ch- 1 fundamentals of physics

8/13/2019 CH- 1 Fundamentals of Physics

1/41

INDIABOILER DOT COMTUTORIAL FOR SECOND CLASS BOILER ENGINEERS PROFICIENCY EXAMINATION

DLP/BOE-II/ I/03012008

CHAPTER - 1

Fundamentals of Phys!s

1"1 #nts fo$ measu$ement

Phys!"# $%"s&'%$%() "#*"ys '%+&'%s s,%!!").( . .)h " "#&% % "(&$%' '%,'%s%()(4 5h.* $&!h67 "( " &() % 5. *h")67 Systems of

measurement "'% .'$"# s)'")%4%s .' (%9(4 "$.&()s . s,%!% ,hys!"#

+&"())%s

1"1"1 #nt%

T. %9,'%ss )h% $"4()&% . " ,hys!"# +&"())y " s)"("' s !h.s%( *h!h s

. )h% s"$% :( "s ,hys!"# +&"())y Ths s)"("' s )":%( "s '%%'%(!% ).

$%"s&'% " ,hys!"# +&"())y *h!h s :(.*( "s &()Th%'%.'% )h% ,'.!%ss . $%"s&'%$%() . " ,hys!"# +&"())y (.#%s

7 Th% s%#%!).( . )h% &() "(

7 N&$%' . )$%s )h% &() s !.()"(% ( )h") ,hys!"# +&"())yI( 4%(%'"#

$%"s&'% . " ,hys!"# +&"())y ; (&$%'!"# "#&% . )h% +&"())y X s


2/41



I( 1?@0 Th% G%(%'"# C.(%'%(!% . %4h)s "( M%"s&'%s ()'.&!% " (%*

sys)%$ . &()s :(.*( "s )I unts I) s "s% .( s%%( "s! "( )*.s&,,#%$%()"'y &()s 4%( "s=

1"1"*"1 Base #nts=

Name of the

P$o+e$ty

#nt of Measu$ement )ym,ol

L%(4)h 5$%)'%6 5$6

M"ss 5:#.4'"$6 5:46

T$% 5s%!.(6 5s6

E#%!)'! C&''%() 5"$,%'%6 5A6

Th%'$.y("$!

T%$,%'")&'%

5:%#(6 5>6

A$.&() . S&s)"(!% 5$.#%6 5$.#6

L&$(.&s I()%(s)y 5!"(%#"6 5!6

1"1"*"& )u++lementa$y #nts=

Name of the

P$o+e$ty


P#"(% "(4#% 5'""(6 5'"6

S.# "(4#% 5s)%'""(6 5s'6

A## ,'.,%')%s . ()%'%s) ). " B.#%' E(4(%%' !"( % %'% '.$ )h% ".%B"s% "( S&,,#%$%()"'y U()s "s !"( % s%%( '.$ )h% .##.*(4=

1"1"*"( De$'ed #nts=

Name of the

P$o+e$ty


A!!%#%'").( 5$%)'% ,%' s%!26 5$/s26A'%" 5s+&"'% $%)'%6 5$26D%(s)y 5:#.4'"$ ,%' !&! $%)'%6 5:4/$26E(%'4y 5.%s6 56 ; 5N$6E()'.,y 5.%s ,%' >%#(6 5/>6

S,%!! %()'.,y .% ,%' 4'"$ >%#( /4>7F.'!% 5N%*).(6 5N6 ; :4$/s2

P.*%' R")% . .':7 5"))6 56 ; /sP'%ss&'% 5P"s!"#6 5P"6 ; N/$2

&"())y . %") 5.%s6 56 ; N$S)'%ss S"$% "sP'%ss&'%7

5P"s!"#6 5P"6 ; N/$2

A-&


3/41



%#.!)y 5$%)'% ,%' s%!.(6 5$/s6.': 5.%s6 56 ; N$M.$%() . .'!% N%*).( $%)%' N$s,%!! %(%'4y .% ,%' :#.4'"$ /:4

1"1"*"* Ad'antae of )I7 I) s " '").("# sys)%$ . &()s - I)s $":%s &s% . .(#y .(% &() .' .(%,hys!"# +&"())y E9 "## )y,%s . %(%'4%s "'% %9,'%ss% ( .%s h%'%"s (

M>S sys)%$ %'%() &()s "'% &s% .' %'%() )y,%s . %(%'4%s F.' %9

$%!h"(!"# %(%'4y s $%"s&'% ( .% h%") %(%'4y ( !"#.'% "( %#%!)'!"#%(%'4y ( *")) h.&'

7 SI s " !.h%'%() sys)%$ . &()s % "## %'% &()s !"( % .)"(% y

(4 "( $),#y(4 )h% "s! "( s&,,#%$%()"'y &()s "( (. (&$%'!"#"!).'s "'% ()'.&!% "s &s% ). % )h% !"s% *)h !%')"( &()s . )h% CGS "(

M>S sys)%$s

7 SI s " $%)'! sys)%$ Th% $),#%s "( s&-$),#%s !"( % %9,'%ss%

"s )h% ,.*%'s . 10

1"1"*". The P$ef/es of the ) I

Th% S I "##.*s )h% s


4/41



Rules

a D%'% &()s *h%( *'))%( ( *.'s "'% (.) *'))%( *)h " !",)"# #%))%'

&(#%ss )h%y "'% ") )h% %4(((4 . " s%()%(!% Th% %9!%,).( s )h% C%#s&s

%4'%% *h!h s "#*"ys *'))%( *)h " !",)"# #%))%'Sy$.#s "'% *'))%( *)h )h% .##.*(4=

(. # s)., %9!%,) ") )h% %( . " s%()%(!% "s s(4"' %%( )h.&4h )h% *'))%( )%'$ s ,#&'"# " s,"!% %)*%%( )h% (&$%'!"# "#&% "( )h% sy$.# %4 12 $ 12

:4/$ 3"( 012 '"

( #.*%' !"s% &(#%ss )h% sy$.# h"s %%( )":%( '.$ " ,'.,%' ("$% %4"$,%'% s *'))%( "s A :%#( "s > "( .#) "s

( #.*%' !"s% &(#%ss )h% ,'%9 s $%4" 44" )%'" ,%)" .' %9" %4$%4"*")) s *'))%( "s M 44"$.#% "s G$.# "( ,%)"h%')< "s P


5/41



Nm !al Btu m ft l, > h

Po0e$%1 M> 3 162 >att 1 M=8 s &(5"5. !al8s 161"4: / 16(

m8s

1(26

met$! h+

.2556

Btu8mn

Calo$f! 'alue and )+e!f! Enthal+y%1 M=8 3 &(5"5.

!al8

161"4: / 16(

m8

((*".. / 16(

ft l,8l,

*&4"4& / 16(

Btu8l,

)+e!f! heat and )+e!f! Ent$o+y%1 =8 ? 3 6"&(55 ?!al8oC 6"&(55 Btu8l,oF

HP%1 met$! HP 3 :(.":. 0att@ 1 B$tsh HP 3 :*2

@ In Bole$ P$of!en!y !al!ulatons; HP s to ,e !onsde$ed as met$! HP

Heat%

*"15: = 3 1 !al 3 &"&6. CH# 3 ("424 BT#

Me!han!al Eu'alent of heat7=9%

3 *&: m 3 *"15: = 3 1 !al

1"& Matte$%

Th% Matte$%9s)s ( )h'%% s)")%s=

)old Lud"( a+ou$

A## $"))%' !.$,'s%s . ").$s "( $.#%!%s Th% %9)%() ). *h!h )h%s%").$s "'% .(% ). %"!h .)h%' %!%s )h% s)")% . )h% $"))%' As #.(4 "s )h%

.((4 .'!% %)*%%( )h% ").$s s #"'4% )h% $"))%' '%$"(s )old"( '%)"(s

)s sh",% "( )%(s ). .,,.s% "(y !"&s% *h!h )%(s ). !h"(4% )s sh",% Thss )h% '%"s.( )h") s.#s h"% )h% ,'.,%')y . %#"s)!)y "( "'% s)'%ss%

s)'"(% Th% B.((4 F.'!%s "'% . s%%'"# )y,%s s&!h "s 4'")").("# ,#

%)*%%( ").$s "( C."#%() B.(s

Th% ").$s "( $.#%!%s . "(y $"))%' s ( " !.(s)"() s)")% . '"(.$

'").(s "( )h% '").(s "$,#)&% (!'%"s%s *)h )%$,%'")&'% . )h%

$"))%' D%,%((4 .( )%$,%'")&'% )h% I()%'-").$! Ds)"(!% "'%s "( *h%()h% I()%'-").$! Ds)"(!% s s&!h )h") .'!% . "))'"!).( %)*%%( ).* ").$s

%+&"#s .'!% . '%,s.( " )h'%sh.# s)")% s '%"!h% *h%( s)")% . $"))%'

!h"(4%s '.$ )old). Lud "( )h% $"))%' (. #.(4%' %9h)s )h% ,'.,%')y. %#"s)!)y "( .%s (.) '%ss) " !h"(4% ( )s sh",%

A) " &')h%' h4h%' )%$,%'")&'% )h% ").$s "( $.#%!%s '%"!h " s)")% .

'").( *h%( )h%'% %9s) (. !.h%s% .'!% %)*%%( )s ").$s .' $.#%!%s

A) s&!h " )%$,%'")&'% )h% $"))%' !h"(4%s )s s)")% '.$ Lud). a+ou$

A-.


6/41



Th% )%$,%'")&'% ") *h!h " s.# $"))%' !h"(4%s )s s)")% ). #+& s !"##% )s

Meltn Pont"( )h% )%$,%'")&'% ") *h!h )h% $"))%' ( L+& s)")% !h"(4%s). ",.&' s !"##% Boln Pont Th%s% )%$,%'")&'%s %,%( &,.( ,'%ss&'%

T. )h% %9)%() )h") )h% )h'%% ,h"s%s . $"))%' '%#")% ). )h% s&%!) . B.#%'T%!h(.#.4y "( E(4(%%'(4 )h% '%"%' s "s% ). '%!"## )h") ")%' s

S.# *h%( ) s I!% h%( h%")% I!% *h!h s *")%' ( s.# s)")%7 !h"(4%s)s s)")% ). L+& ")%'7 "( *h%( &')h%' h%")% *")%' !h"(4%s ). )h% )h's)")% *h!h s ",.&' "( !"##% S)%"$

U(%' ")$.s,h%'! ,'%ss&'% M%#)(4 P.() . I!% s 00C .' 320F "( B.#(4

P.() . ")%' s 1000C .' 2120F .*%%' )h%s% ,.()s . )%$,%'")&'%

%,%( .( ,'%ss&'% Th% !h"(4% ( $%#)(4 ,.() . !% s (.) '%#%"() ).

.#%'s "( s)%"$ %(4(%s "( )&'(%s h%(!% *% *## (.) %"# *)h ) &')h%'.*%%' )h% .#(4 ,.() . *")%' "'%s 4'%")#y *)h )s ,'%ss&'%

Ths $"))%' s !.%'% ( 4'%")%' %)"#s &(%' P$o+e$tes of )team ( )hs

)&).'"# Th% !h"'"!)%'s)!s . !h"(4% . s)")% .' ,h"s% . *")%' ). s)%"$ "'%

%'% %9,%'$%()"##y "( "'% ,sh% y "'.&s '%(.*(% ()%'(").("#

.%s s&!h "s ASME7 "s 5)team Ta,les6

I) s !.(s%'% '%#%"() h%'% ). $%().( )h") ( " .#%' &s) ".% )h% s&'"!%. *")%' ( )h% .#%' '&$ !.()"(s )(y ,"')!#%s . *")%' *h!h )h.&4h

s&s,%(% ".% )h% s&'"!% . *")%' ( )h% '&$ s (.) "!)&"##y ( ",.&'

s)")% "( (%%s ). "s.' h%") ( .'%' ). 4%) !.(%')% (). ",.&' .' s)%"$Th") s *hy )h% s)%"$ &s) ".% )h% *")%' s&'"!% ( .#%' '&$s s !"##%

50et steam6 h%( %"!h "( %%'y )(y *")%' ,"')!#% h"s 4.) #y !.(%')%

(). ",.&' .' s)%"$ ) s !"##% 5d$y satu$ated steam6

1"&"1 Mass%

M"ss s " ,'.,%')y . ,hys!"# .%!)s )h") '.&4h#y s,%":(4 $%"s&'%s )h%"$.&() . $"))%' )h%y !.()"(S)'!)#y s,%":(4 )h%'% "'% )h'%% %'%() +&"())%s !"##% mass=

Inertial masss " $%"s&'% . "( .%!)s (%')"= )s '%ss)"(!% ). !h"(4(4

)s s)")% . $.).( *h%( " .'!% s ",,#% A( .%!) *)h s$"## (%')"#$"ss !h"(4%s )s $.).( $.'% '%"#y "( "( .%!) *)h #"'4% (%')"#

$"ss .%s s. #%ss '%"#y

Passive gravitational mass s " $%"s&'% . )h% s)'%(4)h . "( .%!)s()%'"!).( *)h )h% 4'")").("# %# )h( )h% s"$% 4'")").("# %#"( .%!) *)h " s$"##%' ,"ss% 4'")").("# $"ss %9,%'%(!%s " s$"##%'

.'!% )h"( "( .%!) *)h " #"'4%' ,"ss% 4'")").("# $"ss Ths .'!% s

!"##% )h% *%4h) . )h% .%!) I( (.'$"# &s"4% )h% *.' *%4h) s.)%( &s% sy(.(y$.&s#y *)h $"ss %!"&s% )h% s)'%(4)h . )h%

4'")").("# %# s '.&4h#y !.(s)"() %%'y*h%'% .( )h% s&'"!% . )h%

E"')h I( ,hys!s )h% )*. )%'$s "'% s)(!)= "( .%!) *## h"% " #"'4%'

*%4h) ) s ,#"!% ( " s)'.(4%' 4'")").("# %# &) )s ,"ss%4'")").("# $"ss '%$"(s &(!h"(4%7

A-2


7/41



Active gravitational masss " $%"s&'% . )h% s)'%(4)h . )h% 4'")").("#

%# &% ). " ,"')!"' .%!) F.' %9"$,#% )h% 4'")").("# %# )h").(% %9,%'%(!%s .( )h% M..( s *%":%' )h"( )h") . )h% E"')h %!"&s% )h%

M..( h"s #%ss "!)% 4'")").("# $"ss

Th% SI &() .' $"ss s )h% :#.4'"$ :47 *h!h s %+&"# ). )h% $"ss . )h%

()%'(").("# ,'.).)y,% :#.4'"$

1"&"& Mole%

Th% $.#% s )h% "$.&() . s&s)"(!% Th% &() s !"## )h% $.#% $.#7 "( )s

%(% "s )h% (&$%' . $.#%!%s ,'%s%() ( 0012 :#.4'"$s . !"'.(-12

I( .)h%' *.'s 1 $.#% . !"'.(-12 h"s " $"ss . 12 4'"$s 1 :$.# ; 103$.#

1"&"( olume%

.#&$% . 4"s .' "(y s&s)"(!% s %(% "s )h% s,"!% *h!h ) .!!&,%s

U() . .#&$% . "(y s&s)"(!% s !&! !%()$%)%' .' !&! $%)%'Th% .#&$% s "#s. %9,'%ss% ( #)'%

1 #)%' ; 1000 !$

3

;10

@

$$

3

; 10

-3

$

3

1"&"* )+e!f! 'olume=

Th% s,%!! .#&$% . " s&s)"(!% s )s .#&$% ,%' &() $"ss % $3/:4

Th% &() . s,%!! .#&$% s $3/:4O(% :#.4'"$ . "' ") 00C "( &(%' "( "s.#&)% ,'%ss&'% . 10332 :4/!$2

Q@0 $$ . 47 h"s .#&$% . 0QQ3 $3

Therefore the secific volume of air under these conditions is !.""#$ m#%kg. It

is denoted by v

1"&". Densty )+e!f! $a'ty %

Densty . " s&s)"(!% s4(%s h.* %(s%#y ) s ,"!:% *)h $"ssM")h%$")!"##y ) s %9,'%ss% "s 5$"ss ,%' &() .#&$%6 % :4/$ 3 ) "#s.

)%'$% "s 5M"ss %(s)y6 "( %(.)% y

D%(s)y .' M"ss %(s)y ; $/

D%,%((4 &,.( )h% U()s . M%"s&'%$%()s )h% D%(s)y s %9,'%ss% (

"'.&s &()s s&!h "s 54$/!!6 ' 5:4/ $3.' 5#/ )36 F.' %9"$,#% *")%' h"s "

D%(s)y . 51 4$/!!6 .' 51000 :4/$36 .' 5@2 #/!)6 Th&s )h% (&$%'!"#&% . D%(s)y . " s&s)"(!% s %'%() .' )h% s"$% s&s)"(!% ( %'%()

U()s . M%"s&'%$%()sTh% )+e!f! $a'ty . " s&s)"(!% s )s 5%(s)y !.$,"'% *)h )h") .

*")%'6 S(!% S,%!! G'")y s .(#y " !.$,"'s.( . D%(s)y . " s&s)"(!%

*)h )h% D%(s)y . *")%' ) h"s (. &() "( )s "#&% '%$"(s s"$%''%s,%!)% . )h% U()s . M%"s&'%$%() S,%!! G'")y s 4%(%'"##y &s%

.' #+&s

1"&"2 Con!ent$aton%

A-:


8/41



C.(!%()'").( s )h% "$.&() . " s&s)"(!% !.()"(% ( " 4%( .#&$%

A$.&() . " s&s)"(!% "( 4%( .#&$% !"( )":% $"(y .'$s

1"&"2"1 Mole8olume

*h%( " :(.*( (&$%' . $.#%s . " s&s)"(!% s ss.#% .' s,%'s% ( "

#+& ). 4% " :(.*( .#&$% . s.#&).( .' s&s,%(s.(M.#%s ,%' #)'% $.#/L7 "( $.#%s ,%' !&! !%()$%)'% $.#/!!7 %9,'%ss

!.(!%()'").( ( )h% )%'$s . $.#% ,%' &() .#&$% $.#/7

F% $.#/L s %+&"# ). % $.#% . s&s)"(!% ( .(% #)'% . s.#&).(Th% (&$%' . $.#%s . " s&s)"(!% ( .(% #)'% . s.#&).( s !"##% )h%

$.#"')y . )h") s.#&).(

1"&"2"& Mass8olume

*h%( " $"ss . " s&s)"(!% s ss.#% .' s&s,%(% ( " #+& ). 4% "

:(.*( .#&$% . s.#&).( .' s&s,%(s.(>#.4'"$s ,%' #)'% :4/L7 4'"$s ,%' #)'% 4/L7 $##4'"$s ,%' #)'% $4/L7

"( 4'"$s ,%' !&! !%()$%)'% 4/!!7 %9,'%ss !.(!%()'").( ( )h% )%'$s .$"ss ,%' &() .#&$% *h!h s &s&"##y '%%''% ). "s *%4h)/.#&$% */7

1"&"2"( Mass8Mass

*h%( " $"ss . s&s)"(!% s s,%'s% ( "(.)h%' $"ss ). 4% " :(.*(

'%s)"() $"ssG'"$s ,%' :#.4'"$ 4/:47 "( $##4'"$s ,%' :#.4'"$ $4/:47 %9,'%ss

!.(!%()'").( ( )h% )%'$s . $"ss ,%' &() $"ss *h!h s &s&"##y '%%''% ).

"s *%4h)/*%4h) */*7

1"&"2"* olume8olume

*h%( " .#&$% . s&s)"(!% s s,%'s% ( "(.)h%' .#&$% . s&s)"(!% ).4% " :(.*( '%s)"() .#&$%

M###)'%s ,%' #)'% %9,'%ss%s !.(!%()'").( ( )h% )%'$s . .#&$% ,%' &()

.#&$% *h!h s &s&"##y '%%''% ). "s .#&$%/.#&$% /7

Th&s 80 $###)'%s . "#!.h.# s #&)% ). 2000 $###)'%s *)h *")%' )h%'%s) s " s.#&).( . 2000 $###)'%s .' 2 #)'%s

1"&"2". Pa$ts Pe$ Mllon 7++m9

A ,"') ,%' $##.( s .(% . " +&"())y ( .(% $##.( . "(.)h%' +&"())y P"')s

,%' $##.( s "'%")% ). ,,$

T. !.(%') " !.(!%()'").( '.$ / ). ,,$ )h% !.(!%()'").( $&s) % ($#/$# L/L %)! "( )h%( $),#y y 10@). 4%) ,,$ /

I( )h% s"$% *"y */* !.(!%()'").( !"( .(#y % !.(%')% ). ,,$ &s(4 )h%

"!).' 10@ )h% !.(!%()'").( s %9,'%ss% ( 4'"$s ,%' 4'"$ 4/47

:#.4'"$s ,%' :#.4'"$s :4/:47 %)!Th% .#&$% . " s&s)"(!% ( )h% 4"s%.&s .'$ !"( % %+&")% ). )h% $"ss .

)h% s&s)"(!% )h% %9"!) .#&$% s :(.*( Th&s )h% .#&$% /.#&$%

!.(!%()'").( . " s&s)"(!% !"( % %+&")% ). )h% $"ss/.#&$% !.(!%()'").(. )h") s&s)"(!%

A-5


9/41



1"&"2"2 Pe$!ent

P%'!%() 7 s "#s. &s% ). %9,'%ss !.(!%()'").( $&!h )h% s"$% "s ,"')s ,%'

$##.( ,,$7 Th% %'%(!% s )h") ,%'!%() '%#")%s ). .(% ( " h&('%

!.$,"'% ). ,,$ *h!h '%#")%s ). .(% ( " $##.(

1"&": P$essu$e%P'%ss&'% s %(% "s F.'!% ,%' U() A'%"T":% " "' . 4#"ss *)h " #").)).$ ##% *)h *")%' "( :%%, ) .%' " )"#% Th% *%4h) . *")%' ( )h%"' %9%')s " .'!% .( )h% s&'"!% . )h% )"#% I )hs .'!% s $%"s&'% .%' "&() "'%" . )h% s&'"!% )h%( ) s !"##% )h% ,'%ss&'% Th%'%.'% ,'%ss&'% !"(% %(% "s )h% .'!% %9%')% y "( .%!) .%' )h% s&'"!% . &() A'%"

% ,'%ss&'% ; .'!% / area

I( ,'"!)!% ) s %9,'%ss% .' $%"s&'% ( .##.*(4 &()s=

N/$2>4/!$2

L/(2

"' 1 "';10KN/$27

,"s!"# 1P"s!"#; 1 N/$27 h%4h) . #+& !.#&$( N.'$"##y *")%' M%'!&'y7

1"&"5 Atmos+he$! P$essu$e%

Th% ")$.s,h%'% s&''.&((4 )h% %"')h %9%')s " ,'%ss&'% .( )s s&'"!%%+&"#%() ). )h% *%4h) . "' "!)(4 .%' &() "'%" . )h% %"')hs s&'"!% "( )s :(.*( "s ")$.s,h%'! ,'%ss&'% A) s%" #%%# )h% *%4h) . "' .%' " *%4h). &() "'%" . %"')hs s&'"!% s %+&"#%() ). *%4h) . " !.#&$( . Q@ !$Q@0 $$7 . $%'!&'y !.#&$( 47 ") 00C I) s )":%( "s )h% s)"("'"'.$%)'! ,'%ss&'% Ths s "#s. :(.*( "s " ,hys!"# ")$.s,h%'% .'"'.$%)'! ")$.s,h%'%Th% %(s)y . $%'!&'y s 13 K?K 4'"$s ,%' !&! !%()$%)%'

Th%'%.'% s)"("' "'.$%)'! ,'%ss&'% ; Q@ 9 13 K?K ; 1033 32 4'"$s / s+!$ % 103322 :4/s+!$

1 ")" ; 1 $%)'! .' )%!h(!"# ")$.s,h%'% 1 :4/!$ 2 "7 ; Q@0 /10332 ;Q3K@$$ . 4

P'%ss&'% s "#s. $%"s&'% ( )h% &() . $$ . *")%' !.#&$( O(%A)$.s,h%'! ,'%ss&'% s %+&"#%() ). Q@0913K?K$$ . *")%' !.#&$( Th")s 103322$$ . *")%' Ths s 10332 $%)%' . *")%'

1:4/!$2; Q3K@$$ . 4 ; Q3K@913K?K ; 10$%)%' . *")%'

% :(.* )h") )h% ")$.s,h%'% %9%')s ,'%ss&'% "s $%().(% .*%%' *%)":% " ,'%ss&'% 4"&4% ( .&' h"( ) '%"s J%'. %%( )h.&4h )h% ")$.s,h%'!

,'%ss&'% s ,'%s%() Th&s ,'%ss&'% G"&4% $%"s&'%s )h% ,'%ss&'% *)h '%%'%(!%). A)$.s,h%'! ,'%ss&'% R% F4-17 Th% ,'%ss&'% (!")% y )h% 4"&4%".% ")$.s,h%'% s :(.*( "s 4"&4% ,'%ss&'% Th% ,'%ss&'% (!")% y )h%4"&4% *h%( )h% sys)%$ ,'%ss&'% s #%ss )h"( ")$.s,h%'! s )%'$% "sa!uum;*h!h s 4%(%'"##y $%"s&'% ( $$ . *")%' .' $%'!&'y !.#&$("( )h% 4"&4%s "'% :(.*( "s "!&&$ 4"&4%s

A-4

A,solute P$essu$e

3 Atm" P$essu$e aue P$essu$e

a!uum 3

Atm" P$essu$e - A,solute P$essu$e

A,solute P$essu$e

3 Atm" P$essu$e - a!uum

A,solute e$o P$essu$e

Atmos+he$! P$essu$e

1"6((& 8!m&

a!uum aue P$essu$e

P$essu$e aue Readn

aue P$essu$e


10/41



F" 1

Th&s )h% As.#&)% ,'%ss&'% ; A)$.s,h%'! ,'%ss&'% G"&4% ,'%ss&'%

P" ; P") P4 .'

As.#&)% ,'%ss&'% ; A)$.s,h%'! ,'%ss&'% V "!&&$

P" ; P") - "!&&$

1"&"4 Ba$omete$%

Th% "'.$%)%' s )h% s$,#%s) (s)'&$%() .' $%"s&'(4 ")$.s,h%'! ,'%ss&'%Th% %"')hs ")$.s,h%'% ") s%" #%%# h"s " *%4h) . 1Q ,.&(s .%' " s+&"'%(!h . s&'"!% Ths s )h% *%4h) . " !.#&$( . "' )h") %9)%(s '.$ s%"#%%# ") )h% %"')hs s&'"!% ). )h% %4% . )h% ")$.s,h%'% Ths *%4h) !h"(4%s"s )h% )%$,%'")&'% "( !.$,.s).( . )h% "' $"ss !h"(4%s A "'.$%)%' &s%s" s&s))&)% !.#&$( . $%'!&'y #& ( ,#"!% . )h% "' O(% ")$.s,h%'% ( "$%'!&'y "'.$%)%' s %+&"#% y " !.#&$( . .(#y Q@0 $$ 4

F"&

1"&"16 Manomete$%

Th% $"(.$%)%' s .(% . )h% s$,#%s) )..#s .' $%"s&'(4 4"s ,'%ss&'%

%'%(!%s A $"(.$%)%' s " &-)&% O(% s% . )h% U s .,%( ).

")$.s,h%'% "( )h% .)h%' s% s !.((%!)% ). " !#.s% !.()"(%' Th% U s##% *)h " #& I .)h s%s . )h% U h"% )h% s"$% #+& #%%#s )h%( )h%

,'%ss&'% (s% "( )h% ,'%ss&'% .&)s% "'% )h% s"$% Th% %'%(!% %)*%%(

)h% #+& #%%#s %+&"#s )h% ,'%ss&'% %'%(!% %)*%%( (s% "( .&)s%

Th% $%'!&'y #%%# *## % #.*%' .( )h% s% *)h 4'%")%' ,'%ss&'% Th% h4h%','%ss&'% ,&sh%s )h% $%'!&'y .*( Th% M"(.$%)%' $%"s&'%s )h% G"&4%

A-16

h 3 :26 mm of

H

A sm+le Me$!u$y

Ba$omete$


11/41


12/41



1"&"11"( Cha$less La0

Ch"'#%ss L"* !"( % s)")% "s )h% .#&$% .!!&,% y "(y s"$,#% . 4"s ") "!.(s)"() ,'%ss&'% s '%!)#y ,'.,.').("# ). )h% "s.#&)% )%$,%'")&'%

/ T ;!.(s)"()

s )h% .#&$%

T s )h% "s.#&)% )%$,%'")&'% $%"s&'% ( >%#(7Ch"'#%ss L"* !"( % '%"''"(4% (). )*. .)h%' &s% %+&").(s18 T13 &8 T& < &3 17T&8 T19

1s )h% ()"# .#&$%

T1s )h% ()"# )%$,%'")&'% 2s )h% ("# .#&$%

T2s )h% ("# )%$,%'")&'%Ch"'#%ss L"* .(#y *.':s *h%( )h% ,'%ss&'% s !.(s)"()

&ote= Ch"'#%ss L"* s "'#y "!!&'")% &) 4"s%s )%( ). %")% '.$ ) ") %'y

h4h "( #.* ,'%ss&'%s

1"&"11"* NTPNTP s)"(s .' N.'$"# T%$,%'")&'% "( P'%ss&'% NTP s 0.C%#!&s "( 1

")$.s,h%'! ,'%ss&'% G"s%s ,'.,%')%s !"( % !.$,"'% &s(4 NTP "s "

'%%'%(!%

1"&"11". Com,ned La0

Th% !.$(% 4"s #"* s " !.$(").( . B.y#%s L"* "( Ch"'#%ss L"*h%(!% )s ("$% )h% !.$(% 4"s #"* I( )h% !.$(% 4"s #"* )h% .#&$% .

4"s s '%!)#y ,'.,.').("# ). )h% "s.#&)% )%$,%'")&'% "( (%'s%#y

,'.,.').("# ). )h% ,'%ss&'%

Ths !"( % *'))%( "s P / T ; !.(s)"()

Th%'%.'% *% !"( *')% P118 T13 P&&8 T&" P1s )h% ()"# ,'%ss&'%

1s )h% ()"# .#&$% T1s )h% ()"# )%$,%'")&'% ( >%#(7

P2s )h% ("# ,'%ss&'% 2s )h% ("# .#&$%

T2s )h% ("# )%$,%'")&'% ( >%#(7A#s. t3 6G 1 t 8 &:( "h%'% 0s )h% .#&$% ") 0

0C "() s )h% )%$,%'")&'% ( 0C

1"&"11"2 Ideal as La0

Th% %"# 4"s #"* s " !.$(").( . "## )h% 4"s #"*s Th% %"# 4"s #"* !"(% %9,'%ss% "s P 3 mRsT

P s )h% ,'%ss&'% ( ")$

s )h% .#&$% ( #)%'s $ s )h% $"ss . )h% 4"s !.(s%'%

Rss " !.(s)"() T s )h% )%$,%'")&'% ( >%#(

Ths %+&").( s :(.*( "s Ch"'"!)%'s)! %+&").( . " 4"s

A-1&


13/41



S.$%)$%s R s !"##% )h% Ch"'"!)%'s)! .' s,%!! 4"s !.(s)"()

1"&"11": #n'e$sal as !onstant%

I )h% $.#%!"' $"ss . "(y 4"s s $),#% y )s s,%!! 4"s !.(s)"() Rs )

*## % .&( )h") )h% ,'.&!) s )h% s"$% .' "## 4"s%s Ths !.(s)"() s )%'$%

"s U(%'s"# 4"s !.(s)"()F.' SI sys)%$ )h% "#&% . &(%'s"# 4"s !.(s)"() s 5"(1*( =8 mol ?"Th&s R&; MRs ; 8313 :/:$.# >

h%'% M s )h% $.#%!"' $"ss . )h% 4"s ( :4/ :$.#

I) sh. % (.)% )h") n any !al!ulatons n'ol'n the as la0s; a,solute

+$essu$es and a,solute tem+e$atu$es must ,e usedH

A'oad$os La0%

A) " 4%( )%$,%'")&'% "( ,'%ss&'% %+&"# .#&$%s . 4"s !.()"( %+&"# (&$%'s

. $.#%s' ; constantAn

F.' %9"$,#% I) h"s %%( .&( )h") ") NTP 22 $

3

. y'.4%( 4"s h"s " $"ss .2 :4 )h%'%.'% 1 :$.# . y'.4%(As ,%' A.4"'.s L"* ") NTP 22 $3 . "## .)h%' 4"s *## h"% )h%

!.''%s,.((4 $"ss . 1 :$.# . )h") 4"s

1"&"11"5 Pe$fe!t as= A ,%'%!) 4"s .' %"# 4"s $"y % !.(s%'% "s .(% )h").%ys )h% #"*s . B.y#% "( Ch"'#%s "( )h% Ch"'"!)%'s)! %+&").( . " 4"s

*h!h s .)"(% y !.$((4 )h% ".% #"*s

N. 4"s s ,%'%!) &) $"(y 4"s%s !"( ",,'."!h )hs s)"("' *)h( )h%)%$,%'")&'% #$)s . ",,#% )h%'$.y("$!s

1"( Tem+e$atu$e%

Tem+e$atu$es )h% $%"s&'% . )h% '%#")% *"'$)h .' !..#(%ss . "( .%!)

Th% )%$,%'")&'% . " s&s)"(!% .%s (.) $%"s&'% )s h%") !.()%() &) '")h%')h% "%'"4% :(%)! %(%'4y . )s $.#%!%s '%s)(4 '.$ )h%' $.).(s A

.(%-,.&( #.!: . '.( "( " )*.-,.&( #.!: . '.( ") )h% s"$%

)%$,%'")&'% . (.) h"% )h% s"$% h%") !.()%() B%!"&s% )h%y "'% ") )h% s"$%)%$,%'")&'% )h% "%'"4% :(%)! %(%'4y . )h% $.#%!%s s )h% s"$% h.*%%'

)h% )*.-,.&( #.!: h"s $.'% $.#%!%s )h"( )h% .(%-,.&( #.!: "( )h&s

h"s 4'%")%' h%") %(%'4y

F.' $%"s&'%$%() . T%$,%'")&'% )h%'% "'% )*. s!"#%s . $%"s&'%$%()s .(% s

5Fah$enhet6 "( )h% .)h%' s 5Cent$ade6 .' 5Celsus6 Th% "')'"'y

'%%'%(!% )":%( s )h% '%%


14/41



I( M>S sys)%$s )h% &() . )%$,%'")&'% s %4'%% C%()4'"% C7

I( FPS sys)%$ )h% &() . )%$,%'")&'% s %4'%% F"h'%(h%) F7

I( SI sys)%$ )h% &() . )%$,%'")&'% s %4'%% C%#s&s C7

10C%()4'"% ; 10 C%#s&s

A )%$,%'")&'% '%"(4 .( .(% s!"#% !"( % !.(%')% (). " '%"(4 .( )h%.)h%' s!"#% y )h% .##.*(4 .'$"=

C8166 3 7F-(&98156 .' C3.84 7F-(&9 .' F3 1"5C(&*h%'% C s )%$,%'")&'% ( C%#s&s .' C%()4'"% "( F s )%$,%'")&'% (

F"h'%(h%)

1"("1 A,solute tem+e$atu$e s!ale%

% :(.* )h") )%$,%'")&'% s )h% %%!) !"&s%s y ()%'("# %(%'4y . "

s&s)"(!% &% ). '"(.$ $.).( . $.#%!%s . " s&s)"(!% A .y )h") sh.))%' h"s )s $.#%!%s $.(4 $.'% 4.'.&s#y )h"( )h") . " .y *h!h s

!.#%' Th&s )h%'% !"( % " s)")% *h%( )h%'% s "s.#&)%#y (. '"(.$ $.).(

. )h% $.#%!%s . " s&s)"(!% Th%'% s .(% ,"')!"' )%$,%'")&'% ") *h!h)h% $.#%!"' '"(.$ $.).( . %"!h s&s)"(!% ).)"##y s).,s Ths

)%$,%'")&'% s !"##% A,solute e$o %!"&s% )h%'% !"( (.) % " )%$,%'")&'%

#.*%' )h"( )hs s(!% )h% $.#%!%s !"( (.) % $.'% s)").(%'y )h"( %(4 (

(. $.).( ") "##7

A,solute e$o s )h% )%$,%'")&'% ") *h!h "## '").'y )'"(s#").'y "('.)").("# $.).(s . )h% $.#%!% . " s&s)"(!% s s&,,.s% ). !%"s% %

*h%( ()%'("# %(%'4y %!.$%s %#( s!"#% .' 0>

T%$,%'")&'% > ; T%$,%'")&'% 0C 2Q3

% > ; C 2Q3

As.#&)% )%$,%'")&'% ( %4'%% F"h'%(h%) s :(.*( "s %4'%% Ranne.' 0R"( )h% As.#&)% J%'. ( %4'%% F"h'%(h%) .!!&'s ") V@00F

Th&s T%$,%'")&'% 0R ; T%$,%'")&'% 0F @0% R ; F @0

1"("& The$momete$%

A( (s)'&$%() &s% .' $%"s&'(4 )%$,%'")&'% s !"##% " )h%'$.$%)%' "( s!.(s)'&!)% y &s(4 .(% . )h% .##.*(4 ,'(!,#%s=

)h% !h"(4% . #%(4)h s&!h "s #%(4)h . " $%'!&'y !.#&$(

A-1*


15/41



)h% !h"(4% . .#&$% s&!h "s .#&$% . " 9% $"ss . 4"s ") !.(s)"()

,'%ss&'% )h% !h"(4% . ,'%ss&'% s&!h "s ,'%ss&'% . " 9% $"ss . 4"s ") !.(s)"()

.#&$%

)h% !h"(4% ( %#%!)'! '%ss)"(!% "s ( " )h%'$s).'

)h% #.* . %#%!)'!)y &% ). S%%%!: %%!) "s ( " )h%'$.!.&,#% )h% '"").( "s ( '"").( ,y'.$%)%'s

1"("&"1 lass Bul, 7Me$!u$y the$momete$9% M.s) !.$$.( .' $%"s&'(4 "'

)%$,%'")&'% s )h% #+&-(-4#"ss )h%'$.$%)%' *h!h !.(ss)s . " 4#"ss )&%

%(#"'4% ") )h% .)).$ (). " )h") s ,"')"##y ##% *)h $%'!&'y.'.'4"(! #+&7 Th% )&%s .'% s %9)'%$%#y s$"##W#%ss )h"( 002 (!h 0K

$##$%)%'7 ( "$%)%' Th&s " s$"## "$.&() . %9,"(s.( .' !.()'"!).( .

)h% $%'!&'y ( )h% !"&s% y h%")(4 .' !..#(4 ,'.&!%s " (.)!%"#%'s% .' "## ( )s #%%# ( )h% )&%

1"("&"& Bmetal the$momete$%T*. %'%() $%)"#s "'% .(% ).4%)h%' *)h .(%

%( "))"!h% ). "( (!")(4 (%%#% *h!h "#4(s *)h " !'!"' s!"#% .( )h%"!% . )h% (s)'&$%() S(!% )h% $%)"#s %9,"( ") %'%() '")%s $.%$%().!!&'s %,%((4 .( )h% )%$,%'")&'% #&!)&").( "( )h% (%%#% $.%s

1"("&"( Ind!atn Mate$al= A "'%)y . 5!'"y.(s6 "( ,%##%)s "'% ""#"#% )h")

$%#) ") s,%!! )%$,%'")&'%s Th%s% . (.) '%"##y $%"s&'% )%$,%'")&'%'%!)#y &) . (!")% )h% $"9$&$ )%$,%'")&'% )h") " $")%'"# *"s

%9,.s% ).

1"("&"* a+o$8as Flled%S&!h )h%'$.$%)%' .,%'")%s .( " s$#"' ,'(!,#% ). )h%4#"ss )y,% )h%'$.$%)%'

1"("&". alleo the$momete$% Th%s% )%( ). % &s% ( %!.'")% s%))(4s "'.&(

)h% h.$% .' .!% Th%s% ()%'%s)(4 $.%#s .,%'")% "s% .( ,'(!,#%s .

s,%!! 4'")y1"("&"2 RTD and The$msto$% Th%s% "'% "s% .( )h% !h"(4% ( '%ss)"(!% . "

!.(&!).' *h%( )h% )%$,%'")&'% . )h% *'% !h"(4%s I( .)h )h% (s)'&$%()s

)%$,%'")&'%s "'% 4)"##y s,#"y% "( h"% %))%' "!!&'"!%s

1"("&": The$mo!ou+le% Th%s% .,%'")% "s% .( )h% )%$,%'")&'% !h"(4% )h") .!!&'s

") )h% &(!).( . )*. ss$#"' *'%s h%( )h% )%$,%'")&'% !h"(4%s " s$"##

!&''%() s 4%(%'")% y )h% &(!).( Ths !&''%() s )h%( !.$,"'% ). "'%%'%(!% &(!).( !"#'")% s)"("' .' !% *")%' ")h7 "( !.(%')% ). "

)%$,%'")&'% y %#%!)'! .' %#%!)'.(! $%"(s S. )h% sys)%$ (!#&%s )h%

)h%'$.!.&,#% )s%# !.((%!)(4 *'(4 "( s.$% $%)h. G%(%'"##y " 4)"#$%)%'7 ). s,#"y )h% )%$,%'")&'% '%"(4

A(.)h%' s4(!"() ""()"4% . )h% )h%'$.!.&,#% s )h") )h% (!")(4(s)'&$%() !"( % " %'y #.(4 s)"(!% '.$ )h% )h%'$.!.&,#% %('.($%()

O(!% )h% sys)%$ s !"#'")% "( )h% !&''%() '.$ )h% )h%'$.!.&,#% s!",)&'% " "'%)y . %#%!)'!"# .,).(s "'% ""#"#% .' 4%))(4 )h%

(.'$").( ). " s,#"y &()

1"("( Py$omete$% I) s " (.(-!.()"!)(4 %!% ()%'!%,)(4 "( $%"s&'(4 )h%'$"#'"").( %$))% '.$ "( .%!) ). %)%'$(% s&'"!% )%$,%'")&'% Py'.$%)%'

s %'% '.$ )h% G'%%: *.' ,y'. $%"((4 '%

A-1.


16/41



Th% )%$,%'")&'% . " $")%'"# "%!)s )h% !.#.' Th% ('"'% #4h) s,%!)'&$

*.':s %'y *%## .' )hs "( s )h% "ss .' )h% ('"'% )h%'$.$%)%' .',y'.$%)%' Th%s% &()s . (.) '%+&'% " !.()"!) *)h )h% $")%'"# "( "'%

""#"#% "s h"( h%# &()s Th%y !"( s%(s% " %'y h4h '"(4% .

)%$,%'")&'%s)ome a++l!atons of +y$omete$s

Item Inst$ument used to measu$e tem+e$atu$e

Bole$ !om,uston s+a!e O+t!al +y$omete$

E!onomse$; feed 0ate$ heate$s and

!hmney ases

Base metal the$mo-!ou+le

In!andes!ent flaments O+t!al +y$omete$

In!andes!ent as mantels Radaton +y$omete$

1"* >o$%

I " h%"y $"ss s ). % $.% '.$ .(% ,#"!% ). .)h%' .(% h"s ). ",,#y .'!%.' s,%( %(%'4y Th% F.'!% ",,#% ). " .y $),#% y )h% s)"(!%$.% s )h% "$.&() . *.': .(% .' "$.&() . %(%'4y s,%()

.': ; F.'!% 9 s)"(!% )'"%#% ( )h% '%!).( . .'!%7.': .(#y (.#%s )h% &s% ,"') . " .'!% ("$%#y )h% ,"') )h") s %%!)%

( !"&s(4 )h% $.).(

S&,,.s% " ,"# . *")%' *%4h(4 Q N s !"''% .%' " s)"(!% . 10 $ I(

.'%' ). h.# )h% ,"# &, "4"(s) 4'")y " %')!"# .'!% . Q N s %9%')% .()h% ,"# Th% $.).( h.*%%' s h.'


17/41



1"2 Ene$y=

I( $%!h"(!s s %(% "s 5!","!)y . .(4 *.':6 U()s . E(%'4y "(

.': "'% s"$% E(%'4y %9s)s ( )*. .'$s ("$%#y Potental Ene$y "(

?net! Ene$y

1"2"1 Potental Ene$ys ,.ss%ss% y " .y &% ). )s ,.s).( '%#")% ).

.)h%' .y .' . ,"')s . )h% s"$% .y &(%' )h% "!).( . " .'!% .' .'!%s)%((4 ). "#)%' )h%' '%#")% ,.s).( F.' %9"$,#% " .y *h!h s "##.*%

). "## ).*"'s %"')h $"y % $"% ). . *.': h%(!% %.'% ) %4(s ). "## ),.ss%ss%s ,.)%()"# %(%'4y .' %(%'4y &% ). )s ,.s).( '%#")% ). %"')h

F *

A !.$,'%ss% s,'"# s,'(4 h"s ,.)%()"# %(%'4y %!"&s% ) s "##.*% ).

'%s&$% )s &(s)'"(% .'$ ) !"( % $"% ). . *.': L:%*s% !.$,'%ss%

"' ,.ss%ss%s ,.)%()"# %(%'4y Th% %(%'4y s).'% ( " ,%!% . !."# s ,.)%()"#%(%'4y "( &(%' ".&'"#% !.().(s )h% ").$s . )h% !.(s))&%()s . )h%

!."# "( ").$s . .9y4%( . )h% "' *## '&sh ).4%)h%' "( ,'.&!% h%") *h!h

$"y % !.(%')% (). *.': I " .y . :4 *%4h) s "##.*% ). "## '.$"( %#%").( L2 ). "( %#%").( L1 )h% !h"(4% ( ,.)%()"# %(%'4y

PE ; PE 2- PE 1; L2 V L17

Th% &() . ,.)%()"# %(%'4y s ?lo$ams mete$M>S7 "( Ne0ton met$eSI7

1"2"& ?net! Ene$y. " .y s &% ). )s %(4 ( $.).( *)h '%s,%!) ). "(.)h%'

.y A :#.4'"$ . *")%' ") '%s) ") " h%4h) . 100 $%)'%s ".% #%%# . )h%

s%" ,.ss%ss%s 100 :4$ . ,.)%()"# %(%'4y "( )hs *")%' s "##.*% ). "##'%%#y ). )h% #%%# . )h% s%" *)h.&) .(4 *.': .( )h% *"y ) *## ( %%'y

,.s).( . )s "## ,.ss%ss 100 :4$ . %(%'4y &) "s ) %s!%(s )s ,.)%()"#

%(%'4y *## $(sh "( )h% '%$"(%' . 100 :4$ *## % s).'% ( *")%' "s

net! ene$y h%( )h% 1:4 . *")%' *. h"% "##%( 2K $%)'%s )s

,.)%()"# %(%'4y *. % '%&!% y 2K :4$ ). % .(#y QK :4$ "( )s

:(%)! %(%'4y *. )h%( % 2K :4$ s. )h") ).)"# s QK :4$ P.)%()"#

E(%'4y7 2K :4$ >(%)! E(%'4y7 ; 100 :4$

A .y . *%4h) * :4 $.(4 *)h " %#.!)y ,.ss%ss%s " !%')"("$.&() . :(%)! %(%'4y >E7 *)h '%%'%(!% ). %"')h 4'")").("# .'!%

>E ; * 2/24

Th% &() . >E s "#s. :4$ ( M>S "( N%*).( $%)'% ( SISO)h%' .'$s . %(%'4y "'% "#s. %'%() $"(%s)").(s . )h%s% )*. .'$s

F.' %9"$,#% E#%!)'!)y s).'% ( " C","!).' h"(4 " C","!)"(!% . C

F"'"s "( !h"'4% ). " .#)"4% . .#)s s " P.)%()"# E(%'4y "( )s "#&%

A-1:

h

PE3m

h

PE36

$a'tatonal

Potental

Ene$y


18/41



s ZC2.%s S$#"'#y )h% E(%'4y ( "( I(&!).' h"(4 I(&!)"(!% . L

%('y "( ,"ss(4 "( %#%!)'!"# !&''%() . I A$,s7h"s " >(%)! E(%'4y %+&"#). ZLI2.%s

A## .)h%' .'$s . %(%'4y s&!h "s M"4(%)! L4h) %)! "'% s$#"'#y%9,#"("#% ( )%'$s . P.)%()"# .' >(%)! E(%'4y

1": Inte$nal Ene$y=Th% $.#%!%s . "## s&s)"(!%s "'% !.()(&.&s#y ( $.).(

Th% $.%$%() . $.#%!%s s $.'% ( 4"s%s )h"( ( #+&s E%( *h%( " 4"ss s).'% ( " !#.s% %ss%# "( s s)"4("() )h") s (.) $.(4 ) ,.ss%ss%s "

!.(s%'"#% "$.&() . ()%'("# >(%)! E(%'4y &% ). $.).( . )s $.#%!%s

*)h( )h% #$)s . )s !.()"((4 %ss%# I( ").( . )h% I()%'("# >(%)!

E(%'4y s&s)"(!%s "#s. h"% I()%'("# P.)%()"# E(%'4y &% ). )h% '%#")%,.s).( . )h%' $.#%!%s Th&s )h% I()%'("# E(%'4y E . " s&s)"(!% $"y

% %(% "s )h% "#4%'"! s&$ . I()%'("# >(%)! E(%'4y "( I()%'("#

P.)%()"# E(%'4y . )s $.#%!%s

Th% ()%'("# %(%'4y . s&s)"(!% (!'%"s%s *)h (!'%"s%s . )%$,%'")&'% .

s&s)"(!% &% ). (!'%"s%s . $.#%!"' "!))y Th&s I()%'("# E(%'4y s "&(!).( . T%$,%'")&'% "( )s "#&% (!'%"s%s .' %!'%"s%s y "(4 h%") ).

.' s&)'"!)(4 h%") '.$ )h% s&s)"(!%

1"5 To$ue%

T.'+&% s " $%"s&'% . )h% s)'%(4)h %(4 &s% ( )&'((4 .' "))%$,)(4 ).

)&'(7 s.$%)h(4

A !.$$.( %9"$,#% s )h") . " s,"((%' %(4 &s% ). $.% " (&) A .'!% s

%(4 ",,#% ") .(% %( . )h% s,"((%' Th") .'!% s $),#% y )h%s)"(!% %)*%%( ) "( )h% )&'((4-,.() *h!h ( )hs !"s% s )h% !%()'% .

)h% (&)7 ). 4% " $%"s&'% . )h% ).'+&% *h!h s %(4 ",,#% Ths s%%$s ).% )h% s"$% "s .' *.': *h!h s "#s. " .'!% %(4 $),#% y " s)"(!%&) #..: !#.s%#y ( )h% %().( .' ).'+&% )h%'% s (. $%().( . )h% .'!%

$.(4 "s )h%'% s ( )h% # %().( .' *.':

S. )h%y "'% %'%() )h(4s %%( )h.&4h )h% &()s "'% )h% s"$% "( (. *.':s .(% &()# ( )hs !"s% )h% s,"((%' $.%s - "( %%( )h%( ) s " $"))%' .

h.* "' )h% .'!% $.%s "( (.) )s s)"(!% '.$ )h% !%()'%

Th% SI ,'%%''% &() .' ).'+&% s (%*).( $%)'%s N$H "( .' *.': s

.%s H

1"4 )+e!f! Ene$y %

Ths s " $%"s&'% . )h% "$.&() . %(%'4y !.()"(% ( " &() +&"())y . s.$%s&s)"(!% Th% &() +&"())y $"y % %)h%' . $"ss .' . .#&$% F.' &()

$"ss &s&"##y '%%''% ). "s )+e!f! Ene$y I)s &()s "'% /:4H .' :/:4HF.' &() .#&$% &s&"##y '%%''% ). "s Calo$f! alue &()s s&!h "s :/$[H

.' M/$[H sh. % &s%

1"16 Me!han!al Eu'alent Of Heat= %") "( .': "'% $&)&"##y !.(%')#%'.$ .(% .'$ (). "(.)h%' I( " h%") %(4(% )h% h%") ,'.&!% y !.$&s).(

A-15


19/41



. )h% &%# &s% s !.(%')% (). )h% *.': .(% y )h% %(4(% h%( )h%

'":%s "'% ",,#% ). )h% *h%%#s . " $.(4 )'"( ( .'%' ). '(4 ) ). '%s))h% :(%)! %(%'4y . )h% )'"( s !.(%')% (). h%") ") )h% '&(4 s&'"!%s .

)h% '":% #.!:s "( *h%%#s .' )h% *h%%#s s: )h% h%") s ,'.&!% ") )h%

'&(4 s&'"!%s . *h%%#s "( '"#s C"'% %9,%'$%()s h"% sh.*( )h") "

!%')"( %()% (&$%' .' ..) ,.&( . *.': s %+&"#%() ). .(% &() .h%")

I( B')sh U()s s QQ8 )# .' 1 B)&

"( ( $%)'! &()s 18Q >#..%s ; 1 >#.!"#.'%s

1 >#.!"#.'%s ; 2Q :4-$

1"11 HEAT AND HEAT TRAN)FER

1"11"1 Heat

%") s %#%% ). % 5" $.% . $.).(6 I) s s&,,.s% )h") " .y

,.ss%ss(4 h%") h"s )s ,"')!#%s .' $.#%!%s ( " s)")% . $.).( )h% '")% .$.).( (!'%"s(4 "s )h% .y 4%)s *"'$%' "( $(sh(4 "s )h% .y !..#s

As ). )h% !h"'"!)%' . $.).( . )h% $.#%!%s ) $"y % $"4(% ). % "(.s!##").'y $.).( ( )h% !"s% . s.#s "( #+&s &) ( )h% !"s% . 4"s%s )

s s&,,.s% ). % " $.).( . )'"(s#").(

I) s .&( )h") "## )h% ,h%(.$%(.( . %") $"y % %9,#"(% y )hs )h%.'y

F.' %9"$,#% ) s *%## :(.*( )h") ( 4%(%'"# )h% %%!) . h%") .( $"))%' s ).

%(#"'4% ) A ,%!% . '.( *h%( h%")% 4%)s #.(4%' *%' "( )h!:%' due tothermal eansion7 N.* ) s (")&'"# ). %9,%!) )h") )h% $.#%!% . '.(

h"% $.'% $.).( "s )h% '.( 4%)s h.))%' )h%y *## '%+&'% $.'% '..$ "( *##

)h%'%.'% ,&sh .(% "(.)h%' &')h%' ","') "( !.(s%+&%()#y !"&s% )h% *h.#%

.y ). 4%) #"'4%' &s) "s " !'.* . ,%.,#% )":% &, $.'% s,"!% *h%( )h%y.s)#% .(% "(.)h%' )h"( )h%y . *h%( s)"((4 s)## .' *h%( .s)#(4 ). " #%ss

%9)%()

F.' )h% ,&',.s% . %9,#"((4 h.* h%") s )'"(s$))% )h'.&4h s,"!% )h% #"))%'

s s&,,.s% ). % ##% .' ,%'$%")% *)h "( (s#% $,.(%'"#% "($"4("'y7 #& !"##% the ether*h!h )":%s &, )h% $.).( . )h% $.#%!%s

. " .y "( )'"(s$)s )h%$ ). )h% $.#%!%s . .)h%' .%s ( s,"!% &s) "s

*h%( " .y s $"% ). $.% &, "( .*( ( " )'.&4h . *")%' " s$#"'$.).( s 4%( ). " !.': #.")(4 ( )h% *")%' ") )h% s"$% s)"(!%

D%'%() &()s . $%"s&'%$%() . h%") "'% "s 4%( %##.*

I( B')sh Sys)%$=B')sh Th%'$"# U() BTU7=

Th% +&"())y . h%") '%+&'% ). '"s% )h% )%$,%'")&'% . .(% ,.&( . *")%'

)h'.&4h 1\F s %(% "s " BTU

I( M>S U()s=C%()4'"% %") U() CU7=

Th% +&"())y . h%") '%+&'% ). '"s% )h% )%$,%'")&'% . .(% ,.&( . *")%'

)h'.&4h 1\C s %(% "s " CU

A-14


20/41



Th% +&"())y . h%") '%+&'% ). '"s% )h% )%$,%'")&'% . .(% :#.4'"$s .*")%' )h'.&4h 1\C s %(% "s .(% >#.-C"#.'%

S(!% )h% "$.&() . h%") '%+&'% ,%' %4'%% !%()4'"% "'%s ") %'%()

,.()s .( )h% )%$,%'")&'% s!"#% " $.'% ,'%!s% %().( s )h% "$.&() .

h%") '%+&'% ). '"s% )h% )%$,%'")&'% . .(% :4 . *")%' ()"##y ") 1K! ).1KK! *h#% $"()"(% ") !.(s)"() ,'%ss&'% . Q@0$$ . h4

1 >!"# ; 220K CU ; 3?@? BTU

Th% &() .' h%") ( SI sys)%$ s $%"s&'% ( .%s 71 >!"# ; 18Q .%s ; 18Q >#. .%s

1"11"& )+e!f! Heat. " s&s)"(!% $"y % %(% "s )h% "$.&() . h%") )h") $&s)

% s&,,#% ). )h% s&s)"(!% ). '"s% )h% )%$,%'")&'% . &() $"ss . )h%s&s)"(!% )h'.&4h .(% %4'%% h%( " .y s h%")% )h% h%") %(%'4y s &s%

). s,%% &, )h% ()%'("# $.).( . )s $.#%!%s "( "#s. ). ,'.% )h% *.':

(%!%ss"'y ). %9,%( )h% .y I( " s.# .' " #+& )h% "$.&() . %9,"(s.(

s %'y s$"## "( )h% *.': . %9,"(s.( s s$#"'#y s$"## h%( " 4"s sh%")% %9,"(s.( s !.(s%'"#y $.'% "( "#&%s . s,%!! h%") *##

%,%( .( (")&'% . h%")(4 ,'.!%ss % *h%)h%' )h% h%")(4 s ") C.(s)"().#&$% .' ") C.(s)"() P'%ss&'% Th&s 4"s h"s " )*. $,.')"() )y,%s .

S,%!! %") ("$%#y=

17 S,%!! %") ") !.(s)"() .#&$% C727 S,%!! %") ") !.(s)"() ,'%ss&'% C,7

1"11"&"1 )+e!f! Heat at Constant olume= C.(s%' 1 :4 . 4"s %(4 h%")% ( "

!#.s% %ss%# s. )h") (. %9,"(s.( . 4"s s "##.*% Th% (&$%' . :!"#'%+&'% ). '"s% )h% )%$,%'")&'% . 1 :4 . 4"s )h'.&4h 1 0C &(%' )h%s%

!.().( s !"##% )h% S,%!! %") ") C.(s)"() .#&$% "( s %(.)% yC

I( )hs !"s% )h%'% s (. *.': &% ). %9,"(s.( . 4"s %!"&s% )h% 4"s s

!.()"(% ( !#.s% %ss%# "( "## )h% h%") s&,,#% s &s% .(#y ). (!'%"s% )h%I()%'("# E(%'4y % >(%)! E(%'4y "( P.)%()"# E(%'4y . $.#%!%s . )h%

4"s

1"11"&"& )+e!f! Heat at Constant P$essu$e= C.(s%' 1 :4 . 4"s %(4 h%")% ( "!y#(%' ))% *)h " $."#% ,s).( *h!h %9%')s " !.(s)"() ,'%ss&'% .( )h%

4"s h%( )h% 4"s s h%")% ) *## %9,"( "( $.% )h% ,s).( )h'.&4h s.$%

s)"(!% ( )hs !"s% Th%'%.'% ( )hs !"s% ( ").( ). )h% h%") '%+&'%

.' (!'%"s(4 )h% :(%)! %(%'4y . )h% $.#%!%s &')h%' h%") $&s) % "%). ,%'.'$ )h% *.': . $.(4 )h% ,s).( )h'.&4h )h% s)"(!% Th% S,%!!

%") ") C.(s)"() P'%ss&'% s %(.)% y C,.

The value of the secific heat of gas at constant ressure will therefore

always be greater than that at constant volume by the amount of eansivework done.

A-&6


21/41



Th% &() . s,%!! h%") ( M>S Sys)%$ . &()s s :!"#/:4 0C "( ( )h% SI

sys)%$ . &()s ) s :/ :4 >

1"11"&"( Rato of s+e!f! heats= Th% '"). . )*. s,%!! h%")s C, "( C . "(y

4%( 4"s s "ss&$% ). % !.(s)"() I) s %9,'%ss% y )h% sy$.# 4"$$"7 I) s !"##% G"s C.(s)"() "( s "( &(%'s"# !.(s)"() .' %"#

4"s%s I) h"s (. &()s .' $%"s&'%$%()

; C,/CF.' "' C,; 02 :!"#/:4

0C .' 1003K :/ :4 0>

"( C; 01Q2 :!"#/:40C .' 0Q1@K :/:4 0>

h%(!% ; 02/01Q2 ; 1

1"11"( Enthal+y 7H9 .' Total Heat.' Heat Content%E()h"#,y s (.)h(4 &) ).)"#

h%") %(%'4y !.()%() ( " s&s)"(!% I) s %(.)% y "( s %(% "s.##.*s=

; E P/7 :!"#

h%'% E s )h% I()%'("# E(%'4y P s )h% As.#&)% P'%ss&'% s )h% .#&$%( $3"( ; 2Q :4-$

1"11"* HEAT TRAN)FER %

I( B.#%' h%") %(%'4y s '%#%"s% '.$ )h% !.$&s).( . .ss# &%#s "( )h%

h%") s )'"(s%''% ). %'%() #&s ( )h% sys)%$ "( " ,"') . ) s #.s) .' #%).&) "s &(&)#%))#% '.$ )h% *")%' $$%")%#y ( !.()"!) *)h

*"##s . )h% :%))#% h%( )h% '% s ,&) .&) )h% *")%' s)"')% !..#(4 .*( "s

)'"(s%' . h%") ( *")%' .!!&'s y Con'e!ton'.$ !%()'% . )h% >%))#% ). )h%*")%' #"y%' $$%")%#y ( !.()"!) *)h >%))#% *"##s "( y Condu!ton*)h( *"##s . )h% >%))#% O&)%' s&'"!% . )h% >%))#% )'"(s%'s h%") ). )h%

s&''.&((4s y *"y . Con'e!ton Radaton"

I( B.#%' 4%(%'"##y )h% h%") )'"(s%' )":%s ,#"!% ( "## )h% )h'%% $.%s . h%")

)'"(s%' ,'.!%ss ("$%#y C.(&!).( C.(%!).( "( )h% R"").(

1"11"*"1 Condu!ton%

A-&1


22/41



C.(&!).( s )h% ,'.!%ss . )'"(s%' . h%") )h'.&4h s.#s '.$ .(% ,"') .

)h% .y ). )h% .)h%' y ,hys!"# !.()"!) *)h.&) )h% $.#%!%s $.(4 &)$,"')(4 '").( '.$ .(% $.#%!% ). )h% (%4h.&'(4 .(%

I( " B.#%' )h% *")%' )&%s "'% %9,.s% ). '% Th% h%") )'"%#s y C.(&!).(

'.$ .&)%' s&'"!% ). ((%' s&'"!% . *")%' )&%s "( )h%( )'"(s%'s ). *")%'

") !%()'% . )h% )&%s "( ( )h% '&$ '.$ )h% *")%' $$%")%#y ( !.()"!)*)h ((%' s&'"!% . )h% )&%s y !.(%!).( I( " $%)"# )h% h%") )'"(s%'

)":%s ,#"!% y ,"ss(4 .( h%") '.$ ,"')!#% ). ,"')!#% y !.()"!) *)h.&) "(y

,hys!"# $.%$%() . )h% ,"')!#%s )h%$s%#%sTh% +&"())y . h%") !.(&!)% %,%(s .(=

" )h% %'%()"# )%$,%'")&'% %)*%%( !.$&s).( !h"$%' "( )h% *")%'

(s% )h% )&% )h% )h!:(%ss . )h% )&%

! s&'"!% "'%" . )h% )&%

)h% !h"'"!)%'s)!s . )h% $%)"# "(% )h% !#%"(#(%ss . )h% s&'"!%

1"11"*"& Con'e!ton%

Ths ,'.!%ss !"( .!!&' .(#y ( #&s .' 4"s%s Ths ,'.!%ss . h%") )'"(s%')":%s ,#"!% *h%( )h% $.#%!%s "'% s,#"!% ,hys!"##y Th% #& .' 4"s

*h%( h%")% %9,"(s %!.$%s #%ss %(s% "( '"s%s &, !"&s(4 $.%$%()

"( "##.*(4 )h% !.#%' "( $.'% %(s% 4"s .' #+& ). '%,#"!% ) I( )h%B.#%' )h% h%") '.$ )&% $%)"# 4.%s ). *")%' #.*(4 (s% S$#"'#y *h%(

4"s .' #+& s h%")% ) %9,"(s %!.$%s #%ss %(s% "( 's%s &, !"&s(4

$.%$%() "( "##.*(4 )h% !.#%' "( %(s%' 4"s .' #+& ). '%,#"!% )

M"(#y ( S&,%'h%")%' R%h%")%' "( E!.(.$


23/41



E/am+les

1" Kueston% D%(% "s.#&)% )%$,%'")&'% s!"#%

Fe,-55; Au-547

Ans0e$% As.#&)% )%$,%'")&'% s!"#% .' >%#( )%$,%'")&'% s!"#% s "s% .( "s.#&)%


24/41



Ans0e$%

F'.$ )h% '%#").(

P11/ T1; P22/ T2% h"%

P1; 100 :N/$

2

!.(s%'(4 ,'%ss&'% 4%( ( As.#&)%7T1; 11K 2Q3 ; 388 > T2; 180 2Q3 ; K3 >

2; 1/12

O( s&s))&).( . "#&%s *% 4%)100 9 1/ 388 ; P29 1/ 12 9 K37

.' P2; 1*61 N8m&101 "'7 "s.#&)%

." Kueston% C"#!")% )h% $.#%!"' .#&$% . "## 4"s%s ") 200 :N/ $2"( 30^C

A!!.'(4 ). )h% !h"'"!)%'s)! %+&").( . " 4"s *% h"% , ; $RT *h%'% , s )h%,'%ss&'% . )h% 4"s ( N/$2 s )h% .#&$% . $"ss $ :4 . 4"s ( !& $%)'% R s

)h% !h"'"!)%'s)! 4"s !.(s)"() "( T s )h% "s.#&)% )%$,%'")&'% . )h% 4"s (>%#(

Ans0e$%

I $ s )h% $.#%!"' $"ss )h%( *## % $.#%!"' .#&$% . )h% 4"s "(

$R ; 8313 :/ :4 $.#% >% h"% P ; 200 :N/ $2 T ; 2Q3 30 ; 303 >

Th%'%.'% 200 9 ; 8313 9 303

; 8313 9 3037 / 200 ;1&".42 m(

2" Kueston% A s)%%# !y#(%' . QQ #)'%s . !","!)y !.()"(s CO 2") 2Q D%4 C "(,'%ss&'% . 110 ")" C"#!")% )h% *%4h) . 4"s !.()"(% ( )h% s)%%# !y#(%'

)oluton%%'%

.#&$% ; QQ #)%'s ; QQ 9 10-3$3

P'%ss&'% ; 110 ")" ; 110 :4/!$2" ; 110 9 0?81 ; 10Q?1 "' "

; 10Q?1 9 102:N/ $2

T%$,%'")&'% ; 2Q.C ; 2Q 2Q3 ; 300 >

% :(.* MR ; 8313 :/:4 $.# > "( M . CO2; :4

S, G"s !.(s)"() R . CO2; 8313/ ; 018? :/ :4 >

F'.$ )h% '%#").( P ; $RT

10Q?1 9 1029 QQ 9 10-3; $ 9 018? 9 300

.' $ ; 10Q?1 9 1029 QQ 9 10-37/ 018? 9 3007 ; 1*"2.

:" Kueston% D%(% " (%* )%$,%'")&'% s!"#% s"y .D ( *h!h )h% .#(4 "('%%


25/41



)h% C%()4'"% s!"#% Th% .D '%"(4 .( )hs s!"#% s " !%')"( (&$%' . %4'%%s .(

" !.''%s,.((4 "s.#&)% )%$,%'")&'% s!"#% h") s )hs "s.#&)% )%$,%'")&'% ").D_

)oluton% %'% )h% '%%


26/41



E/am+les fo$ +$a!t!e

1" Kueston% 7D%'%()")% %)*%%( )h% $"(.$%)%' "'.$%)%'

7 D%'%()")% %)*%%( ,'%ss&'% 4"&4% "( "!&&$ 4"&4%

&" Kueston%Fll the a+ 7O!t-4.9

" 1$3; bbbbC&! F%%)

1: ; bbbbbbb P

! 1# ; bbbbbbbb G'"(

1000 !$3; bbbbbb $3

% 1$3/h' ; bbbbb !$

1 "' ; bbbbbb #/s+ (

4 1$3/s%! ; bbbbbb !&! %%)/sh 1: h ; bbbbb >!"#

(" Kueston% Fll n the a+ 7Au-429

7 1 :4/!$2; --------- #/$2 1 "' ; --------- #/s+ )

7 T%$,%'")&'% > ; T%$, ----------- ----------T%$,%'")&'% R ; T%$, ---------------- --------------

7 1 $%)'! h.'s% ,.*%' ; --------- *"))s1 B')sh h.'s% ,.*%' ; ------------- *"))s

*" Kueston% "7 C.(%') )h% .##.*(4 '%"(4 . ,'%ss&'% ). "'

7 800 :P" 7 10 ")$ 7 2 M," 7 112000 N$2 7 200 >N/$2

7 7 A "!&&$ 4&"4% .( !.(%(s%'s '%"s @20 $$ . $%'!&'y "( ") )h% s"$%

)$% "'.$%)%' '%"s Q0 $$ . $%'!&'y h") s )h% "s.#&)% ,'%ss&'% ( )h%!.(%(s%' ( M,"7 F( )h% h%") %+&"#%() . *.': .(% ( > *h%( " *%4h) . K00 :4 s

'"s% )h'.&4h h%4h) . @000 !$s

7 A ,'%ss&'% 4"&4% '%"s 23 M," "( "'.$%)%' '%"s ?0 >," !"#!")%"s.#&)% ,'%ss&'% ( ,"s!"# Fe,-&66&9

." Kueston% A #.!.$.)% %(4(% h"(4 *%4h) . 3K00 :4 '&(((4 ") Q2 :$,h,.ss%s !%')"( s).'% %(%'4y &% ). )h% $.).( D%)%'$(% )h% s).'% %(%'4y ( : "(

:

7 A )'"( *%4h(4 1K0 MT s ,#% &, " 2 %4'"% QK > %(4(% T'"(

'%ss)"(!% s 8QK0 >4 A) *h") s,%% )h% )'"( s '&(((4 Fe,-&66&9

2" Kueston% Th% ,'%ss&'% . " 4"s s&,,#% ). "( %(4(% s $%"s&'% "s 100$$ .

*")%' 4"&4% *h%( "'.$%)%' '%"s QK@ $$ . $%'!&'y D%)%'$(% )h% .#&$% .1K:4 . )hs 4"s )s )%$, s 8K0C Th% 4"s !.(s)"() . )h% 4"s s 0@8@ : :4 >

7Au-&66&9

A-&2


27/41



:" Kueston%A .y *%4h)s K0:4 .( %"')h F( )s *%4h) .( )h% "7 M..( *h%'%

4'")").("# "!!%#%'").( s 1QM/s%!27 S&( *h%'% 4'")").("# "!!%#%'").( s2Q0 M/s%!2

5" Kueston%A )h%'$.$%)%' $$%'s% ( #& )h% "#&% . )%$,%'")&'% ( F "( C

sh.*s s"$% *h") *## % "#&% . )%$,_ E9,'%ss )hs "#&% . )%$, ( %4R %4>

4" Kueston%A "!&&$ 4"&4%s '%"s )h% "!&&$ ( " !h"$%' "s 300 MM . 4*h") s )h% "s.#&)% ,'%ss&'% ( )h% !h"$%' )h% ")$.s,h%'! ,'%ss&'% s Q@0 $$

. 4 Th% s,%!! *%4h) . $%'!&'y ") )hs )%$, s 13KK0 :4/M 3

7Fe,"419"

16" Kueston% A $"(.$%)%' .(% ). " 4"s !y#(%' (!")%s 20 :P" *h#% )h%

"'.$%)%' '%"s Q@0 $$ . $%'!&'y h") *## % )h% '%"(4 . )h% $"(.$%)%' )h% "'.$%)'! ,'%ss&'% '.,s ). Q30 $$ $%'!&'y_

11" Kueston%A s)%"$ ,.*%' ,#"() %%#.,s @0 : h") s )h% %+&"#%() .)hs ,.*%' ( )h%'$"# &()_

1&" Kueston% Th% 4"s &s% ( 4"s %(4(% )'"# *"s )%s)% ( " B.ys !"#.'$%)%'

Th% ,'%ss&'% . 4"s s&,,#y *"s Q0 $$ . *")%' !.#&$( h") s )h% "s.#&)%,'%ss&'% . )h% 4"s )h% "'.$%)'! ,'%ss&'% s Q@0 $$ . $%'!&'y_

A-&:


28/41



APPENDI

HEAT TRAN)FER CALC#LATION)

Th% 4%(%'"# %+&").( .' h%") #.* '")% y "(y . )h% ".% )h'%% $.%s .

h%") )'"(s%' '.$ .(% $%" ). .)h%' $"y % *'))%( "s

3 #) t

h%'% + ; h%") #.* '")% ( >C"#/h'

S ; S&'"!% "'%" (.#% ( )h% h%") )'"(s%' ( $ 2

) ; T%$,%'")&'% %'%(!% !"&s(4 h%") #.* ( \C

U ; O%'"## h%") )'"(s%' !.%!%() ( >!"#/$2/h'/\C

; 1/R *h%'% R s .%'"## '%ss)"(!%

Condu!ton%

I " #") ,#")% s h%")% .( .(% s% "( !..#% .( .)h%' s% h%") *## #.*

'.$ h.) s% ). )h% !.# Th% h%") #.* '")% + !"( % %9,'%ss% "s %#.*=

3 ?) 7t1 t&98l

h%'% + ; '")% . h%") #.* V >C"#/h'> ; Th%'$"# !.(&!))y .' 1 !$ )h!:(%ss V >!"#/$2/h'/\C

S ; %")(4 s&'"!% ( $2

) ; )%$,%'")&'% %'%(!% !"&s(4 h%") #.* )1V )27 ( \C# ; #%(4)h .' )h!:(%ss . )h% ,#")% ( !$

>/# s %9,'%ss% "s !.(&!)"(!% "( h%(!% #/> s )h% '%ss))y

Con'e!ton%

%") )'"(s%' y !.(%!).( %)*%%( " #& "( " s.# s&!h "s ( " .#%'

)&% s %9,'%ss% "s %#.*=

! 3 #!) t 37

h%'% +!; '")% . h%") #.* y !.(%!).( ( >C"#/h'

U ; C.(%!).( #$ !.(&!)"(!% ( >!"#/$2/h'/\C

S ; h%") )'"(s%' s&'"!% ( $2

) ; )%$,%'")&'% %'%(!% %)*%%( #& : )%$,%'")&'%

"( s.# s&'"!% )%$,%'")&'% ( \C

Radaton%

R"").( %$))% y " .y %,%(s &,.( )s s&'"!% "'%" "( )%$,%'")&'%

Th% '%#").(sh, %)*%%( )h%$ s 4%( y S)%"(-B.#)


29/41



F.' .%s .)h%' )h"( #"!: .%s *h.s% %$ss)y *## % #%ss )h"( 1 )h%

.'$" *## % !h"(4% "s

3 E) T*

*h%'% E s %$ss)y . )h% .y

I *% !.(s%' )*. ,"'"##%# ,#"(%s . (()% s


30/41



Ms!ellaneous Nume$!al P$o,lems on Elementa$y Con!e+ts

E/am+le%1A %')!"# )"(: !.()"(s *")%' Th% h%4h) . !y#('!"# )"(: s 120 !$

"( "$%)%' s 30 !$ Th% )"(: s 3/T# . *")%' I " !&! ,%!% . '.( .

10!$ s%s s '.,,% ( )h% )"(: !"#!")% )h% 's% ( h%4h) . *")%' #%%# "(("# h%4h) . *")%' ( )h% )"(: 7Fe, 14559

)oluton%As )h% )"(: s d )h # )h% h%4h) . *")%' ( )"(: ; 120 a d ; ?0 !$

R"&s . )h% !y#('!"# )"(: ' ; / 2 ; 30/ 2 ; 1K !$

.#&$% . !&! ,%!% . '.( ; 10 a 10 a 10 ; 1000 !$3

Th% !&! ,%!% . '.( *h%( '.,,% ( )h% )"(: *## s,#"!% )s %+&"# .#&$% .*")%'

I )h% h%4h) . )h% *")%' 's%s y s"y h !$ ")%' )h% ,%!% . '.( s '.,,%

Th% (!'%"s% .#&$% . *")%' ( )h% !y#(%' ; a '2a h ; a1K2a h; Q0@8@ a h !$3

N.* Q0@8@ a h !$3

; 1000 !$3

O' h ; 1"*1 !mA( ("# h%4h) . *")%' ( " )"(: ; ?0 11 ; 41"*1 !m

E/am+le%&A &%# s).'"4% )"(: s ( )h% .'$ . " !y#(%' 2@ $ " *)h .(% %(

h%$s,h%'% "( )h% .)h%' %( ,#"( C"#!")% )h% !","!)y . )"(: ( #)'% "( ( :4 ) !.()"(s .# h"(4 S, 4'")y 0?0 L%(4)h . )h% !y#('!"# ,.').( s @0 $

A#s. %)%'$(% )h% "'%" . )h% sh%%) $%)"# &s% ( !.(s)'&!).(

)oluton% G%(

D" . !y#(%' ; 2@ $ ' ; 13 $

L%(4)h . !y#('!"# ,.').( ; @ $O(% %( h%$s,h%'% .(% %( ,#"(

S,%!! 4'")y . .# ; 0?

.#&$% . h%$s,h%'!"# %( ; Z a7/37 '3; (2/3)'3

.#&$% . !y#('!"# ,.').( ; '2 L

T.)"# .#&$% ; '2 L (2/3)'3

;1372 a @ 2/37 1373

; 318@ @0 ; 3@@ $3

Th% !","!)y . )h% )"(: ; 3@@ a 1000 ; (2*26 lte$s"N.* s,%!! 4'")y ; %(s)y . .#/ %(s)y . *")%'

D%(s)y . .# ; s,%!! 4'")y a %(s)y . *")%' ; 0? a 1000 :4/ $3

; ?00 :4/ $3

Th% !","!)y . )h% )"(: ; 3@@ a ?00 ; (&51*

A-(6


31/41



A'%" . sh%## $%)"# &s% ; A'%" . h%$s,h%'% A'%" . !y#('!"# ,.').(

A'%" . ,#"( %(

; 2'2 2'L '2 ; 21372 2a 13 a @ 1372

; 10@2 ?00 K31 ; 2*"4( m&

E/am+le%( h") *## % )h% .#&$% . %"')h '%$.% y 44(4 )h% *%## . 2K

$%)'% Th% " . )h% *%## s 10 $%)'% I )h% %"')h s &(.'$#y s,'%" .%' "( "'%"

. 1K0 $2 h") *## % 's% ( #%%# _ Ass&$% )h% "'%" ). % s+&"'%

7 Fe," 144.9

)oluton%.#&$% . %"')h '%$.% ; / 7 a 2a h ; / 7 a 102a 2K ; 1?@3K $3

L%) &s "ss&$% )h% 's% ( #%%# s h $ *h%( )h% %"')h s &(.'$#y s,'%"

Th% .#&$% . )h% %"')h ; A'%" a h%4h) ; 1K0 a h

1K0 h ;1?@3K.' h ; 1?@3K/1K0 ;1"(64 m"

E/am+le%* C"#!")% )h% "'%" . "( %##,)!"# $"(h.#% h"(4 $".' "9s . @0 !$

"( $(.' "9s . K0 !$ 7Fe,"144.9

)oluton% A'%" . %##,s% ; a " a h%'% " ; s%$ $".' "9s "( ; s%$ $(.' "9s

G%( $".' "9s ; @0 !$ "( $(.' "9s ; K0 !$

S%$ $".' "9s " ; 30 !$ "( s%$ $(.' "9s ; 2K !$A'%" ; a 30 a 2K ; &(.2"&6 !m&

E/am+le%.A h%", . !."# s ( )h% .'$ . !.(% "s% "$%)%' . *h!h s K0 $%)%' h%4h) s 12 $%)%'s F( .&) )h% T.(("4% . !."# ( )h% h%", "s !."# s h"(4

: %(s)y . 11 ).(s / 1K $3 71.-2-14459

)oluton%%'%B"s% "$%)%' . !.(!"# h%", . !."# ; K0 $

%4h) . !.(!"# h%", . !."# ; 12 $

B: %(s)y ; 11 T.(s / 1K $

3

.#&$% . !.(% ; A'%" . "s% a P%',%(!"' h%4h)/ 3

; / aK02a 12/ 3 ; Q8K3?8 $3

%4h) . )h% !."# h%", ; 11/ 1K7 a Q8K3?8 ; .:.4".5 Tons

A-(1


32/41



E/am+le%2 A s)%%# ,,% 3 $%)%'s #.(4 *)h "( .&)s% "$%)%' . 31QK $$ "(

)h!:(%ss . K2K $$ I %(s)y . $")%'"#s s Q@ 4$/ !! F( .&) )h% $"ss .,,%

)oluton%%'%L%(4)h . ,,% ; 3 $ ; 30 !$

O&)s% "$%)%' . ,,% ; D ; 31QK $$ ; 31QK !$

Th!:(%ss . ,,% ; K2K $$

I(s% "$%)%' . ,,% ; 31QK V 2 a K2K ; 212K $$ ; 212K !$

.#&$% . ,,% $")%'"# ; e/7 a L a D2- 27 ; e/7 a 30 a 31QK2V 212K27 ; 18@0K !$3

D%(s)y . )h% $")%'"# ; Q@0 4/ !!

M"ss . )h% ,,% ; 18@0K a Q@0 ; 112?3?8 4 ; 11"&4*

E/am+le%:A h.'


33/41



M"ss . *")%' $ ; 200 :4

I()"# )%$, . *")%' ; )I; 30.C

F("# )%$, . *")%' ; )0 ; 80.C

I(!'%"s% ( )%$,%'")&'% ` ) ; 80 V 30 ; K0.C

% :(.* )h") s,%!! h%") . *")%' CP; 18Q :/ :4.C

%") '%!%% y )h% *")%' ; $CP` ) ; 200 a 18Q a K0 ; 18Q0 :T$% )":%( ). h%") )h% *")%' f 1K :/ s%! ; 18Q0/ 1K ; 2Q?1333 s%!; 2Q?1333/ 3@00 ; :":.( hou$U()s . %#%!)'!)y !.(s&$% ; 1K a QQK3 ; 11"2( >H

Po0e$ of a +um+%Th% ,.*%' . " ,&$, '%( y s)%"$ *")%' .' "' s ). % .&( .&) "s &(%'

% :(.* )h") P.*%' ; '")% . *.': .(% *h%'% *.': ; .'!% a s)"(!% *h%'%.'!% ; P'%ss&'% a "'%"

In a +um+; the +ston s d$'en ,y the 0o$n su,stan!e 7"e" steam o$ 0ate$ o$

a$9 unde$ a +$essu$e th$ouh the lenth of the !ylnde$"

Th%'%.'% )h% .'!% "!)(4 .( )h% ,s).( *)h "( "'%" A '%( y )h% *.':(4s&s)"(!% &(%' " ,'%ss&'% P; P A"

N.* )h% *.': .(% y )h% ,s).( *h#% ) $.%s )h'.&4h )h% #%(4)h . )h% !y#(%' L( " s(4#% s)'.:% ; .'!% a s)"(!% ; P A LI )h% ,&$, $":%sN *.':(4 s)'.:%s ,%' $(&)% )h%( )h% ,.*%' . )h% ,&$, ; )h%

'")% . *.': .(% ,%' $(&)% ; P A L NI( SI &()s Ps ( N/ $2 Ls ( $ As ( $2"( Ns ( (&$%' . )h% s)'.:%s ,%'

$(&)% )h%( '")% . *.': .(% P A L N *## % (N $2 $ ; N-$/ $(

$2 $(; / $( ; / @0 s%! ; /@0 / s%! ; "))7

S. *% !"( s%% )h") )h% ".% '%#").( *h%( %9,'%ss% "s P A L N8 26 *## 4%&s )h% ,.*%' . )h% ,&$, ( ")) If P s taen n N8 m&; then the $esult 0ll ,e n

>"

T. ( .&) )h% h.'s% ,.*%' . " ,&$, *% !"( ( .&) )h% ,.*%' ( ")) "( )h%(

( .&) )h% P '.$ )h% '%#").( 1 HP 3 :(.":. >att"A#)%'(")%#y *% :(.* )h") 1 HP 3 :. -m8 se!"N.* )h% ,'%ss&'% Ps )":%( ( 8 !m& L%(4)h L( m "'%" A( !m&"( Ns (

(&$%' . s)'.:%s ,%' $(&)% )h%( '")% . *.': .(% P A L N8 26 *## % (

:4 !$2 $ ; :4-$/ s%!!$2 s%!

S. *% !"( s%% )h") )h% ".% '%#").( *h%( %9,'%ss% "s P A L N8 726 :.9 .'

P A L N8 *.66 *## 4% &s )h% ,.*%' . )h% ,&$, ( HP "s 1 P ; QK :4-$/s%!7

[Unless HP is asked, while finding out the power of a pump or an engine, always

work out in SI unit and find out the power in Watt or kilo Watt]

A-((


34/41



E/am+le%4 h") s )h% h.'s% ,.*%' %%#.,% ( " s$,#% s)%"$ ,&$, !y#(%'

200 $$ "$%)%' 300 $$ s)'.:% *)h ,&$, $":(4 K0 *.':(4 s)'.:%s ,%'$(&)% *)h s)%"$ ,'%ss&'% Q :4/!$24

7 Fe,"14559

)oluton%G%(

D" . ,s).( ; 200 $$ ; 20 !$L%(4)h . s)'.:% ;300 $$ ; 030 $

N ;K0 s)'.:%s /$(

P'%ss&'% P ; Q :4/ !$2

% :(.* P ; P a A a L a N / K00

%'% "'%" A ; e a 2/ ; e a 202/ ; 311@ !$2

P ; Q a 311@ a 030 a K0/ K00 ; :"((HP

E/am+le%16F( )h% P ") )h% sh") . )h% ,&$, '%+&'% ). #) K0000 #) . *")%'

,%' h.&' )h'.&4h " ).)"# h%" . 100 $%)%' Th% %!%(!y . )h% ,&$, s @0F()h% P . )h% $.).' *h!h '%( " ,&$, )h% %!%(!y . )h% $.).' s 80

7Fe, 14559

)oluton%

%'% ,&$, s!h"'4% ; K0000 #/ h' ; K0 $3/ h'

; K0/ 3@00 ; 0013? $3/ s

; hg ; 100 a 1000 ; 10K:4/ $2

P&$, % P&$, ;@0

P ") )h% sh") . )h% ,&$, ; / QK P&$,; 0013? a 10K7/QK a 0@07 ; (6"54 HP

s(!% $.).' % $.).' ; 80

P . $.).' ; 308?/ 080 ; (5"21 HP

E/am+le%1113@0 L)'%s . *")%' s ,&$,% (). )"(: ,%' $(&)% &(%' ,'%ss&'% .

11 :4/!$2 y ,&$, F( )h% P '%+&'% .' ,&$,(4 )h% *")%' Ass&$% (.

#.ss "( ,&$, %!%(!y s 8K

)oluton% %'%

; 13@0 #)'%s/$(&)% ; 13@ $3/ $( ; 13@/ @0 ; 0023 $3/s%! ; 11 :4/!$2; 11 a 10:4/ $2

; 8K

P ; a 7 / QK a ; 0023 a 11 a 107 / QK a 08K ; ."64

A-(*


35/41



E/am+le%1& D%)%'$(% )h% *.': ( .'!(4 K #)'%s . *")%' (). " %ss%# "4"(s) "

,'%ss&'% . 12 MN / $2

)oluton% As *% :(.*

.': ; &"())y . *")%' ( $3a ,'%ss&'% ( N/ $2

G%( K #)'%s . *")%' ; 000K $

3

P'%ss&'% ; 12 MN/$

2

; 12 a 10

@

N / $

2

.': ; 000K a 12 a 10@3 2666 N-m

E/am+le%1( A &,#%9 %% ,&$, s&,,#%s *")%' ). " .#%' *.':(4 ") ,'%ss&'%1

"' Th% #.ss . h%" . )h% *")%' ( %% #(%s %!.(.$%s %)! . 20 . )h% .#%'*.':(4 ,'%ss&'% Th% "$%)%' "( #%(4)h . )h% s)'.:% .' )h% ,&$, "'% K0 !$

"( 80 !$ '%s,%!)%#y Th% ,&$, '&(s ") @0 s)'.:%s ,%' $(&)% F( )h% '":%

h.'s% ,.*%' ). '% )h% ,&$, )h% ,&$, %!%(!y s @K N%4#%!) )h% #.ss &%). #%":"4% "( s,##"4% 7Fe,"&6669

)oluton%

G%( B.#%' *.':(4 ,'%ss&'% ; 1 "' ; 1 102:N/ $2

D" . ,#&(4%' ; K !$ ; 00K $

L%(4)h . s)'.:% ; 8 !$ ; 008 $

N ; @0 s)'.:%s ,%' $(&)%

,&$, ; @K T.)"# #.ss . h%" s 20 . .#%' *.':(4 ,'%ss&'%

R%+&'% ,'%ss&'% .' )h% ,&$, ). %#%' *")%' ( .#%' ; 1 a 12; 1@80 102:P"S(!% *.': .&) ,&) . " &,#%9 ,&$, s .% )h% s(4#% !y#(%' ,&$,

B'%": P.*%' '%+&'% ). '% )h% ,&$, ; 2 PLAN/ @0 0@K; 2 1@80 008 e/7 00K2@0/ @0 0@K ; 0812 :BP ; 0812 103/ Q3KQK ; 110

A#)%'(")%#y

P'%ss&'% P ; 1 101?Q ; 12Q :4/ !$2

R%+&'% ,'%ss&'% ). %#%' *")%' ( .#%' ; 12Q a 12 ; 1Q12 :4/ !$2

D" . ,#&(4%' ; K !$ "'%" A ; e/7 K2; 1?@3 !$2

L%(4)h . s)'.:% L ; 8 !$ ; 008 $

A( ,&$, ; @K

BP ; 2 PLAN/ K00 ,&$,; 2 1Q12 008 1?@3 @0/ K00 0@K

; 1"16 HP

E/am+le%1* A s)%"$ ,,% . ()%'("# " 12 !$ !"''%s s)%"$s ") 12 :4/!$ 2" I)

s #"44% ). " '"&s . 12 !$ *)h "s%s).s . )h%'$"# !.(&!))y . 1 >!"# / $-h'

A-(.


36/41



%4C Th% )%$, . )h% s&''.&((4 s 2K %4 C "( )h% #.ss '.$ )h% #"44(4

s&'"!% s 12 >!"# / $2h' %4C C"#!")% )h% #.ss ( >!"# ,%' $%)%' #%(4)h . )h%,,% Th% h%") #.ss )h'.&4h "( (s")% ,,% ,%' $%)%' #%(4)h s 4%( y

T1-T27

; 2 > L.4 %'2/'17

; 2 > T1-T27/ 23 #.410'2/'17

*h%'% T1 T2"'% ((%' "( .&)%' s&'"!% )%$, . (s")% ,,% "( '1 '2 "'% )h%((%' "( .&)%' '"&s . (s").( "( > s )h% !.(&!))y . (s")(4 $")%'"#

)oluton% A) 12 :4 / !$2" ,'%ss&'%

T1 ; )%$, . 'y s")&'")% s)%"$ ; 18Q08 %4C F'.$ s)%"$ )"#%7T2 ; 2K %4C

'2 ; 12 !$ ; 012 $'1 ; @ !$ ; 00@ $

; 2 > T1-T27 / 23 #.410'2/'17 i

; 2 a1 18Q08-2K7 / 23 #.410012/0@7 i

; 2 a 1@208/ 0@?2; 1*:1"2* ?!al 8 m h$

E/am+le%1.T'"( 5X6 12K $%)'% L.(4 s '&(((4 ") " s,%% . 80 >$ ,%' h' I(*h") )$% *## ) ,"ss "(.)h%' )'"( 5Y6 80 $%)'% #.(4 '&(((4 ") K >$ ,%' h'

h%(

7M.(4 ( .,,.s)% '%!).( 7 M.(4 ( s"$% '%!).( "( 7Y S)"((4.( " s)").(

)oluton%G%( T'"( X #%(4)h ; 12K $ S,%% . )'"( ; 80 :$/h'

T'"( Y #%(4)h ; 80 $ S,%% . )'"( ; K :$/h'

Case I

h%( )'"(s $.(4 ( )h% .,,.s)% '%!).(; '%#")% %#.!)y ; 80 K ; 12K :$/h' ; 3Q22 $/s%!S ; Ds)"(!% ). % )'"%#% ; 12K 80 ; 20K $

Us(4 )h% '%#").( S ; )

3Q22 a ) ; 20K

) ; 20K /3Q22 ; ."46 se!"

A-(2


37/41



Case II

h%( )'"(s $.(4 ( )h% s"$% '%!).(; '%#")% %#.!)y ; 80 - K ; 3K :$/h' ; ?Q22 $)/s%!

S ; Ds)"(!% ). % )'"%#% ; 12K 80 ; 20K $)

Us(4 )h% '%#").( S ; )

?Q22 a ) ; 20K) ; 20K /?Q22 ; &1"64 se!"

Case - III

h%( )'"( Y s)"((4 .( s)").(

; '%#")% %#.!)y ; 80 0 ; 80 :$/h' ; 2222 $/s%!

S ; Ds)"(!% ). % )'"%#% ; 12K 80 ; 20K $)Us(4 )h% '%#").( S ; ) 2222 a ) ; 20K

) ; 20K / 2222 ;4"&( se!onds

E/am+le%12 T*. )'"(s *h.s% #%(4)hs "'% 100 $ "( K0 $ '%s,%!)%#y "'%$.(4 .( ,"'"##%# )'"!:s "( )":% K s%!.(s ). !'.ss %"!h .)h%' !.$,#%)%#y I )h%

sh.')%' )'"( s $.(4 *)h .% )h% s,%% . )h% #.(4%' .(% ( )h% s,%% . )h%)'"(

7 h%( ")h )h% )'"(s "'% $.(4 ( )h% s"$% '%!).(

7 h%( )h% )'"(s "'% $.(4 ( .,,.s)% '%!).(

)oluton% %'%

L%(4)h . T'"( A ; 100 $

L%(4)h . T'"( B ; K0 $L%) s,%% . )'"( A s 9 $/s%!

S,%% . )'"( B ; 2 9 $/s%!

Case I

h%( .)h T'"(s "'% $.(4 ( s"$% '%!).( )h%( '%#")% %#.!)y . )'"( B

; 29 V 9 ; 9 $/s%!

T. !'.ss )h% )'"( A s)"(!% s '%+&'% ). % )'"%#% y )'"( B ; 100 K0 ;1K0 $

F'.$ )h% '%#").( S ; )

1K0 ; 9 a K .' 9 ; 1K0/ K ; 30 $/ s%!

S,%% . )'"( A ; (6 m8 se!"A( s,%% . )'"( B ; 26 m8 se!

Case II

h%( .)h T'"(s "'% $.(4 ( )h% .,..s)% '%!).( )h%( '%#")% %#.!)y .

)'"( B ; 29 9 ; 39 $/s%!T. !'.ss )h% )'"( A s)"(!% s '%+&'% ). % )'"%#% y )'"( B ; 100 K0 ;

1K0 $

F'.$ )h% '%#").( S ; )

1K0 ; 39 a K .' 9 ; 1K0/ 1K ; 10 $/ s%!

A-(:


38/41



S,%% . )'"( A ; 16 m8 se!"A( s,%% . )'"( B ; &6 m8 se!

E/am+le%1:T*. )'"( A B #%"%s )h% s"$% s)").( .( ,"'"##%# #(%s A s)"')s

*)h &(.'$ "!!%#%'").( . 1/ @ $%)%'/ s%!2

"( "))"( " s,%% . 2K :$/ h' h%()h% s,%% s '%"!h% ). $"()"( )h% s,%% . A )'"( !.(s)"() ") 2K >M/ h' B )'"(

#%"%s 0 s%! ")%' A )'"( #%) *)h &(.'$ "!!%#%'").( . 1/3 $%)%'/ s%!2). "))"(

" $"9$&$ s,%% . K0 :$ /h' h%( *## B )'"( .%')":% A )'"(_ 7Fe, 14449

)oluton%

G%( T'"( AA ; &(.'$ "!!%#%'").( ; 1/@ $ /s

2

A ; F("# s,%% ; 2K:$/h' ; @? $/ s%!

& ; I()"# s,%% ; 0 $/s%!T'"( B

B; &(.'$ "!!%#%'").( ; 1/3 $ /s2

B ; F("# s,%% ; K0 :$/h' ; 13888 $/ s%!

& ; I()"# s,%% ; 0 $/s%!

% :(.* )h") ; & )

Th%'%.'% )h% )$% )":%( y )'"( A ). "))"( )s ("# s,%% s)A; A/ A; @?a@ ; 1@@ s%! "(

") " s)"(!% SA; @?a1@@/2 ; 1@ $

S$#"'#y )h% )$% )":%( y )'"( B ). "))"( )s ("# s,%%

)B; 13888a3 ; 1@@ s%! "( SB; 13888a1@@/2 ; 28?28 $

L%) &s !.(s%' )h% )$% T ; 0 *h%( )'"( A s)"')s '.$ )h% s)").( I) '%"!h%s )s

("# s,%% *h%( T ; 1@@ s "( ") )$% T;81@@ s%! )h% )'"( B '%"!h%s )s ("#

s,%%

By )h% )$% )'"( B '%"!h%s )s ("# s,%% )h% )'"( A $.%s 1@&'(4 1@@s%!7 @?a0 &'(4 0 s%! ") !.() s,%%7H ; 220 $ "*"y '.$ )h% s)").(

P.s).( . .)h )h% )'"( ") T; 81@@ s%! s

T'"( B s 13312 $ %h( )h% )'"( A "( .)h )h% )'"(s "'% )'"%#(4 ") )h%'

!.''%s,.((4 &(.'$ s,%%

L%) &s "ss&$% )h%y $%%) ") " s)"(!% ")%' )$% )

Th% '%#")% s,%% . )'"( B *)h '%s,%!) ). )'"( A *## % 13888 V @?; @? $/ s

A-(5

22 $

28?28 $ 13312 $

AB


39/41



Th%'%.'% @? 9 ) ; 13312 .' ) ; 13312/@? ; 1?1Q s

S.

The t$an B 0ll o'e$tae the t$an A afte$ 51"22 14"1: 3 166"5( se! afte$

t$an A lea'es the staton

E/am+le%15 A T'"( s &(.'$#y "!!%#%'")% "( ,"ss%s s&!!%ss% :#.$%)%'

s).(%s *)h %#.!)y . 18 >MP "( 3@ >MP '%s,%!)%#y C"#!")% )h%

%#.!)y *h%( ) ,"ss%s )h% )h' :#.$%)%' s).(% A#s. ( .&) )h% )$% )":%( .'%"!h . )h%s% )*. ()%'"#s . .(% :#.$%)%' s).(%

)oluton% Us(4 )h% '%#").( %)*%%( 's) "( s%!.( :#.$%)%' s).(%S ; U 7/2i a )

%'%

S ; 1 :$ ; 1000 $U ; 18 >MP ; 18/ 3@ ; K $/ s

; 3@ >MP ; 3@/ 3@ ; 10 $/ s1000 ; K 107 a ) .' ) ; 1000/1K ; 22"2: se!onds% !"( ( &(.'$ "!!%#%'").( &s(4 )h% '%#").(

; & ) *h%'% ; "!!%#%'").( ( $/ s2

10 ; K a @@@Q ; K/@@@Q ; 00QK $/ s2

N.* %)*%%( s%!.( "( )h' s).(%U ; 10 $/s

S ; 1000 $

A( ; 00QK $/s2

% 4%) !"( ( .&) %#.!)y ") 3's).(% y &s(4 )h% '%#").(

2; U2 2 S

2 ; 102 2 a 00QK a 1000

2 ; 2K0 .' ; 2K0 ; 1K81 $/s ; 1K81 a 3@00/ 1000 ; .2"4& m+h

A4"( &s(4 )h% '%#").( S ; U 7/2i a )

h%'% ) s )h% )$% )":%( ). )'"%# '.$ 2(s).(% ). 3's).(%U ; 10 $/ s

; 1K81 $/s

1000 ; 10 1K817 a ) .' ) ; (5":* se!onds

E/am+le fo$ +$a!t!e

E/am+le%1 A &%# s).'"4% )"(: s ( )h% .'$ . !y#(%' *)h h%$s,h%'!"# %(sTh% "$%)%' . !y#(%' s 2Q M)'s Th% #%(4)h . !y#(%' s Q M)'s Th% )"(: s

'%+&'% ). !.()"( .# . s,%!! 4'")y . 0?1 D%)%'$(% )h% !","!)y . )h%

)"(: ( L)'s "( :4 . .# A#s. %)%'$(% )h% #%(4)h . *%#(4 "s )h% )"(: s

A-(4


40/41


41/41



A %% *")%' )"(: s 10 $%)%' ( " "( 1K $%)%' ( h%4h) s s&,,#y(4 *")%' ).

.#%' )h'.&4h " %"%'").' K $%)%' " K #.(4 .)h %(s h%$s,h%'!"# I )h%

*")%' #%%# ( %% )"(: '%$"(s # ( %"%'").' ") h"# #%%# *h") s )h%

+&"())y . %% *")%' ( s).'"4% . .)h_ I " .#%' . 1K MT/ h' s '&(((4 .( )hs

sys)%$ *)h 10 MT/ h' %9)'"!).( !.(%(s(4 ,#"() !.(%(s%' %9)'"!).( ,&$,

s s&,,#y(4 *")%' '%!)#y ). %"%'").' h.* $&!h )$% ,#"() !"( % .,%'")%s"%#y DM s&,,#y s ).)"##y s).,,%

7&66.9

E/am+le% 4

"7 A .'!% "( s&,,#%s "' ). )h% &'("!% . )h% .#%' ") )h% h%" . 0$$ *")%'

!.#&$( D%)%'$(% )h% "s.#&)% ,'%ss&'% . )h% "' s&,,#y )h% "'.$%)'! '%"(4

s Q@0 $$47 A ,&$, %#%'s 1200 #)%'s . *")%' ,%' h.&' "4"(s) !.(s)"() h%" . 328 )

C"#!")% )h% *.': .(% ,%' h.&' ( h%") &()

7&6629

E/am+le% 16A 10!$ #%%' #."% s"%)y "#% s ))% .( s&,%' h%")%' s)%"$ .&)#%) ,,%#(% I

.#%' '&$ ,'%ss&'% s 101K "' ,'%ss&'% '., '.$ '&$ ). s&,%'h%")%' s 2

"' Th% !%()%' #(% . %" *%4h) s @0 !$ !%()%' #(% . "#% s 10 !$ !%()%'#(% . #%%' s 20 !$ '.$ !'&$ '%s,%!)%#y )h% *%4h) . #%%' s 2 :4

!.$(% *%4h) . s,(#% "#% s 1 :4 T. ( )h% %" *%4h) '%+&'% ).

!.()'.# )h% ,'%ss&'%

7&66:9

ch- 1 fundamentals of physics

Documents