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the branch of physical science that deals with the relations between heat and other forms of energy (such as mechanical, electrical, or chemical energy), and, by extension, of the relationships between all forms of energy.
Typology: Lecture notes
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Formule Units
Pressure
Pa
1 Pa = 1 N /m
5
1 bar = 10 Pa =0.1Mpa
1 atm = 101325 Pa
Specific Volume
v
m
3
m /kg
Density
m
ρ =
v
ρ =
3
kg /m
Static Pressure Variation
∆ P = ρgh ↑= − ,↓ = +
Pa
Absolute Temperature
T K( ) = T ( °C ) +273.
Formule Units
Quality
vapor
tot
m
x
m
(vapour mass fraction)
liquid
tot
m
x
m
(Liquid mass fraction)
Specific Volume
f fg
v = v +xv
3
m /kg
Average Specific Volume
f g
v = − x v +xv
(only two phase
mixture)
3
m /kg
Ideal –gas law
c
c
Pv = RT PV = mRT =nRT
kJ /kmol K
M
= molekulêre mass
kJ /kg K
Compressibility Factor
Z
Pv =ZRT
Reduced Properties
r
c
,
r
c
Formule Units
Conduction Heat Transfer
dT
Q kA
dx
,
k
=conductivity
Convection Heat Transfer
Q = hA T∆
,
h
=convection coefficient
Radiation Heat Transfer 4 4
( ) s amb
Q = εσA T −T
Terminology
= heat
1 2
= heat transferred during the process between state 1 and state 2
= rate of heat transfer
= work
1 2
= work done during the change from state 1 to state 2
= rate of work = Power. 1 W=1 J/s
Formule Units
Total Energy
E = U + KE + PE → dE = dU+ d KE( +) d PE( ) J
Energy
2 1 1 2 1 2
Kinetic Energy 2
KE = 0.5mV J
Potential Energy
2 1 2 1
PE = mgZ → PE − PE = mg Z( −Z ) J
Internal Energy
liq vap liq f vap g
U = U + U → mu = m u +m u
Specific Internal Energy
of
Saturated Steam
(two-phase mass
average)
f g
f fg
u x u xu
u u xu
kJ /kg
Total Energy 2 2
2 1
2 1 2 1 1 2 1 2
m V V
U U mg Z Z Q W
Specific Energy 2
e = u + 0.5V +gZ
Enthalpy
Specific Enthalpy
h = u + Pv kJ^ /kg
For Ideal Gasses
Pv = RT and u =f T( )
h = u + Pv = u +RT
u = f t( ) → h =f T( )
Specific Enthalpy for
Saturation State
(two-phase mass
average)
f g
f fg
h x h xh
h h xh
kJ /kg
Formule Units
Volume Flow Rate
V = V dA =AV
∫
(using average velocity)
Mass Flow Rate
m VdA AV A
v
= ρ = ρ = ∫
(using average values)
kg /s
Power
p
W =mC T
v
m
v
Flow Work Rate
flow
W = PV =mPv
Flow Direction From higher P to lower P unless significant KE or PE
Enthalpy
2 1
tot
h = h + V +gZ
Instantaneous
Process
Equation
C V.. i e
m = m − m ∑ ∑
Equation
C V.. C V.. C V.. i tot i e tot e
E = Q − W + m h − m h ∑ ∑
First Law
( )
2 2 1 1 ( )
i i i e e e
dE
Q m h V gZ m h V gZ W
dt
∑ ∑
Steady State
Process
A steady-state has no storage effects, with all properties
constant with time
C V C V
m = E =
Equation
i e
m = m ∑ ∑
(in = out)
Equation
C V.. i tot i C V.. e tot e
Q + m h = W + m h ∑ ∑
(in = out) First Law
( )
2 2 1 1 ( )
i i i e e e
→ Q + m h + V + gZ = W + m h + V +gZ ∑ ∑
Heat
Transfer
C V..
q
m
kJ /kg
Work
C V..
w
m
kJ /kg
Flow Eq.
tot i tot e
q + h = w +h
(in = out)
Transient Process Change in mass (storage) such as filling or emptying of a
container.
Equation
2 1 i e
m − m = m − m ∑ ∑
Equation
2 1 C V. C V.. i tot i e tot e
E − E = Q −W + m h − m h ∑ ∑
( ) ( )
2 2
2 1 2 2 2 2 1 1 1 1
E − E = m u + V + gZ − m u + V +gZ
( ) ( )
2 2
. 2 2 2 2 1 1 2 1.. ..
C V i tot i e tot e C V
C V
Q m h m h m u V gZ m u V gZ W
∑ ∑
Formule Units
All
W Q ,
can also be rates
W ,Q
& &
Refrigerator
L L
REF Carnot REF
REF H L
β = ≤ β =
Absolute Temp.
L L
H H
Formule Units
Inequality of Clausis
Ñ∫
Entropy
rev
dS
kJ /kgK
Change of Entropy 2
2 1
1 rev
δ
∫
kJ /kgK
Specific Entropy
f g
s = − x s +xs
f fg
s = s +xs
kJ /kgK
Entropy Change
2
1 2
2 1
1
H H
− = δ = ∫
Reversible Adiabatic (Isentropic Process):
rev
dS
Reversible Isothermal Process:
4
3 4
4 3
3 rev^ L
δ
− = =
∫
Reversible Adiabatic (Isentropic Process): Entropy
decrease in
process 3-4 = the entropy increase
in process 1-2.
Heat-Transfer
Process
2 2
1 2
2 1
1 1
(^1 1) fg
fg
rev
h Q q
s s s Q
m T mT T T
δ
δ
∫ ∫
Gibbs Equations
Tds = du +Pdv
Tds = dh −vdP
Entropy Generation
gen
dS S
irr gen
δW = PdV −T δS
2 2
2 1 1 2
1 1
gen
S S dS S
δ
∫ ∫
Entropy Balance Eq.
VEntropy = + in − out +gen
Ideal Gas Undergoing
an Isentropic Process
2 2
2 1 0
1 1
0 ln ln
s s Cp R
T P
0
2 2
1 1
R
Cp
T P
but
0 0
0 0
p v^1
p p
R k
C C k
,
0
0
p
v
k
= ratio of
specific heats
1
2 1 2 1
1 2 1 2
k k
T v P v
T v P v
−
Special case of polytropic process where k = n:
k
Pv =const
Reversible Polytropic
Process for Ideal Gas
1 1 2 2
n n n
PV = const = PV =PV
1 1
2 1 2 2 1
1 2 1 1 2
n n n n
P V T P V
− −
2 2 1 1 2 1
1 2
1 1
n
dV PV PV mR T T
W PdV const
V n n
∫ ∫
Isothermal Process:
Isentropic Process:
Isochronic Process:
n = ∞ , v =const
Formule Unit
s
2
nd Law Expressed as a
Change of Entropy
c m..
gen
dS Q
dt T
∑
Entropy Balance Eq.
rate of change = + in − out +generation
C V.. C V..
i i e e gen
dS Q
m s m s S
dt T
∑ ∑ ∑
where
....
C V c v A A B B
S = ρsdV = m s = m s + m s +
∫
and
..
gen gen gen A gen B
S = ρs dV = S + S + ∫
Steady State Process
.. 0
C V
dS
dt
.. ..
C V
e e i i gen
C V
m s m s S
∑ ∑ ∑
i e
m& = m& =m&
.. ..
C V
e i gen
C V
m s s S
∑
Polytropic
Process
for Ideal Gas
e
n n
i
w = − vdP and Pv = const =C
∫
( ) ( )
1
e e
n i i
e e i i e i
dP
w vdP C
n nR
P v Pv T T
n n
∫ ∫
Process (n=1) ln
e e
e
i i
i i^ i
dP P
w vdP C Pv
∫ ∫
Principle of the
Increase of Entropy
.. 0
net C V surr
gen
dS dS dS
dt dt dt
∑
Efficiency
a i e
s i es
w h h
w h h
η
Turbine work is out
(Pump)
s i es
a i e
w h h
w h h
η
Compressor work is in
Compressor
T
w
w
η =
2
2
e
es
η =
Kinetic energy is out
