14.06.2! L2
henmodynamícs Them +Dynomics
Greek
Ererad
Enenag
Heot
Forces
Energ. neither
cam
be
eTeoted
non
be
destrojed
deals with the
Themodynomies
enray transfer
nd it efects with the
physico
poper
ties of the
Aubs tamce.
Work
doiarar
but both are
Both heat and work
fonms ( medium) of energis not eneray
## Heat amd wonk
PTocess
ove
both are looses theln properties once the
Transient fom
of enerat y40
Heat and work both are
boundartphenomena
Nian
t Heat and work both ore path function
1
Heat and wopk both ave not properties,
Boundor massless,
Swmoundirg
S8stem
Volumeless, Unit thikness
Boundo
Real.
V12/titf
System
Enerat
Rigid, Flexibe, Imaging
Mass
Examp
Humar Bod ,
Open
Closed
X
Tunbine, Punp
Ballaon,Electrie
Bulb._
Flux10p
Isolated
Imdividual Behavror
Statisticall approach
irgo
MacTOScopic
Avg behavior of molecuule.
aro Classical approoach of themodymamics
Lanaagian opproach Can be analyze, low as twellas high
density
Low densi
High altictude
mass stem.
ud da0
m
Conticl
stemControl
09V 93
Open
4at em
volume
j
A
Jgoo
Jour
Continuum
Knudsen
number
=
M e a n free path.
L characteris tic Length.
govf oh 2 0 01Continuum applicable
o
o:01
(0
0-1
Slip conditiom
A L10 Transition low.
102
Free molecular 1theorgod br
13olh
rapertyoF System:
ntensive properties
PreAbUTe, tempeTature, den6it, pedH
tHpTopeties, partial molar properties.o
2
itod
Extensive proPTUS Mass
T
br
volume.
T
E
F/2 E2
K
P
M
Intensive
PTOperies,
ExensheM2M/2
Propear
S/2S/2
ioli, opli
*
All
propertles
ane
point furictton (State unction)
UDloal
roimt PrOpeT
Path Proper ty
Internal enerat entholpt, ero
WoPk heot.
,
O0r
njbivio
Properties depends on mol are extensive propertie
All forms of energies ane extensive properties.
Ratio of tuo extenoíve
pTOper ties aUusays mtensive
ties.
All specific
AIl
proper
roberhies
Teversible pTace A
ane
a1e low
mot correct.
#
All
pnachco pToce
mtensîve
broperties
fo fo
he
proceAs but vice
lTre versibla
procos8.
versa ane
16-06.21 L4
her modynamic Equilibrium
nermal
equilibrium,
Equatg of temp. (4T -0)
Mechonial equililrium.
Equality of PoATe, (AP =0)
Chemical equiibrium
No chemical reoction
Phase cqui li bri um.
Di fferont phase exist
p
Pure substance
Any oubstance
4t
homogemeous
in (
i
baid to be pure Aubbtance
chemical compositton-chemicat -
A a m e ,.chemical aggregation -~ sevaral things mixed
togethep coider as one.
water
AiThreated as þume substance.
MiIR
not pire substance.(
*Dry ai+ wet a
ngradient chonges Continuaus
not pwe substonee,
ab4np
*Pure ubstances Con exist im more than one phase.
G1850.6
rto
VT-
bvol9 to
h,oteye r
v1
V
I7 06.21
5
Gibbs phase rule
P+F
F
mmimm|
number of mdep2ndent imdensive
FDegree of feedom
C+2
CP+2
on
vrnble.(DOF) ' i
NAmber of Phase
P
Number of Coponent
For Azeotrope mixture
P+F
Ases
D.0.Fo
C+2 -
Phase
l 1
F C-P+
Soud water
F
Vapor
- 3 +2
0,
The point ot which oul
threea
phase ex ist ie n equulibrium
For waker:
Pee
a
oTuiple point
22-6 M.
oreoladud
Te 373.3'e
&
K
Triple point tempeTatre
water 0.01 '
0-o0 3106 m7
°c +27315
273-16K
32
2106.21 L7
R-Ro (14 &T+PT)
PV nRT
22-06.21
Wonk
Lg
=P dv fon elosed yphem
W=P4V
fom open AyAtem, dw - - d(PV)
Sign donvection.
Wa-Vdp
W
otem =+Ve.
W on
system =Ve.
W
-
byHstem
on
=Ve
s t e m = +Ve.
Area under pV
diagram is
Bounday wwOrk: W= JPdv
Shaft wark
W -vdP
Sprimg wok
work.
23.06.2
L9
Nonk transfen through various procesS
oi
l
il
Cons tant pessure proceM: (1sobaric process
W SpdvP(V,-V)
Constant volume process, Clsochonic process)
dv 0 . w SPdv
pmcess
Isothermal
T Const
0.
(Constant
tenperature)
40, W*0
icleal gas, pV=nRT
Fan an
N= pdv-nRT
9. Adiabatie process:
nRT n
V
nRTb
rrohd
(9 =-o)
py Constant
/
G-cy =R.
moncatomie 1 - 6 6 3 1 U
W
Pdv
ows iseoirddiakomie
PV-P2V2
iriotomie
Y-1
Polytropic
1:33.
tr
3
Proces5
PV=Constant(16
3
V1U
W
S-1
.1)1
6) Isolated system
W=0,
=0.
Wonk.dane for open system adiabatic pTocess
ss Wopen
H
35
PV-BV] = Wclosel
24.06.21 o
Pv= Cons tant
n =0, P Const. lsobariC pTOceSs
n
PV= Constamt (T
=Const.) Isothermal process
V= Const. IsochoriC þrocessr
t
0
n-6,
n=,
Pvo=Const. Polytropic. procoss. KS
pv= Const
Tbp
Adiabatic proces
#b-(vyae)b
25.06.21 4
Finst law
of
themodynamics
w
Heat
=
4U
FW
Valid for Cycle.
mcAT,
Adiababic
22.06 21 La
=0
=
m
Codia 0
Can4T
V
>q>
wates
Cadia
t-18
mel-k
Imternal enerat
dE = d(mv)
U
+
d
(mgz) + dU,ano
fCT, v) Real Gas
U- f(T
ldeat Gas nternal eneri
y9
=
k.E
&
P.E s
4E =4U
vh
negliglble.
oriqpol
Enthalpy
3
31)nntergo)-"y9
H Ut PV.
V
H- f(P,TD
woie itolo:l (a
Dp0W
de dE + dh.nriShukh
E
KE +t
dA d +dh
dE ddu
29.06-21 L13
+,
Inten ral enea88
dW= Pdv.
e.aso
-+Ne
WaW
Heat tronsfer
+Ve.
jhjeoD
through
vaouius procoss:
o9
Constont pressuTe process
Jeno
dg dU+dutndib ano
d
dU+ Pdv
dlp ro (U4 PV)
=
dH
mCpdT,
V
yg
kgk
2)
Isokrie process
d
(4V=0
dU+ du
de du
0
m dT
Adiabatie proeess
da = dU+dur
mGdr+ y-B%
y-1
mRdr.
P
b
-
Y-I
) Palythopic
d
=
ub
-I
TOcesS
7
1tl
V
du+ dw
VPr0
umCy dT +
to
o
PV2-Pv
PVRV2
Y
1S-1
boearir
at
ya"
daA fuid contasn
a cylinder with the help of rictionless piston
pressuTe the eylkindar a
b P P a+ bV (a,b constant). function of volume and it 8iven
e
the
mterml enera
AHAtem is8iven U= 14+3.15 PV, nkt
P in K, V in
m3.
So
thot
im
in
the
changes from
40 KAa *V2 =0-06 m. then find the P =170 kfa,V=0:03
magnitude anddirection
heat and wok transfer
f
tD
d= du+dw
dU U2-U = M+315 PV--316 RV
= 59.53518 55 kJ
68 KJ,.
P atbV
P2a4 b Va
b(-V) = P-Pa
b(4co-17o]y1
Td06-0.03
dw
3:15
-170xIo xo03 + 400x 10x006)
8-15x
-
0.03x 10x 630
J=59 535k
JPdy fatbv)dv av+ bv-)
Pla
100
dw =
170
170+400)*(o.06-0.03)
=285 x0 03 kJ
003
006 V(m)
F8.55 kk3
Free ex pansim
or
daihA
Wexp =O
sdu+o
dU = 0
mcy dT =0
U
dT
=0
T T
P'dv #0, U =Us, T
T
A Cndes contams
of am
H
90e.The
SOC.
compressed o-03 m. Final pressue is 6 bap find The
the
dex ot Combre ssion, internaL eneTaH and heat
transer.
aie is
P
-
29
a bar
W
PV,
PV
-1
n
29-
0.2068
1-Ei*
and
and
CyF11 k
1xo12-6xo-03
124-)
96
29
10+273 15)T3s-214
K
du mCy dT
.
at
= PV
n4
-
0-12
.
m fV
RT
4
11-(-M4
Open System
Htmytmg
A
*
U2 A, Va
O1.
# 4m+mgz2 t
21 Li6
SFE
continuty equation fon Meady flour.
, A
CompressOrT
h,
7 Z2
V2
W Wo
Ke
-hha (ha -h)
'W
=
- Ve,
Heat eehonger
hg
0089 h
(1-0 (
Tur bine
hi
1
Nozzle & Diffuser
A
Lpiuindu.iL
stunau
01/008
T
DIFfuser
Norzle
h+
h +
2
21a/sso
d u ndl
uol
nofe
sa
2
Al 1
i
Throttliong
2
Work transfer neglected (friciona sork
2KE
Heat:
PE neglacted.
tansferNegucted(Due
to, ve Ahot tme
transfer does not takes blace)
Thiotting Is an
4
irTeversible adiabati proco.
I t is an isenthalpic proces
(, h
h
Unstendy lo
t
mh;
+Q)
emttapt
not vaying
du
h +
(ene tMav
0 . t time
- mehe-W
heab
Aie
02.0121 L
enters
a
im an
adiabatic nozzle at 300ka, 500k .uith
ms. It leoves
at lo kft wth a veloaty of 80
nozzle
180 ms
the&Co
oC
he inlot anea 80 cm
of air
1008 J/k9k 0ExH tempehat
of
voloci
10
of ar
576 k
300KA
484k,) 468K.
(8) 532k ,
b
T+
l008 x 500 +
2
Std
n)
l0okA
180 nys
S00K
h
,
Exrt' anea of nozle
in cm
equation.
A2
A2
P
300X10
PRT,
314X 500
RT
3:314x 500
R T2
s
(A)
90
I, 8)
t0
56:3,
c)4.4 D 12;9.
A
10x80L 4.441 3
v2 V2.
72-147
10Ox10
8314X 484 24
Stean flos through a noZzle
kals with heat loss of 5
1002X T
2
483.97 k 484 k
Fnom continuit
AV2
2
A12:39 e?
35
Qt a
meam
flsw
iote of_o1
kW.
The
enthalples
atrimlutt ond
autlat ane 2500
Ks/ad 2350 K/k Nespectivel
Assumtn
Yeaigible velocity at mlat. Caculata
veloeity at exit V.
h44g+=ht
2
h-h
+
iaworni
2500x 102350x0XI3
j00 x 10
.
x
-
50 kT
Temp. & pressure of air in a large veser vor ano 4o0 k &3 ba
respective
A Convergim duveging nozzle of exit anea 005 m
Hed to he servoir as xhown in figure, "The saic proTO of air
or exit Aechion for 1evereible
adinbnic flos thragh mtnle
Na, R0287 k/kak,
4
O DensitR
ensitg(S) of, air ka/m a
5p
hen
0540, 9) o600,
mozule exlt is )
A0 005 m
50x1o50x10
RT
fuiaa
N
Mass low
of ai through
nate
A) 13, (6) I77,
35 ,
2:06,
kg/s
s
6
KAS
NPIL)= V2xpo8x(400-2397)
V
2h-h
968 12 m/s
JAA
: 1 2 4 ka,x o005 x
A migid tank Whose volume
its wall Aim fram
final pressuse
in
the nozzle
naAz
till
23973 K
400 x(0
T
02811x 22113
568 42
is 075 m
AuProundmg a t i
neacA
to
2.066 es
daveloped a smoul hole on
bar
2 5 ' laaked intot
banThe brocess OccUUTS Sla
and heat transfars maintained the temperaturë in the tanKa
25'e. Determine heat rans ferftank initialevacuated
dt
dU
dt
m-Me
=
m
mhh +-pehe
0
du dm ki+
dt
du-dm.hi
= (Ua-¥)-(ma-)
hi
m a hi=mu2 -mahi
m 2 (uhi) =mC-4T
= - 7 5 26 kT
ox05 ba13-10
0-287 x2
econdlaw of thermodynam
transfer ie to
of heat
quantity
the
with
cols
the
hou m uch k
Astem me emstate to another e"State
heat transfer
reguired but it never ives the direction of
the direc
1t was
ohich gives
nd lar of
las of Thermn
and hence 2
thTough the comcept thermodynamies
of entroP
las
mamits is knoun as direciiom law
appucable it doc} not meon
LaLA of themodynamics
process
i prachcally possible. To knou tho faas1 biluty
the process t s t apply 2nd law ag hemadynamics and i t
2nd laus o
modynamics
Heat is
than opply 17 las of ti
applionble
tRaTmodynamits
aolan4
kgnown
high
Jrade
era
nto
as
A
low 9rode ene9-4 and WoTk 3 Knaun
enera. and Complete conveTsion
hiR qrade eneTay
Statements of
2md law of
Kelvn Planck statementt:
nto
is
mpassiba,
o
in
iada
a yel
thermodynamuCs
t i s impossibla to doo
conversion of heat ()
uwork wl
=
1 0n 1007.fiaency
dte 2)
Claussius Statement' 1D
.
t is impossible to the tronsfer
a
Coder to a hotter bod
ipro
of heot fronm
Heot engine: CLow ode eneA8)
TSouTce
H.E
1rit
Sink
Ub
W
- 1/P9
H-E
-02
03.07 21 I
Saurce
o/P
P M 1/P
W
a/p
coP1/
1/P
W
-2
2
w
COP
4(gh grads
(cop=
y
i 9 AyE
(Hioh Grade Energ8)
Kefriganior
R.CiDesired e
RE
w
P
P/P
Cooling efpoct
herkinpuE
-
EnergyP
ldior9v
Heat Pump
T
Heat effect
col
Wp
-2
Work input
W
T
COP
Resistance heater is g0od
COP
Blourer 2 d 4 o
Carnot cyele
ysldierv2
T 2 sotherma expanssisn.
Adiotatie mversi bla exp
3-4 1sotherial Cmnpressian
2-3
4-1
ReverAsbtadiabatic
Cmpumio
eannot EMaximum
Reversible Heat Engine
Valid for amy le
Revesible.
Jmax
heannot
Reversi ble
n
Refrigerator
COPg
Valid
-2
for cony Hcle
-
Kev. cyce
2
COPaR
T-T2
Reversi ble Heot
Pump
CoPHP
S-C2
COP.HP
T
2
-SL
2
WmaxO(1
Wact.
-62
Ivevessibility (1)= WmaxWact
T
103
109
Reversible cycle
T
ie
inibA
S2
W2
g
(-3)
W=,
T-T .
(-T)
Sa
7-) =(T-7) =y-T)
T
T-T2 T-T3
Tn
T3-T4
Kelationship between
HP
-
cOPHe & CoP
TL
L
COP
dy,y
TTL
L
COPR
HE
THTL
coPaS
SHOL
utCoR
- L
+COPR
core
1
1+COPR
0o0O
Clausius Ineauality
de
0.
T
O
9
6Inventor has
Teceives1000 k
cyole is yeversible r
Jo9rli
45r
T2)
mpossible otosqu stibsnitni
3 bsh A R i b i } (
claimed,
thot
he has deyeloped on engme whi
heot at a temperature 0ob K andreje
200
kT
ct
o heot at a
temperiotua of 600k
the emoining mput as wTk check uoteth deliveun
his
ia
possible OT not using clausius mequality in caxe elaim
t a3 a
Yevetpible
determne tha amoUnt Kaat
608
ThoOK
Tejecteda
ODoks
W=\50020
B6d kJ
200KT
T600K
200= 80
0ant
1o00 !
Sot
posible
)000
A
031-
8)
that
h a u s oystem
during which it exohamge
a
t00Ok
HU
Reservai
and
di
B
5a00
0
XAg=-2250k
5-
500
300
e 5
300
500
de 6250 kr
300
500
10C0
1000 KJ.
3dg +54d Oe 7500do
=
900 Kc
3(4000-) + 5@e
5000=Gg +1000+ Ge
g
thermaL
the magnitude
unk. Find
500
000R
uoith three
heat
and
develop 1000kJ of
Tectiom Se and
6c
n e ver'sible
a
underg0es
12000 +2
t@e 4000
7500
Cc= 7500
Oc--t
=-2250 kJ
B-4000 e
Sg
=
=6250 kJ
1600+ 2250
GTwo reversible heot engines a and 8 ane anianget mkivs
Engme A Teject
heot a t 427'c
it
drectly
to
B.engine Areceives 300 ks
while BTeject heat to Aimk at 7 e F the
tuo times of B.Find
Intermediate temperature of A and B,
Ork output
of
A
() ESficiency of A and B.
dergviri
(.
GHeat
rejeckad by A that s heat absrbed by B.
.raat Tejected to the snk
iidoup
62
300
=
O->W
1- 420
T00
40/
280k. '=1
=l- 20
120
33-33
2
420 K
T
900 280 1 2 0 kJ
G-gW, 2Ha-2 (G-0s
300.-02
32
=
540
2
(2-120)
2= 180 kJ,
.W= 300-180 =l20 kJ.
7
t240-180-6ok
#If
hen Ta T13
1-
T
TT
T2 T73
f W = Wa
TT2
GM.
the T2
9
T2
AM GM
T
wO engimes A and 8 ane Corunectecd in series then
is
noS tkat the overoll efficiencH g the combined engine
overoIT4t2Tnari
overou 9P2
+W
61
/P
W
62
W2
S+aG2
nS
22n,+ h, 2
loverall
ouco t
M2+ n,n2
04.07.21
Entropy
ds
ds de
T/Rev S2-S =
ds de)
'iorgKev
tor a proces
dsd
45Universe0
dseys t dssun 0
For
iTre versitble roceAs :
dSsys+ dSsurT
for Tevesibl.
proces
dSsys t dsqur
O,
Lig
30'C
ds- d t dm
ds- dSyst dSsurp.
ds= dssys. + dssuTT
ds
=
Ag ds
dsn 0
ds
t
34330
Physieal meaning of EmroPy
+Ve
d
EntoPy 6 a measure of degreé of Trandomnes8
molucwe . Greakey s
the entropy, lesser will be the
efficienc
It is
m
an
o
6p. enthoP
an
extensive
ntensive
þropeTties
=
prqparf
dsdg.
and
s
generaly donoteß
m.
05-01.21Le
AdiohatBe
Revessiblde
ds=dAo
wrevcrsible
ds
ds SSpen
(ve)
0
8Sgen.
Caninot cyele (T-s Diagram)
4-0
s
e
GO
V
Z4-ZH
2
Y-0
/14
st s
S Cos t
Combined
finst
de
=
&Second law
dU +t Pdv.
of
Finst
ds d
taw.
dsTds
Tds= du + Pdv
thevmodynamies,
lau
p-a
2
H
U +
u
At Votume, V=Const. dV=0
Tds
dU- mCydT
PV
I(-)
dH du+ Pdv+ V dP.
d
R
= dH vdP,
Tds-dH-ydP
dP=0.
At press ure constant
dH = mpdT,
0 ) V Tds
as /p=C
At
m
m-1. (3T
DR
DR
=
TA
p=Cmst
19
old
19149
Kepresentation of various process,0n T-s diagram'tay
ie
Prcmat
()
Tdia
-o
a,Pe
Te cmst
Pstytspict 031
Polytepie
VConst iabotic
s S t Tt.
V
SR
183/
Change in entrop
of an ideal ga8
Tds = dU + Pdv
T
ds =
6
neydT
Pv RTi
P
MRT
P3
dagl i
ds =nCdT +R dv
T
1
fro n=1 ,
V
S, TV
=0
S =C.
2. Tds
A
dH VdP
Tds nCpd
nRT
dsnCpldT
nR
Ch+(G-6)»
T
P
p n)
Pn
-
-Gn+Rh
=G+h
quids
ng in entopy
Tds = dH VdP
T ds =du + Pdv
T ds dU nCy dT,
=
V= Constmt,
=
Cy
=
ds nCy . o nG
S-S =n'Cp m
into a lake
which is at 8'c.Caleulate () EntroPH EnETabion f blck
'6 at a temp. of 10o'c I f same block is drapped
A copper
ACopper
block of
mass 8
kg dropped
from a haight of 1oo m. CP-4-187 K3/kg k , clheab
Copa.city) of Cu = 150 / k
m)au B0 3/k. O dsun6Sn
dt ds
=
6Sgen.
mce In+
SSan
- 150 In 21315t 100 mce100-ss.
213-15+8)
150
dSgen
lss mgh + ma4T
8x9.81x
21-64
(27315t3)
In S15]t 56X 32
281 15
-
8Sgen
E9h548 6.62 /K
VLtUb
l0o + 150x (100-)
bT
d
kJ,
SndSe + dS s 150 ln28 1S+264*
0
264x1o
(373.15
345 3k
+
281 IS