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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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PRESSURE – KINETIC THEORY
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$e* This assu%tion
si%(i6es the %hysica( conce%ts, 'ut the resu(t is 7ust as &enera(*
R B
A QP
Ʋ Ay
88Ʋ A₁ Ʋ A₂
β β
ƲBy
ƲB₂ ƲB₂
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PRESSURE – KINETIC THEORY
E(astic co((ision eans, as sho#n in Fi&* 142,that #hen o(ecu(e A stri/es the %(anesur+ace o+ MN at an an&(e o+ inci$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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PRESSURE – KINETIC THEORY
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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PRESSURE – KINETIC THEORY
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$+u(.contains soe 1 o(ecu(es*
2
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PRESSURE – KINETIC THEORY
Manometer for a Bourdon PressureGage* This %icture sho#s the
o)eent in one ty%e o+ %ressure&a&e /no#n as the sin&(e>tu'e &a&e* The ui$ 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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ABSOUTE PRESSUREPROBLE5 0
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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ABSOUTE PRESSUREPROBLE5 0
So(ution cont@$0
F < >>>>>> < -*HH3 s(u&.:3*2 +t4sV; < *22 ('
1 ne#ton < *22 ('
1 (' < * ne#tons
a
/+
+
+
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ABSOUTE PRESSUREPROBLE5 0
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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ABSOUTE PRESSUREPROBLE5 H0
So(ution0
-a. % < % % < 1*G < J*G %sia
% < >>>>>>>>>>>> < * atos%heres
&
%si&
1*G >>>>>>>%sia
at
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ABSOUTE PRESSUREPROBLE5 H0
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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ABSOUTE PRESSUREPROBLE5 H0
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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ABSOUTE PRESSUREPROBLE5 H0
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*