Ther 1 - 111114

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Eng’r Armando C. EmataNovember 13, 2014

THERMODYNAMICS 1

BASIC PRINCIPLES,CONCEPTS AND DEFINITIONS

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TOPIC OBJECTIVESPressure – Kinetic Theory

What are anoeters!

"o# $o #e easure %ressure!What is a &a&e %ressure!

What is atos%heric %ressure!

What is a'so(ute %ressure!

So()e sa%(e %ro'(es on %ressure*

Assi&nent +or net eetin&

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PRESSURE – KINETIC THEORY

The pressure o+ a &as, i+ &ra)itation an$ other'o$y +orces are ne&(i&i'(e -as they &enera((y are+or a &as., is cause$ 'y the %oun$in& o+ a (ar&e

nu'er o+ &as o(ecu(es on the sur+ace*

The e(eentary /inetic theory %resues the+o((o#in&0

1* the )o(ue o+ the o(ecu(e itse(+ is ne&(i&i'(e

2* the o(ecu(es are so +ar a%art they eertne&(i&i'(e +orces on one another, an$

3* the o(ecu(es are ri&i$ s%heres that $o ha)ee(astic co((isions #ith #a((s an$ #ith each other*

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Consi$er Fi&* 142 to e(a'orate this*

5 N

L

L

Fig 1/2 – Consi$er this to 'e a cu'ica( container, L on a si$e* This assu%tion

si%(i6es the %hysica( conce%ts, 'ut the resu(t is 7ust as &enera(*

R B

A QP

Ʋ Ay

88Ʋ A₁ Ʋ A₂

β β

ƲBy

ƲB₂ ƲB₂

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E(astic co((ision eans, as sho#n in Fi&* 142,that #hen o(ecu(e A stri/es the %(anesur+ace o+ MN at an an&(e o+ inci$ence α #iththe nora( PN, it re'oun$s syetrica((y onthe other si$e o+ PN #ith an an&(e α, an$ #ithno (oss o+ /inetic ener&y or oentu9 :Ʋ ;< :Ʋ ;*

The %ressure is a conse=uence o+ the rate o+chan&e o+ oentu o+ the o(ecu(esstri/in& the sur+ace*

A₂

A₁

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Si%(y %ut, pressure is $e6ne$ as the nora(+orce %er unit area*

We s%ea/ o+ the %ressure at a %oint, 'utactua( %ressure>easurin& e=ui%ent -Fi&* 143sho#s one ty%e. ty%ica((y re&isters not $o?enso+ o(ecu(ar stri/es, 'ut or$inari(y i((ions, in

a sa(( +raction o+ a secon$*Ece%tions to this &enera(i?ation inc(u$e

etree )acuus an$ the outs/irts o+ theearth@s atos%here*

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At an a(titu$e o+ 3 i(es, the mean free path -5FP. o+ a o(ecu(e is a'out 1 in*, re(ati)e(y=uite +ar9 at i(es, the 5FP is a'out i(es*

This $ecreasin& $ensity eans +e#er stri/es,an$ i+ the %ressure %ro'e is struc/ 'y a

o(ecu(e on(y no# an$ then, there is noeanin& to the %ressure at a %oint*

A cu'ic inch o+ atos%here -a han$+u(.contains soe 1 o(ecu(es*

2

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Manometer for a Bourdon PressureGage* This %icture sho#s the

o)eent in one ty%e o+ %ressure&a&e /no#n as the sin&(e>tu'e &a&e* The ui$ enters the tu'e throu&h thethrea$e$ connection* As the %ressureincreases, the tu'e #ith an e((i%tica(section ten$s to strai&hten, the en$

that is nearest the (in/a&e o)in&to#ar$ the ri&ht* The (in/a&e causesthe sector to rotate* The sectoren&a&es a sa(( %inion &ear* The in$ehan$ o)es #ith the %inion &ear* The#ho(e echanis is, o+ course,

enc(ose$ in a case, an$ a &ra$uate$$ia( +ro #hich the ressure is rea$ is

Fig. 1/3

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PRESSURE – KINETIC THEORY Barometers are use$ to easure atos%heric

%ressure* It is con)enient to ha)e a stan$ar$re+erence atos%heric %ressure, #hich is GH " or e)en 2J*J2 in "& at 32F, or 1*HJH%sia -1*G ty%ica(., or 1 at*

Pressure is one o+ the ost use+u(thero$ynaic %ro%erties 'ecause it is easi(yeasure$ $irect(y*

Pressure>easurin& instruents rea$ a$ierence o+ %ressures, ca((e$ gage pressure9

in %oun$s %er s=uare inch, #e sha(( use thea''re)iation si , the stan$in +or a e*

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PRESSURE – MANOMETERSManometers &i)e a rea$in& as the (en&th o+

soe (i=ui$ co(un0 ercury, #ater, a(coho(,etc* Fi&* 14 'e(o# sho#s a anoeter set>u%*

Fig. 1/3

A BA B A B

Atos%heric Pressure at AMacuu %ressure at A

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PRESSURE – MANOMETERSI+ a (en&th o+ co(un o+ (i=ui$, o+ cross>

sectiona( area A, is d, then the )o(ue is V = Ad an$ the +orce o+ &ra)ity on the co(un is = !Ad, #here ! is the s%eci6c #ei&ht o+ theui$*

! = "g#g$%& E=* -1>H.

The corres%on$in& %ressure is p = #A = !d

g

g

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MEASURING PRESSURE-% < % % .&

-% < , % < %.&

-% < % – % .&

-% < , % < %.&

Atos%heric %ressure

A'so(ute %ressure

ero a'so(ute or tota( )acuu

A'so(ute %ressure

%&

%

%

P

– % )acuu&

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GAGE PRESSURE

h %

%

%

& &

%en to atos%here % < % % .

% < >>>>>> >>>>>>> >>>>>>>>>

% < Qh < >>>>>>>> < >>>>>>>>

F&

A A A

Q M QAh&&

& &&h&

/ /)

&h&

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GAGE PRESSUREPROBLE5 10

A 3> )ertica( co(un o+ ui$ -$ensity <

1G /&4U. is (ocate$ #here & < J*H %sV*Fin$ the %ressure at the 'ase o+ the co(un*

So(ution0

% < >>>>>>>>> < >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> -3.

% < 3,H N4V or 3*H /Pa -&a&e.

&

&&h&

/

:J*H 4sV; :1G /& 4U;

1 >>>>>>>>>>/& >

N>sV&

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ATMOSPHERIC PRESSUREAs %re)ious(y entione$, a 'arometer is use$

to easure atos%heric %ressure*Atos%heric %ressure $iers accor$in& to(ocation as #e(( as #eather con$itions*

Where h < the hei&ht o+ co(un o+

(i=ui$ su%%orte$ 'yatos%heric %ressure %%

h

Sc!"#$ic %'i(g )* +i",-!

"!&c& 0#&)"!$!& 'i$ !&$ic#-"!&c& c)-"( #(% &!+!&)i& #$ 0#+!

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ATMOSPHERIC PRESSUREPROBLE5 20

A )ertica( co(un o+ #ater #i(( 'e su%%orte$ to#hat hei&ht 'y stan$ar$ atos%heric%ressure!

So(ution0

At stan$ar$ con$ition,

Q < H2* ('4+tU % < 1*G %si

h < >>>>>> < >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> < 33*J +t

"O

%Q"O

:1*G ('4inV;:1 inV4+tV;

H2* ('4+tU

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ATMOSPHERIC PRESSURE The spe()*( gra+)ty -s%*&r. o+ a su'stance is the

ratio o+ the s%eci6c #ei&ht o+ the su'stance to thato+ #ater*

s%* &r* < >>>>>>>

PROBLE5 0

The %ressure o+ a 'oi(er is J* /&4cV* The'aroetric %ressure o+ the atos%here is GH "* Fin$ the a'so(ute %ressure in the 'oi(er* -5EBoar$ %ro'(e – Oct 1JG.*

QQ"O

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ATMOSPHERIC PRESSUREPROBLE5 0

So(ution0

% < J* /&4cV h < GH "&At stan$ar$ con$itions,

Q < 1 /&4U

% < -Q .-h. < -s%*&r*. -Q .-h.

< >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> < 1*>>>>>

&

"O

"& "O"&

-13*H.:1 /&4U.-*GH .

1, cV4V cV

/&

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ABSOUTE PRESSURE The a'so(ute %ressure, say %sia, can 'e

$eterine$ +ro the &a&e %ressure as +o((o#s0

a'so(ute %ressure < atos%heric %ressure X

&a&e %ressureE=* -1>.

#here0 the %ositi)e si&n a%%(ies #hen a'so(ute

%ressure is &reater than atos%heric, an$ the

ne&ati)e si&n +or a'so(ute %ressure (ess thanatos%heric*

The ne&ati)e si&n is +or &a&e rea$in& ca((e$

+a(uum pressure or +a(uum*

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ABSOUTE PRESSUREEach ter in -1>. shou($, o+ course, 'e in the

sae %ressure unit*

E=uation -1>., #ritten to a%%(y #hen the&a&e %ro%er is (ocate$ in the atos%here,ay 'e &enera(i?e$ 'y this stateent0

, -he gage pressure )s the d).eren(e )n

pressures of the reg)on to /h)(h )t )s atta(hed"+)a the threaded (onne(t)on% and the reg)on)n /h)(h the gage )s 0o(ated12

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ABSOUTE PRESSUREIn e=uation +or,

% < Qh

#here0 h < h X h , the hei&ht o+ co(un o+(i=ui$ su%%orte$ 'y a'so(ute %ressure %*

I+ the (i=ui$ use$ in the 'aroeter is ercury,the atos%heric %ressure 'ecoes,

% < Q h < -s%*&r*. -Q .-h.

< >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

&

"O & "O"&

-13*H.:H2* ('4+tU.-h in.

1G2 inU4+tU

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ABSOUTE PRESSURE

% < *J1 h, ('4inV

#here0 h < co(un o+ ercury in inches

then,% < *J1 h , ('4inV

an$, % < *J1 h, ('4inV

& &

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ABSOUTE PRESSUREPROBLE5 0

A %ressure &a&e re&isters %si& in a re&ion#here the 'aroeter rea$s 1* %sia* Fin$ thea'so(ute %ressure in %sia an$ in /Pa*

So(ution0

1* < * %sia

1 /&

a < 1 4sV

1 ne#ton 1 s(u&

a < 1 +t4sV

1 ('+

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So(ution cont@$0

1 /& < >>>>>>>>>>>>>>>>>>>>>>>>>>>>> < *H3s(u&

1 4sV < :1 4sV;:3*2 +t4; < 3*2 +t4sV

:1 /& ;:2*2 >>>>>>/&

('

32*1G >>>>>>>('s(u&

*H3 s(u& F, ('+

A < 3*2 +t4sV

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So(ution cont@$0

F < >>>>>> < -*HH3 s(u&.:3*2 +t4sV; < *22 ('

1 ne#ton < *22 ('

1 (' < * ne#tons

a

/+

+

+

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So(ution cont@$0

1 >>>>> < >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

1 >>>>> < HJ >>>>>

% < :* >>>>>; HJ >>>>> < 3G,GPa or3G*G /Pa

-1 ('.:* N4(';:3J*3G 1n4;

inVinV

('

inV

('

V

N

inV

('

('

inV

NV

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ABSOUTE PRESSUREPROBLE5 H0

i)en the 'aroetric %ressure o+ 1*G %sia-2J*J2 in "& a's., a/e these con)ersions0

-a. %si& to %sia an$ to atos%here,

-'. 2 in* "& )acuu to in* "& a's an$ to %sia,

-c. 1 %sia to %si )acuu an$ to Pa,

-$. 1 in* "& &a&e to %sia, to torrs, an$ to Pa*Note0 1 atos%here < GH torrs

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So(ution0

-a. % < % % < 1*G < J*G %sia

% < >>>>>>>>>>>> < * atos%heres

&

%si&

1*G >>>>>>>%sia

at

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So(ution cont@$0

-'.

h < 2J*J2 in*

h < 2 in*&

h

h < J*J2 in* "& a's

% < *J1 h

% < -*J1.-J*J2.

< *G %sia

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So(ution cont@$0

-'.

% < 1*G %sia

%&

% < 1 %sia

% < *G %si )acuu

% < -1*G %si.:HJ Pa4%sia;

< 32,G Pa -&a&e.

&

&

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So(ution cont@$0

-c.

h

h < 1 in&

h < 2J*J2 in

h < 2J*J2 1 < *J2 in* "& a's

% < *J1 h < -*J1.-*J2. < 22*H

% < >>>>>>>>>>>>>> < 31 torrs

< :*J1 %si4in;:1 in;:HJ Pa4%si;

< ,G Pa -&a&e.

&

-1.-GH.

2J*J2

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ASSIGNMENT – NOVEMBER 14

2516 For net eetin&, su'it in one sheet o+ 'on$ %a%er* Write your nae,

su'7ect4section, $ate an$ #rite the %ro'(e stateent* P(ease #rite (e&i'(y*

Non>co%(iance #i(( ean non>acce%tance o+ your assi&nent*

1*A )acuu &a&e ounte$ on a con$enser rea$s

*HH "&* What is the a'so(ute %ressure in thecon$enser in /Pa #hen the atos%heric %ressure is11*3 /Pa!

2*Con)ert the +o((o#in& rea$in&s o+ %ressure to /Pa

a'so(ute, assuin& that the 'aroeter rea$s GH "&0 -a. J c "& a's9 -'. c "& )acuu9-c. 1 %si&9 -$. in* "& )acuu, an$ -e. GH in* "&&a&e*

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Ther 1 - 111114