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Eng’r Armando C. EmataNovember 6, 2014

THERMODYNAMICS 1

BASIC PRINCIPLES,CONCEPTS AND DEFINITIONS

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TOPIC OBJECTIVES

Study the system of units as

used in Thermodynamics

no! more a"out acce#eration as de$ned"y Ne!ton

Distin%uish "et!een mass and !ei%ht

Di&erentiate amon% s'eci$c (o#ume,density and s'eci$c !ei%ht

So#(e sam'#e 'ro"#ems on a"o(e discussion

Assi%nment for ne)t meetin%

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SYSTEM OF UNITS

“The acceleration of a particular body is directly proportional to the resultant force acting on it andinversely proportional to its mass.” * Sir Isaac

Ne!ton

a = kF/m

+any systems of units ha(e "een "ased on thismomentous statement

-e de$ne a consistent system of units as one for!hich the 'ro'ortiona#ity constant k is unity. ine/uation form,

F 0 ma 1232A4

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SYSTEM OF UNITS

!here force is de$ned in terms of mass and mass interms of force

Acce#eration has the dimensions of #en%th 'er unit

time s/uared, L/t²A dimension is an attri"ute to somethin% in %enera#

terms. thus, #en%th L is a#so an attri"ute of (o#ume L

5nits are dimensiona# characteristics e)'ressed in

de$ned /uantities The #en%th of a foot is accurate#y de$ned 1in terms of

the Internationa# meter 0 2,678,96:9: !a(e#en%ths

from e#ectrica##y e)cited ry'ton ;64

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SYSTEM OF UNITS

De$ned units of time are seconds, minutes,hours, days, etc

In En%#ish units, a unit /uantity of acce#erationis most often ta, or f's>4

From E/ 232A, a unit force is one that 'roducesunit acce#eration in a "ody of unit mass On the"asis of this de$nition, one can decide u'on theunits for terms in %rou's of sym"o#s !here it issaid that units must "e consistent

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SYSTEM OF UNITS

Systems of units !here ! is unity "ut notdimension#ess?

c%s system ? 2 dyne force acce#erates 2 %mass at 2 cm=s>

m

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SYSTEM OF UNITS

< 0 33333333333 < 0 2 33333333333333333 < 0 2

333333333333

2 %m 2

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SYSTEM OF UNITS

Systems of units !here ! is not unity?

If the same !ord is used for "oth mass and

force in a %i(en system, C is neither unity nordimension#ess

2 #" force acce#erates a 2 #" mass at :@29ft=s>

2 % force acce#erates a 2 % mass at ;866cm=s>

2

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SYSTEM OF UNITS

< 0 :@29 3333333333 < 0 ;866 3333333333 < 0

;866 3333333333

2 #"m 2 %m 2 ;866 cm=s> ;866 m=s>

f m

#" 3 s>f

#" 3 ftm

% 3 s>f

% 3 cmm

f

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SYSTEM OF UNITS

Re#ation "et!een

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SYSTEM OF UNITS

Re#ation "et!een 'ound mass 1#" 4 and s#u%

< 0 2 333333333333 < 0 :@29 33333333333

Therefore, 2 33333333333 0 :@29 33333333333

2 s#u% 0 :@29 #"

m

#" 3 s>f

s#u% 3 ft

#" 3 s>f

#" 3 ftm

#" 3 s>f

s#u% 3 ft

#" 3 s>f

#" 3 ftm

m

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ACCELERATION

A unit force is one that 'roduces unitacce#eration in a "ody of unit mass

F 0 m=

m

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ACCELERATION

F 0 m=

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MASS AND WEIGHT

The mass of a "ody is the a"so#ute /uantity ofmatter in it

The /uantity of matter has to do !ith Ne!tonsuni(ersa# %ra(itation #a!, in e/uation form, is

F = " ##########

!here ? F is the force of attraction 1for theearths attraction on an earth#y system, thisthe force of %ra(ity4

gm$ m%

r²g

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MASS AND WEIGHT

"et!een the masses m$ and m% that are r distancea'art, and " is the %ra(itationa# constant

The &eight of a "ody means the force of gravity F on the "ody. it may "e determined "y a so3ca##eds'rin% sca#e

ra(ity 'roduces a force 'eld and a "ody in this

$e#d is su"ected to a body forceSince the force $e#d on the moon is much #ess than

that on the earth, the !ei%ht of a "ody is #ess there

g

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MASS AND WEIGHT

E)'ressed in e/uation

3333 0 3333 0 33333

!here ? % 0 acce#eration 'roduced "y force F

a 0 acce#eration 'roduced "y another

force FAt or near the surface of the earth,

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SAMPLE PROBLEMS

PROBLE+ 2?

-hat is the !ei%ht of a 663

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SAMPLE PROBLEMS

PROBLE+ @?

The !ei%ht of an o"ect is 78 #" -hat is its

mass at standard conditionGSo#ution?

F 0 78 #" % 0 :@29 ft=s>

m 0 33333 0 33333333333333333333333333333333333 0 78#"

% f

F%

<

H78 #" H:@29 33333333333 f #" 3 s>f#" 3 ftm

:@29 ft=s>m

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SAMPLE PROBLEMS

PROBLE+ :?

Fi(e masses in a re%ion !here the acce#erationdue to %ra(ity is :87 ft=s> are as fo##o!s? mJ 0

788 % of mass. mK !ei%hs ;88 %. m !ei%hs 27'ounda#s. mM !ei%hs : #" . m is 82 s#u% of mass-hat is the tota# mass e)'ressed 1a4 in %rams, 1"4in 'ounds, and 1c4 in s#u%sG

So#ution?

% 0 1:87 ft=s>412@ in=ft41@7 cm=in4 0 @6cm=s>

f

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SAMPLE PROBLEMS

PROBLE+ :?

So#ution cont(d?

1a4 mK 0 3333333 0 33333333333333333333333333333333333 0;:2 %

3333 0 333333 3333333333333 0 H8 #" H7:6 33333

F

%

H;88 % H;866 33333333333 f % 3 s>f

% 3 cmm

@6 cm=s>m

m

<

F%

%

27 333333333s>

#" 3 ftm

:87 3333ft

s>

%

#"

m

m

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SAMPLE PROBLEMS

PROBLE+ :?

So#ution cont(d?

3333 0 @@@@6 %

mM 0 3333333 0 33333333333333333333333333333 H7:633333

m

<m

F f

#" 3 ftm

:87 3333ft

s>

%#"

m

m

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SAMPLE PROBLEMS

PROBLE+ :?

So#ution cont(d?

mM 0 2,:7 %

33333 0 1828 s#u%s4H:@29 3333333H7:6333333

33333 0 2,72 %

m

m

< s#u%

#"m %

#"

m

m

m<

m

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SAMPLE PROBLEMS

PROBLE+ :?

So#ution cont(d?

Tota# mass 0 mJ Q mK Q m Q mM Q m0 788 Q ;:2 Q @@@@6 Q 2,:72 Q

2,72

Tota# mass 0 ,6289 %

1"4 Tota# mass 0 333333333333333333 0 ;: #"

m

,6289 %m

7:6 % =#"m mm

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SAMPLE PROBLEMS

PROBLE+ :?

So#ution cont(d?

1c4Tota# mass 0 333333333333333333333333 0 8:86 s#u%: #"m

:@29 #" =s#u%m

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SAMPLE PROBLEMS

PROBLE+ ?

Note that the %ra(ity acce#eration ate/uatoria# sea #e(e# is % 0 :@8;; f's> andthat its (ariation is * 888: f's> 'er 2888 ftascent Find the hei%ht in mi#es a"o(e this'oint for !hich 1a4 the %ra(ity acce#eration"ecomes :878 f's>, 1"4 the !ei%ht of the%i(en man is decreased "y 7, 1c4 -hat is the!ei%ht of a 2;8 #" man ato' the @,2:23ft+t E(erest in Ti"et, re#ati(e to this 'ointG

m

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SAMPLE PROBLEMS

PROBLE+ ?

So#ution?

1a4 chan%e in acce#eration 0 :878 * :@8;; 0 * 27; f's>

ei%ht, h 0 33333333333333333 0 7@;,888 ft or 288mi#es

* 27; f's>* 888: f's> 2888 ft

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SAMPLE PROBLEMS

PROBLE+ ?

So#ution contd?

1"4 F 0 87 F Let F 0 !ei%ht of the man at

sea #e(e#

33333 0 33333

3333333333 0 33333

a 0 87% 0 18741:@8;;4 0 :8; f's>

% %

F

a

F%

%

87 F%a

F%%

a

F%

% 0 :@8;; f's>

h

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SAMPLE PROBLEMS

PROBLE+ ?

So#ution contd?

h 0 33333333333333333333333333333 0 7:,698 ft or282: mi#es

1:8; * :@8;;4 f's>

* 333333333333333888: f's>

2888 ft

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SAMPLE PROBLEMS

PROBLE+ ?

So#ution contd?

1c4 % 0 :@8;; f's> m 0 2;8 #"

a 0 :@8;; f's> * H333333333333331888: f's>4

0 :@882 f's>

F 0 333333 0 33333333333333333333333333333 0 298: #"

m

@2:2 ft

2888 fta

F%

@2:2 ftma

<

12;8#" 4H:@882 ft=s>m

:@29 3333333333#" 3 s>f

#" 3 ftmf

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SPECIFIC VOLUME, DENSITY

AND SPECIFIC WEIGHT The density ) of any su"stance is its mass 1not

!ei%ht4 'er unit (o#ume In e/uatione)'ression,

) = #####

The speci'c volume v is the (o#ume of a unitmass and is the reci'roca# of density

v = ##### = #####

m*

*

m

+

)

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AND SPECIFIC WEIGHT The specific &eight , of any su"stance is the force

of %ra(ity 1in the %i(en #oca#ity4 on unit (o#ume

) = , #### or , = ) ####

Since the s'eci$c !ei%ht is to the #oca# acce#erationof %ra(ity as the density is to the standard

acce#eration, ,/g = )/k , con(ersion is easi#y madeence,

) = , #### or , = ) ####

k g

gk

k

g

g

k

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AND SPECIFIC WEIGHTAt or near the surface of the earth, k and g

are numerica##y e/ua#, so are ) and ,

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SAMPLE PROBLEMSPROBLE+ 7?

1a4 -hat is the s'eci$c !ei%ht of !ater atstandard conditionG

So#ution?

% 0 ;866 m=s> 0 2888

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1"4 T!o #i/uids of different densities 1J 0 2788

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So#ution contd?

mJ Q mK 0 m JVJ Q KVK 0 m

2788VJ Q 788VK 0 ;8 124

VJ Q VK 0 8288 1@4

so#(in% e/uations 124 and 1@4 simu#taneous#y,

VJ 0 88: m

VK 0 889 m

m

m

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So#ution contd?

mJ 0 JVJ 0 12788

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ASSIGNMENT – NOVEMBER 11,

2014 For ne)t meetin%, su"mit in one sheet of "ond 'a'er -rite your name,

su"ect=section, date and !rite the 'ro"#em statement P#ease !rite #e%i"#y

Non3com'#iance !i## mean non3acce'tance of your assi%nment

A mass of 828 s#u% in s'ace is su"ected to an

e)terna# (ertica# force of #" If the #oca# %ra(ityacce#eration is % 0 :87 f's> and if friction e&ects arene%#ected, determine the acce#eration of the mass ifthe e)terna# force is actin% 1a4 u'!ard, and 1"4do!n!ard

The mass of a Wuid system is 8:22 s#u%, its density is

:8 #"=ft and % is :28 f's> Find 1a4 the s'eci$c(o#ume, 1"4 the s'eci$c !ei%ht, and 1c4 the tota#(o#ume

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Ther 1 - 110614