Transcript Slide 1

111302
Aero Engineering
Thermodynamics
by
Mr.Suresh Chandra Khandai
Unit - I
Thermodynamic Systems, States and
Processes
Objectives are to:
• define thermodynamics systems and states of systems
• explain how processes affect such systems
• apply the above thermodynamic terms and ideas to the laws of
thermodynamics
Internal Energy of a Classical ideal gas
“Classical” means Equipartition Principle applies: each
molecule has average energy ½ kT per in thermal equilibrium.

At room temperature,
for most gases:
3
KE  kT
2
monatomic gas (He, Ne, Ar, …)
3 translational modes (x, y, z)
diatomic molecules (N2, O2, CO, …)
3 translational modes (x, y, z)
+ 2 rotational modes (wx, wy)
UN
3
3
kT  pV
2
2
5
KE  kT
2
Internal Energy of a Gas
A pressurized gas bottle (V = 0.05 m3), contains
helium gas (an ideal monatomic gas) at a pressure p =
1×107 Pa and temperature T = 300 K. What is the
internal thermal energy of this gas?
3
3
U  N kT  pV
2
2



 1.5  107 Pa  0.05m3  7.5 105 J
Changing the Internal Energy

U is a “state” function --- depends uniquely on the state of the
system in terms of p, V, T etc.
(e.g. For a classical ideal gas, U = NkT )

There are two ways to change the internal energy of a system:
WORK done by the system
on the environment
Wby = -Won
HEAT is the transfer of thermal energy
into the system from the surroundings
Thermal reservoir
Q
Work and Heat are process energies, not state functions.
Work Done by An Expanding Gas
The expands slowly enough to
maintain thermodynamic equilibrium.
dW  Fdy  PAdy
Increase in volume, dV
dW  PdV
+dV Positive Work (Work is
done by the gas)
-dV Negative Work (Work is
done on the gas)
A Historical Convention
+dV Positive Work (Work is
done by the gas)
Energy leaves the system
and goes to the environment.
-dV Negative Work (Work is
done on the gas)
Energy enters the system
from the environment.
Total Work Done
dW  PdV
Vf
W   PdV
Vi
To evaluate the integral, we must know
how the pressure depends (functionally)
on the volume.
Pressure as a Function of Volume
Vf
W   PdV
Vi
Work is the area under
the curve of a PV-diagram.
Work depends on the path
taken in “PV space.”
The precise path serves to
describe the kind of
process that took place.
Different Thermodynamic Paths
The work done depends on the initial and final
states and the path taken between these states.
Work done by a Gas


When a gas expands, it does work on its environment
Consider a piston with cross-sectional area A
filled with gas. For a small displacement dx,
the work done by the gas is:
dWby = F dx = pA dx = p (A dx)= p dV
 We generally assume quasi-static processes (slow
enough that p and T are well defined at all times):
dx
Wby 
This is just the area under the p-V curve
p
 p dV
Vi
p
p
V
Vf
V
V
Note that the amount of work needed to take the system from one
state to another is not unique! It depends on the path taken.
What is Heat?

Up to mid-1800’s heat was considered a substance -- a
“caloric fluid” that could be stored in an object and
transferred between objects. After 1850, kinetic
theory.

A more recent and still common misconception is that
heat is the quantity of thermal energy in an object.

The term Heat (Q) is properly used to describe energy
in transit, thermal energy transferred into or out of a
system from a thermal reservoir …
Q

U
(like cash transfers into and out of your bank account)
Q is not a “state” function --- the heat depends on the
process, not just on the initial and final states of the system
Sign of Q :
Q > 0 system gains thermal energy
Q < 0 system loses thermal energy
An Extraordinary Fact
The work done depends on the initial and final
states and the path taken between these states.
BUT, the quantity Q - W does not depend
on the path taken; it depends only on the initial
and final states.
Only Q - W has this property. Q, W, Q + W,
Q - 2W, etc. do not.
So we give Q - W a name: the internal energy.
The First Law of Thermodynamics
(FLT)
-- Heat and work are forms of energy transfer
and energy is conserved.
U = Q + Won
change in
total internal energy
heat added
to system
State Function
work done
on the system
Process Functions
or
U = Q - Wby
1st Law of Thermodynamics
U  Q  W
positiveQ : heat added to system
positiveW : work done by system
• statement of energy conservation for a thermodynamic
system
• internal energy U is a state variable
• W, Q process dependent
The First Law of Thermodynamics
dEint  dQ  dWby
What this means: The internal energy of a system
tends to increase if energy is added via heat (Q)
and decrease via work (W) done by the system.
dEint  dQ  dWon
. . . and increase via work (W) done on the system.
dWby  dWon
Isoprocesses
• apply 1st law of thermodynamics to closed
system of an ideal gas
• isoprocess is one in which one of the
thermodynamic (state) variables are kept
constant
• use pV diagram to visualise process
Isobaric Process
• process in which pressure is kept
constant
Isochoric Process
• process in which volume is kept
constant
Isothermal Process
• process in which temperature is held
constant
Thermodynamic processes of an ideal gas
( FLT: U = Q - Wby )

Isochoric (constant volume)
Wby   pdV 0
U   Nk T   V p
FLT:
2
p
Q  U
Q
1
Temperature
changes
V

Isobaric (constant pressure)
Wby   pdV  pV
U   Nk T   p V
FLT: Q  U  Wby    1 p V
p
1
2
p
Q
V
Temperature and
volume change
( FLT: U = Q - Wby )

Isothermal (constant temperature)
U  0
p
1
V2
V2
Wby   p dV  NkT n
V1
V
2
p
Q
1
FLT:
1
V
Thermal Reservoir
Q Wby
V
T
Volume and
pressure change
The First Law Of Thermodynamics
§2-1.The central point of first law
§2-2. Internal energy and total energy
§2-3.The equation of the first law
§2-4.The first law for closed system
§2-5.The first law for open system
§2-6.Application of the energy equation
§2-1.The
central point of first law
1.Expression
In a cyclic process, the algebraic sum of the
work transfers is proportional to the algebraic
sum of the heat transfers.
Energy can be neither created nor destroyed;
it can only change forms.
The first law of thermodynamics is simply a
statement of energy principle.
§2-1.The
central point of first
law
2.Central point
The energy conservation law is used to
conservation between work and heat.
Perpetual motion machines of the first
kind.(PMM1)
Heat: see chapter 1;
Work: see chapter 1;
§2-2.Internal
Energy
1.Definition:
Internal energy is all kinds of micro-energy in system.
2. Internal energy is property
It include:
a) Kinetic energy of molecule (translational kinetic,
vibration, rotational energy)
b) Potential energy
c) Chemical energy
d) Nuclear energy
§2-2.Internal
Energy
3.The symbol
u: specific internal energy, unit –J/kg, kJ/kg ;
U: total internal energy,
unit – J, kJ;
4.Total energy of system
E=Ek+Ep+U
Ek=mcf2/2
Ep=mgz
ΔE=ΔEk+ΔEp+ΔU
per unit mass:
e=ek+ep+u
Δe=Δek+Δep+Δu
§2-3.
The equation of the first law
1. The equation
( inlet energy of system) – (outlet energy of
system) = (the change of the total energy of the
system)
Ein-Eout=ΔEsystem
§2-4.The first law in closed system
1. The equation
Ein-Eout=ΔEsystem
Q
W
§2-4.The first law in closed system
Q-W=ΔEsystem=ΔU
Q=ΔU+W
Per unit mass:
q= Δu+w
dq=du+dw
If the process is reversible, then:
dq=du+pdv
This is the first equation of the first law.
Here q, w, Δu is algebraic.
§2-4.The first law in closed system
The only way of the heat change to mechanical
energy is expansion of working fluid.
§2-5.
The first law in open system
1. Stead flow
For stead flow, the following conditions are
fulfilled:
① The matter of system is flowing steadily, so that
the flow rate across any section of the flow has
the same value;
② The state of the matter at any point remains
constant;
③ Q, W flow remains constant;
§2-5.
The first law in open system
2. Flow work
Wflow=pfΔs=pV
wflow=pv
p
V
§2-5.
The first law in open system
3. 技术功
“ Wt” are expansion work and the
change of flow work for open system.
4. 轴功
“ Ws” is “ Wt” and the change of kinetic
and potential energy of fluid for open
system.
§2-5.
The first law in open system
5. Enthalpy
for flow fluid energy:
U+pV +mcf2/2+mgz
H =U+pV
unit: J, kJ
For Per unit mass:
h=u+pv
unit: J/kg, kJ/kg
§2-5.
The first law in open system
6. Energy equation for steady flow open system
, 1mc
U1+p
H
V1 f12/2, mgz1
W
Q
U2+p
H
V2 f22/2, mgz2
, 2mc
§2-5.
The first law in open system
1
2
Ein  Q  H1  m1c f 1  mgz 1
2
1
2
Eout  Ws  H 2  m2c f 2  mgz 2
2
Esystem  0
1
1
2
2
(Q  H1  m1c f 1  mgz 1 )  (Ws  H 2  mc f 2  mgz 2 )  0
2
2
§2-5.
The first law in open system
1
2
Q  H  mc f  mg z  Ws
2
Per unit mass:
1 2
1 2
(q  h1  c f 1  gz1 )  ( ws  h2  c f 2  gz 2 )  0
2
2
1
2
q  h  c f  gz  ws
2
§2-5.
The first law in open system
If neglect kinetic energy and potential energy , then:
q  h  wt
If the process is reversible, then:
q  h  vdp
This is the second equation of the first law.
§2-5.
The first law in open system
7. Energy equation for the open system
Q
Inlet flows
Out flows
1
1
2
Open system
2
……
……
i
j
W
§2-5.
The first law in open system
Energy equation for the open system
n
.
.
.
.
.
.
1 2
1 2
Q Ws   (hi  c fi  g zi ) mi   ( h j  c fj  g z j ) m j   Esystem
2
2
i
i
.
.
n
.
§2-6. Application of The Energy Equation
1. Engine
a). Turbines energy equation:
Ein-Eout=Esystem=0
Wi=H2-H1
wi=h2-h1
Q
Q≈0
, 1mc
U1+p
H
V1 f12/2, mgz1 =0
Wi
U2+p
H22V2
mcf22/2, mgz2=0
§2-6. Application of The Energy Equation
1. Engine
b). Cylinder engine energy equation:
Wt=H2-H1+Q=(U+pV) 2-(U+pV) 1 +Q
Ek1, Ep1≈0
H2
Q
H1
Ek1, Ep1≈0
Wt
§2-6. Application of The Energy Equation
2. Compressors
Energy equation:
Wc=- Wt =H2-H1
Ek1, Ep1≈0
H2
Wc
H1
Ek1, Ep1≈0
Q≈0
§2-6. Application of The Energy Equation
3. Mixing chambers
Energy equation:
m1h1 + m2h2 -m3h3=0
Mixing water:
m3h3
hot water: m2h2
Cold water: m1h1
§2-6. Application of The Energy Equation
4. Heat exchangers
Energy equation:
m3h3
m２h２
m5h5
m1h1
m4h4
m6h6
(m1h1 + m2h2 + m3h3)-(m4h4 + m5h5 + m6h6)= 0
§2-6. Application of The Energy Equation
5. Throttling valves
Energy equation:
h1 -h2 =0
h2
h1
Unit - II
Air Cycles
OTTO CYCLE
OTTO CYCLE
Efficiency is given by
 1
1
r
 1
Efficiency increases with increase in
compression ratio and specific heat
ratio (γ) and is independent of load,
amount of heat added and initial
conditions.

r
1
0
2
0.242
3
0.356
4
0.426
5
0.475
6
0.512
7
0.541
8
0.565
9
0.585
10
0.602
16
0.67
20
0.698
50
0.791
CR ↑from 2 to 4, efficiency ↑ is 76%
CR from 4 to 8 efficiency is 32.6
CR
from 8 to 16 efficiency
18.6
OTTO CYCLE
Mean Effective Pressure
It is that constant pressure which, if exerted
on the piston for the whole outward stroke,
would yield work equal to the work of the
cycle. It is given by
W
m ep 
V1  V2

 Q23
V1  V2
OTTO CYCLE
Mean Effective Pressure
We have:
 V2 
V1  V2  V1 1  
 V1 
 1
 V1 1  
r

Eq. of state:
To give:
R0 T1
V1  M
m p1
m ep  
p1m
MR0T1
1
1
r
Q23
OTTO CYCLE
Mean Effective Pressure
The quantity Q2-3/M is heat added/unit
mass equal to Q’, so
p1m
Q
R0T1
m ep  
1
1
r
OTTO CYCLE
Mean Effective Pressure
Non-dimensionalizing mep with p1 we get


 1   Q m 
m ep




1
p1
1    R0 T1 
 r
Since:
R0
 cv   1
m
OTTO CYCLE
Mean Effective Pressure
We get
m ep
Q
1

p1
cvT1  1 
1  r   1
Mep/p1 is a function of heat added, initial
temperature, compression ratio and
properties of air, namely, cv and γ
Choice of Q’
We have
Q23
Q 
M
For an actual engine: Q23  M f Qc
 FM a Qc in kJ / cycle
F=fuel-air ratio, Mf/Ma
Ma=Mass of air,
Qc=fuel calorific value
Choice of Q’
FM
Q
a
c
We now get: Q 
M
M a V1  V2
Now

M
V1
V1  V2
1
And
1
V1
r
Thus:
 1
Q  FQc 1  
r

Choice of Q’
For isooctane, FQc at stoichiometric
conditions is equal to 2975 kJ/kg, thus
Q’ = 2975(r – 1)/r
At an ambient temperature, T1 of 300K and
cv for air is assumed to be 0.718 kJ/kgK,
we get a value of Q’/cvT1 = 13.8(r – 1)/r.
Under fuel rich conditions, φ = 1.2, Q’/ cvT1 =
16.6(r – 1)/r.
Under fuel lean conditions, φ = 0.8, Q’/ cvT1
= 11.1(r – 1)/r
OTTO CYCLE
Mean Effective Pressure
Another parameter, which is of importance,
is the quantity mep/p3. This can be
obtained from the following expression:
m ep m ep 1


p3
p1 r
1
Q
1
 1
cvT1r
Diesel Cycle
Thermal Efficiency of cycle is given by
1  rc  1 
  1   1 

r   rc  1

rc is the cut-ff ratio, V3/V2
We can write rc in terms of Q’:
Q
rc 
1
 1
c pT1r
We can write the mep formula for the
diesel cycle like that for the Otto cycle in
terms of the η, Q’, γ, cv and T1:
m ep
Q
1

p1
cvT1  1 


1



1
 r 
Diesel Cycle
We can write the mep in terms of γ, r and
rc:




mep  r rc  1  r rc  1

r  1  1
p1
The expression for mep/p3 is:
m ep m ep  1 

 
p3
p1  r 
DUAL CYCLE
Dual Cycle
The Efficiency is given by

r r 1
1 
  1   1 

r  rp  1   rp rc  1

p c
We can use the same expression as
before to obtain the mep.
To obtain the mep in terms of the cut-off
and pressure ratios we have the
following expression
Dual Cycle

mep  rp r rc  1  r rp  1  r rp rc  1

r  1  1
p1




For the dual cycle, the expression for mep/p3
is as follows:
Dual Cycle

mep  rp r rc  1  r rp  1  r rp rc  1

r  1  1
p1



For the dual cycle, the expression for mep/p3
is as follows:
m ep m ep  p1 
 

p3
p1  p3 

Dual Cycle
We can write an expression for rp the
pressure ratio in terms of the peak
pressure which is a known quantity:
p3  1 
rp    
p1  r 
We can obtain an expression for rc in terms
of Q’ and rp and other known quantities as
follows:
Dual Cycle

1   Q  1 



rc 



1




 1


   cvT1r  rp 

We can also obtain an expression for rp in
terms of Q’ and rc and other known
quantities as follows:
 Q

 c T r   1  1
v 1


rp 
1   rc  
Unit – IV & V
Refrigeration &
Air Conditioning
Objectives
• Basic operation of refrigeration and AC
systems
• Principle components of refrigeration and
AC systems
• Thermodynamic principles of refrigeration
cycle
• Safety considerations
Uses of Systems
• Cooling of food stores and cargo
• Cooling of electronic spaces and
equipment
– CIC (computers and consoles)
– Radio (communications gear)
– Radars
– ESGN/RLGN
– Sonar
• Cooling of magazines
• Air conditioning for crew comfort
Definition Review
• Specific heat (cp): Amount of heat
required to raise the temperature of 1 lb
of substance 1°F (BTU/lb) – how much
for water?
• Sensible heat vs Latent heat
• LHV/LHF
• Second Law of Thermodynamics: must
expend energy to get process to work
Refrigeration Cycle
• Refrigeration - Cooling of an object and
maintenance of its temp below that of
surroundings
• Working substance must alternate b/t
colder and hotter regions
• Most common: vapor compression
– Reverse of power cycle
– Heat absorbed in low temp region and
released in high temp region
Generic Refrigeration Cycle
Thermodynamic Cycle
Typical
Refrigeration
Cycle
Components
• Refrigerant
• Evaporator/Chille
r
• Compressor
• Condenser
• Receiver
• Thermostatic
expansion valve
(TXV)
Refrigerant
• Desirable properties:
– High latent heat of vaporization - max cooling
– Non-toxicity (no health hazard)
– Desirable saturation temp (for operating
pressure)
– Chemical stability (non-flammable/nonexplosive)
– Ease of leak detection
– Low cost
– Readily available
Evaporator/Chiller
• Located in space to be refrigerated
• Cooling coil acts as an indirect heat
exchanger
• Absorbs heat from surroundings and
vaporizes
– Latentsuperheated
Heat of Vaporization
Slightly
(10°F) – Sensible
Heatcarryover
of surroundings
ensures
no liquid
into
compressor
•
Compressor
• Superheated Vapor:
– Enters as low press, low temp vapor
– Exits as high press, high temp vapor
•
Temp: creates differential (T)
promotes heat transfer
• Press: Tsat
allows for
condensation at warmer temps
• Increase in energy provides the driving
force to circulate refrigerant through the
system
Condenser
• Refrigerant rejects latent heat to cooling
medium
• Latent heat of condensation (LHC)
• Indirect heat exchanger: seawater absorbs
the heat and discharges it overboard
Receiver
• Temporary storage space & surge
volume for the sub-cooled refrigerant
• Serves as a vapor seal to prevent vapor
from entering the expansion valve
Expansion Device
• Thermostatic Expansion Valve (TXV)
• Liquid Freon enters the expansion valve
at high pressure and leaves as a low
pressure wet vapor (vapor forms as
refrigerant enters saturation region)
• Controls:
– Pressure reduction
– Amount of refrigerant entering evaporator
controls capacity
Air Conditioning
• Purpose: maintain the atmosphere of an
enclosed space at a required temp,
humidity and purity
• Refrigeration system is at heart of AC
system
• Heaters in ventilation system
• Types Used:
• Self-contained
• Refrigerant circulating
• Chill water circulating
AC System Types
• Self-Contained System
– Add-on to ships that originally did not have
AC plants
– Not located in ventilation system (window
unit)
• Refrigerant circulating system
– Hot air passed over refrigerant cooling coils
directly
• Chilled water circulating system
– Refrigerant cools chill water
– Hot air passes over chill water cooling coils
Basic AC System
Safety Precautions
• Phosgene gas hazard
– Lethal
– Created when refrigerant is exposed to high
temperatures
• Handling procedures
– Wear goggles and gloves to avoid eye irritation and
frostbite
• Asphyxiation hazard in non-ventilated spaces
(bilges since heavier than air)
• Handling of compressed gas bottles
THANK U