

results

in

generation

of

heat.

So

when

they

leave

they

take

away

heat;

when

they

come

back

they

generate

heat.

Of

course

when

there

is

no

net

evaporation

the

result

is

nothing—the

water

is

not

changing

temperature.

If

we

blow

on

the

water

so

as

to

maintain

a

continuous

preponderance

in

the

number

evaporating,

then

the

water

is

cooled.

Hence,

blow

on

soup

to

cool

it!

Of

course

you

should

realize

that

the

processes

just

described

are

more

complicated

than

we

have

indicated.

Not

only

does

the

water

go

into

the

air,

but

also,

from

time

to

time,

one

of

the

oxygen

or

nitrogen

molecules

will

come

in

and

“get

lost”

in

the

mass

of

water

molecules,

and

work

its

way

into

the

water.

Thus

the

air

dissolves

in

the

water;

oxygen

and

nitrogen

molecules

will

work

their

way

into

the

water

and

the

water

will

contain

air.

If

we

suddenly

take

the

air

away

from

the

vessel,

then

the

air

molecules

will

leave

more

rapidly

than

they

come

in,

and

in

doing

so

will

make

bubbles.

This

is

very

bad

for

divers,

as

you

may

know.

Figure

1–6

Figure

1–7

Now

we

go

on

to

another

process.

In

Fig.

1–6

we

see,

from

an

atomic

point

of

view,

a

solid

dissolving

in

water.

If

we

put

a

crystal

of

salt

in

the

water,

what

will

happen?

Salt

is

a

solid,

a

crystal,

an

organized

arrangement

of

“salt

atoms.

”

Figure

1–7

is

an

illustration

of

the

three-dimensional

structure

of

common

salt,

sodium

chloride.

Strictly

speaking,

the

crystal

is

not

made

of

atoms,

but

of

what

we

call

ions.

An

ion

is

an

atom

which

either

has

a

few

extra

electrons

or

has

lost

a

few

electrons.

In

a

salt

crystal

we

find

chlorine

ions

(chlorine

atoms

with

an

extra

electron)

and

sodium

ions

(sodium

atoms

with

one

electron

missing).

The

ions

all

stick

together

by

electrical

attraction

in

the

solid

salt,

but

when

we

put

them

in

the

water

we

find,

because

of

the

attractions

of

the

negative

oxygen

and

positive

hydrogen

for

the

ions,

that

some

of

the

ions

jiggle

loose.

In

Fig.

1–6

we

see

a

chlorine

ion

getting

loose,

and

other

atoms

floating

in

the

water

in

the

form

of

ions.

This

picture

was

made

with

some

care.

Notice,

for

example,

that

the

hydrogen

ends

of

the

water

molecules

are

more

likely

to

be

near

the

chlorine

ion,

while

near

the

sodium

ion

we

are

more

likely

to

find

the

oxygen

end,

because

the

sodium

is

positive

and

the

oxygen

end

of

the

water

is

negative,

and

they

attract

electrically.

Can

we

tell

from

this

picture

whether

the

salt

is

dissolving

in

water

or

crystallizing

out

of

water?

Of

course

we

cannot

tell,

because

while

some

of

the

atoms

are

leaving

the

crystal

other

atoms

are

rejoining

it.

The

process

is

a

dynamic

one,

just

as

in

the

case

of

evaporation,

and

it

depends

on

whether

there

is

more

or

less

salt

in

the

water

than

the

amount

needed

for

equilibrium.

By

equilibrium

we

mean

that

situation

in

which

the

rate

at

which

atoms

are

leaving

just

matches

the

rate

at

which

they

are

coming

back.

If

there

is

almost

no

salt

in

the

water,

more

atoms

leave

than

return,

and

the

salt

dissolves.

If,

on

the

other

hand,

there

are

too

many

“salt

atoms,”

more

return

than

leave,

and

the

salt

is

crystallizing.

In

passing,

we

mention

that

the

concept

of

a

molecule

of

a

substance

is

only

approximate

and

exists

only

for

a

certain

class

of

substances.

It

is

clear

in

the

case

of

water

that

the

three

atoms

are

actually

stuck

together.

It

is

not

so

clear

in

the

case

of

sodium

chloride

in

the

solid.

There

is

just

an

arrangement

of

sodium

and

chlorine

ions

in

a

cubic

pattern.

There

is

no

natural

way

to

group

them

as

“molecules

of

salt.

”

Returning

to

our

discussion

of

solution

and

precipitation,

if

we

increase

the

temperature

of

the

salt

solution,

then

the

rate

at

which

atoms

are

taken

away

is

increased,

and

so

is

the

rate

at

which

atoms

are

brought

back.

It

turns

out

to

be

very

difficult,

in

general,

to

predict

which

way

it

is

going

to

go,

whether

more

or

less

of

the

solid

will

dissolve.

Most

substances

dissolve

more,

but

some

substances

dissolve

less,

as

the

temperature

increases.

1–4Chemical

reactions

In

all

of

the

processes

which

have

been

described

so

far,

the

atoms

and

the

ions

have

not

changed

partners,

but

of

course

there

are

circumstances

in

which

the

atoms

do

change

combinations,

forming

new

molecules.

This

is

illustrated

in

Fig.

1–8.

A

process

in

which

the

rearrangement

of

the

atomic

partners

occurs

is

what

we

call

a

chemical

reaction.

The

other

processes

so

far

described

are

called

physical

processes,

but

there

is

no

sharp

distinction

between

the

two.

(Nature

does

not

care

what

we

call

it,

she

just

keeps

on

doing

it.

)

This

figure

is

supposed

to

represent

carbon

burning

in

oxygen.

In

the

case

of

oxygen,

two

oxygen

atoms

stick

together

very

strongly.

(Why

do

not

three

or

even

four

stick

together?

That

is

one

of

the

very

peculiar

characteristics

of

such

atomic

processes.

Atoms

are

very

special:

they

like

certain

particular

partners,

certain

particular

directions,

and

so

on.

It

is

the

job

of

physics

to

analyze

why

each

one

wants

what

it

wants.

At

any

rate,

two

oxygen

atoms

form,

saturated

and

happy,

a

molecule.

)

Figure

1–8

The

carbon

atoms

are

supposed

to

be

19 Name: VIPPER 2016-12-09 04:06

generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to
generalizations—to m(_ _m) You're finally back.

20 Name: VIPPER 2016-12-09 04:33

penis

21 Name: VIPPER 2016-12-09 04:33

penis

22 Name: VIPPER 2016-12-09 04:33

penis

23 Name: VIPPER 2016-12-09 04:34

penis

24 Name: VIPPER 2016-12-09 04:34

penis

25 Name: VIPPER 2016-12-09 04:34

Quoted by: >>26

penis

26 Name: VIPPER 2016-12-09 04:43

>>25
(ノjДj)ノ \

27 Name: VIPPER 2016-12-12 08:02

You haven't fooled me since I was 5, dad.

28 Name: VIPPER 2016-12-12 15:47

You haven't folded me since I was last open, quoth the anthropomorphic map to the north pole, not unlike a dissatisfied wife or cute but petulant imouto

29 Name: VIPPER 2016-12-12 16:05

big fat santa cock cumming down in my boi chimney

30 Name: VIPPER 2016-12-12 19:46

goof butts

31 Name: VIPPER 2016-12-13 19:00

Quoted by: >>32

an unwilling oli-oni wrapped up in lots of hemp "ribbon"

32 Name: VIPPER 2016-12-14 03:41

>>31 to receive a poorly-bound Ao Oni instead.

33 Name: VIPPER 2016-12-15 17:22

Put the Mithras back in Mithrasmas.

34 Name: VIPPER 2016-12-21 21:06

Lo Wang's nuclear missile launcher

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