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Engineering Thermodynamics
Course objective:
The students will be given a comprehensive and rigorous treatment of engineering thermodynamics from the
classical point of view. This course will prepare students to use thermodynamics in professional practice and
gives them the necessary foundation for subsequent courses in thermodynamics, fluid mechanics and heat
transfer.
Course materials:
Required text:	
   M.J. Moran and H.N. Shapiro, Fundamentals of
engineering Thermodynamics, 5th ed. John
Wiley and sons, 2004.	
  
Organization:	
   	
   	
   2 lectures per week (1.5 h/lecture).	
  
Course evaluation: 2 term quizzes 10%	
  
	
   	
   	
   	
   	
   Assignments	
   	
   10%	
   	
  
	
   	
   	
   	
   Midterm exam 30%
Final exam 50%
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐	
  
2
Introductory Concepts and definitions: thermodynamics 1.1-1.7
Systems;	
  property,	
  state,	
  process	
  and	
  equilibrium;	
  unit	
  for	
  mass	
  	
  
length,	
  time	
  and	
  force;	
  specific	
  volume	
  and	
  pressure;	
  temperature;.	
  
methodology	
  for	
  solving	
  thermodynamics	
  problems	
  (2	
  lectures)	
  
Energy and the First law of thermodynamics:	
  Mechanical	
  concepts	
  2.1-­‐2.6	
  
of	
  energy;	
  energy	
  transfer	
  by	
  work;	
  energy	
  of	
  a	
  system;	
  energy	
  transfer	
  	
  
by	
  heat;	
  energy	
  balance	
  for	
  closed	
  systems;	
  energy	
  analysis	
  of	
  cycles.	
  
(3	
  lectures)	
  
Evaluating properties:	
  State	
  of	
  a	
  system;	
  simple	
  compressible	
  system;	
   3.1-­‐3.8	
  
p-­‐v-­‐T	
  realtion;	
  thermodynamic	
  property	
  data;	
  ideal	
  gas	
  model;	
  polytropic	
  
process	
  of	
  an	
  ideal	
  gas.	
  (	
  6	
  lectures)	
  
Control	
  Volume	
  Energy	
  Analysis:	
  conservation	
  of	
  mass	
  for	
  a	
  control	
  volume,	
   4.1-­‐4.3	
  	
  
Conservation	
  of	
  energy	
  for	
  a	
  control	
  volume;	
  analysis	
  of	
  control	
  volumes	
  
At	
  steady	
  state.	
  (	
  4	
  lectures)	
  
The second law of thermodynamics:	
  Statements	
  of	
  the	
  second	
  law;	
   5.1-­‐5.6	
  
Irreversible	
  and	
  reversible	
  processes;	
  applying	
  the	
  second	
  law	
  to	
  cycles;	
  
Kelvin	
  temperature	
  scale;	
  maximum	
  performance	
  for	
  cycles	
  operating	
  	
  
between	
  two	
  reservoirs;	
  Carnot	
  cycle.	
  (3	
  lectures)	
  
Entropy: Clausius inequality; entropy change definition; entropy
6.1-6.7, 6.9
of a pure, simple compressible substance; entropy change in
internally reversible processes; entropy balance for closed systems;
entropy	
  rate	
  balance	
  for	
  control	
  volumes	
  (steady	
  state	
  only);	
  isentropic	
  	
  
processes;	
  heat	
  transfer	
  and	
  work	
  in	
  internally	
  reversible,	
  steady	
  state	
  
	
  flow	
  process.	
  (7	
  lectures)	
  
Thermodynamics
Study of heat and its interconversion to other kinds of energy
Heat?
Energy
Energy transformation
The principle of energy conservation
Energy forms
Chemical, mechanical, thermal, etc
Systems that transform energy
power plants
refrigeration systems
Internal combustion engine
Fuel cells
Rockets
4
Powerplant
5
System: A quantity of matter
A system is a specific part of the universe that is of interest for study.
Surroundings: ” Everything else”
Concepts
System boundary: Separates system from surroundings
The boundary could be real or abstract. It is sometimes called control surface
All types of interaction between system and surroundings occur through the boundary.
6
Example systems as defined by boundary
Defining the system boundary will specify the types of interactions between
system and surroundings
7
Types of system
Closed system = Control mass
No mass crosses boundary
Energy can cross the boundary
Control volume = open system
Mass and energy exchange
A gas in piston-cylinder
assembly. example of a control volume ( open system. An
automobile engine
8
Thermodynamics
Classical StatisticalVs
Macroscopic
Temperature
pressure, etc
Overall behavior is a
result of
Microscpic
Atoms, molecules
molecular interactions
Engineering thermodynamics
Energy Total Energy = E
E = U + KE + PE
9
Engineering thermodynamics
Classical thermodynamics:
Concerned with overall behavior of a system. Do not deal with the structure of
matter at atomic, molecular or subatomic level.
Objective: Evaluation important aspects of system behavior from observations
of the overall system
Applications: Chemical engineering in general and many others
Statistical thermodynamics:
The microscopic approach to thermodynamics.
Objective: to characterize by statistical means the average behavior of
particles making up a system.
Applications: Lasers, plasma, high speed gas flows, chemical kinetics,
cryogenics ( very low temperature ) and others
10
Thermodynamical concepts
Property: Macroscopic characteristic of a system to which a numerical value
can be assigned at a given time without knowledge of the previous behavior
( history) of the system.
Ex. Mass, volume, energy, pressure and temperature
If the value of a property for an overall system is the sum of its values for the
parts into which the system is divided, it is called an Extensive property.
Depend on the size or extent of the system.
Ex. Mass, volume, energy, and several others
Two types of properties:
Extensive properties
Intensive properties
If the value for property is independent of the size or extent of the system it is
called Intensive property.
Ex. Temperature, density, ..
11
State: refers to the condition of a system as described by its properties.
Steady state: A state in which the properties of the system do not change
with time
Process: Transition from one state to another.
Thermodynamic cycle: a sequence of processes that begin and end at the
same state.
How many properties do you need to describe the state of a system?
Thermodynamical concepts
State 1
State 2
Process path : The succession of states during a process
12
Thermodynamical concepts
P
V
(V1, P1)
(V2, P2)
Example of processes
Gas
13
Process nomenclature
Isothermal process
A process that occurs under constant temperature conditions.
example: melting of ice or evaporation of water
Isobaric process
A process that occurs under constant pressure conditions.
example: melting of ice or evaporation of water
Isometric or isochoric process
A process that occurs under constant volume conditions.
Adiabatic process
A process that occurs with no heat transfer between the system and surroundings
14
A condition in which all the competing influences are in balance.
Ex. Isolate a system and all its properties will go toward a uniform value
Quasiequilibrium process:
A process in which the departure from thermodynamic equilibrium is at most
infinitesimal. i. e. a process that very close to equilibrium.
Ex. The crystallization of glass. Glass is a quasi state of SiO2 but very slowly
it goes toward the equilibrium state which is the crystalline state of it.
Thermodynamical concepts
Equilibrium
Can a process take place when you have a state at equilibrium?
15
Phase:
A quantity of matter that is homogenous throughout in both chemical
composition and physical structure
Ex. Air, homogenous liquid mixtures such as alcohol
Pure Substance:
A quantity of matter that is uniform and invariable in chemical composition.
It can exist in more than one phase but its chemical composition must remain
the same in all phases.
Ex. Liquid water and water vapor
Thermodynamical concepts
16
SI units
SI units: Systéme International d’Unités or International System of unites.
Legally accepted system in most countries.
Quantity Dimensions Units symbol
Mass M kilogram	
   kg
Length	
   L meter m
time t second s
Quantity Dimensions Units symbol Name
Velocity Lt-­‐1 m/s 	
   	
  
Acceleration Lt-­‐2 m/s2 	
   	
  
Force MLt-­‐2 kgm/s2 N newotons
Pressure ML-­‐1t-­‐2 kg/ms2	
  (N/m2) Pa pascal
Energy ML2t-­‐2 kgm2/s2	
  (Nm) J joule
Power ML2t-­‐3 kgm2/s3	
  (J/s) W watt
Primary dimensions
Secondary dimensions
17
Density and Specific volume
Continuum hypothesis: matter is described as distributed continuously throughout a
region.
ρ = lim
V→ #V
m
V
$
%
&
'
(
)
Density: When substances can be treated as continua, thus at any instant the density
at a point is defined as.
V´ is the smallest volume for which the matter can be considered as continuum
Density or local mass per unit volume is an intensive property that might vary from
point to point within a system.
Specific volume: defined as the reciprocal of the density. m3/kg
Intensive property that may vary from point to point.
Specific molar volume: defined as the volume occupied by 1 mole of the substance.
m3/kmol
Intensive property that may vary from point to point.
v = Mv
18
Pressure
Pressure: from the continuum viewpoint, the concept of pressure at any point is
defined as
P = lim
A→ "A
Fnormal
A
#
$
%
&
'
(
A´ is the smallest area at a point for which the matter can be considered as continuum
The SI unit for pressure is Pascal (Pa) = 1 N/m2
Unit SI	
  unit
1	
  Pa 1	
  Pa
760	
  mmHg	
  (Torr) 1.0325x105Pa
1	
  atm 1.0325x105Pa
1	
  bar 105Pa
Ordinary vacuum gauge
△P = Patm - Pabs,2
19
Absolute vs Gage pressure
Gage pressure: is the pressure measured with respect to the atmospheric pressure
0
Barometer reads
atmospheric pressure
Patm
Ordinary vacuum gauge
△P = Pabs,1 - Patm
Patm
Pabs,2
Pabs,1
20
h
A
V=A*h
W = mg = ⍴Vg = ⍴gAh
p = F/A = W/A = ⍴gh
PT
A B
PA = PB
PT = PA
PB = Patm + ⍴gL
PT = Patm + ⍴gL
A
Pressure measurement
The gauge pressure is highly
dependent on gravitational constant,
so the gauge pressure on moon is
completely different from that on
Earth
21
Absolute vs Gage pressure
Bourdon tube gage Manometer
P – Patm = ρgL
22
Thermal equilibrium
When changes in temperature, electrical resistance and all properties related to the
energy of the bodies cease to exist, then the two bodies are in thermal equilibrium.
Adiabatic process: a process with no thermal interaction with the surrounding.
Temperature is the indication to see the thermal equilibrium.
Isothermal process: a process in which the temperature of the system remains
constant.
Zeroth law of Thermodynamics
When two bodies are in thermal equilibrium with a third body they are in thermal
equilibrium.
A C B
Then A B
23
Temperature scale
Kelvin scale: the absolute thermodynamical temperature scale that provides a
continues definition of temperature. Denotes as K
Celcius scale: uses the triple point of water as the standard fix point. The fix point is
273.16 K which is the 0 C.
24
Methodology for solving thermodynamics problems
1. Known: state briefly in your own words what is known. Careful
reading.
2. Find: Identify the objective. What has to be determined.
3. Schematic and given data: draw a sketch of the system and
determine which system is appropriate for the analysis.
4. Assumptions: list all simplifying assumptions and idealizations
made to reduce it to one that is manageable.
5. Analysis: use the assumptions and idealizations, reduce the
appropriate governing equations and relationships to forms that will
provide the desired results.
25
Example
Vacuum system
IR spectrometer
A wind turbine-electric generator is mounted atop a tower. As wind blows steadily across the turbine
blades, electricity is generated. The electrical output of the generator is fed to storage battery.
a) Considering only the wind turbine-electric generator as the system. Identify locations on the system
boundary where system interacts with the surroundings. Describe changes occuring within the system
with time.
b) Repeat for a system that includes only the storage battery.
Solution:
Known: A wind turbine-electric generator provides electricity to a storage battery.
Find: For a system of a) the wind turbine-electric generator b) the storage battery. Identify the locations
where the system interacts with its surroundings, and describe the changes within the system with
time.
26
Example
Assumptions
1.In part (a) the system is the control volume
shown by the dashed line.
2.In part (b) the system is closed system
shown by dashed line
3.The wind is steady, i. e. blows at constant
rate
Analysis
(a)1st interaction between the system and surroundings is the air crossing the boundary of the control volume. 2d
interaction is the electrical current passing through the wires. In terms of macroscopic interaction this is not a mass
transfer. The changes of the system with time is none existent since the system reaches a steady state by the
steady blowing wing. The rotational speed of the blades are constant thus the electricity generation also.
(b)There is no macroscopic mass transfer. The system is closed. As the battery is charged and chemical reactions
occur within it, the temperature of the battery surface may increase and a heat transfer to the surrounding may
occur.
27
Using specific volume and pressure
15 kg of carbon dioxide (CO2) gas is fed to a cylinder having a volume of 20 m3 and
initially containing 15 kg of CO2 at a pressure of 10 bar. Later a pinhole develops and
the gas slowly leaks from the cylinder.
a)Determine the specific volume in m3/kg of the CO2 in the cylinder initially. Repeat for
the CO2 after the addition of 15 kg.
b)Plot the amount of CO2 that has leaked from the cylinder in kg versus the specific
volume of the CO2 remaining in the cylinder. consider v ranging up to 1.0 m3/kg
Solution:
28
Patm
Patm
hB
hAh

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Lecture 1 introduction of engineering thermodynamics

  • 1. Engineering Thermodynamics Course objective: The students will be given a comprehensive and rigorous treatment of engineering thermodynamics from the classical point of view. This course will prepare students to use thermodynamics in professional practice and gives them the necessary foundation for subsequent courses in thermodynamics, fluid mechanics and heat transfer. Course materials: Required text:   M.J. Moran and H.N. Shapiro, Fundamentals of engineering Thermodynamics, 5th ed. John Wiley and sons, 2004.   Organization:       2 lectures per week (1.5 h/lecture).   Course evaluation: 2 term quizzes 10%             Assignments     10%             Midterm exam 30% Final exam 50% -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐  
  • 2. 2 Introductory Concepts and definitions: thermodynamics 1.1-1.7 Systems;  property,  state,  process  and  equilibrium;  unit  for  mass     length,  time  and  force;  specific  volume  and  pressure;  temperature;.   methodology  for  solving  thermodynamics  problems  (2  lectures)   Energy and the First law of thermodynamics:  Mechanical  concepts  2.1-­‐2.6   of  energy;  energy  transfer  by  work;  energy  of  a  system;  energy  transfer     by  heat;  energy  balance  for  closed  systems;  energy  analysis  of  cycles.   (3  lectures)   Evaluating properties:  State  of  a  system;  simple  compressible  system;   3.1-­‐3.8   p-­‐v-­‐T  realtion;  thermodynamic  property  data;  ideal  gas  model;  polytropic   process  of  an  ideal  gas.  (  6  lectures)   Control  Volume  Energy  Analysis:  conservation  of  mass  for  a  control  volume,   4.1-­‐4.3     Conservation  of  energy  for  a  control  volume;  analysis  of  control  volumes   At  steady  state.  (  4  lectures)   The second law of thermodynamics:  Statements  of  the  second  law;   5.1-­‐5.6   Irreversible  and  reversible  processes;  applying  the  second  law  to  cycles;   Kelvin  temperature  scale;  maximum  performance  for  cycles  operating     between  two  reservoirs;  Carnot  cycle.  (3  lectures)   Entropy: Clausius inequality; entropy change definition; entropy 6.1-6.7, 6.9 of a pure, simple compressible substance; entropy change in internally reversible processes; entropy balance for closed systems; entropy  rate  balance  for  control  volumes  (steady  state  only);  isentropic     processes;  heat  transfer  and  work  in  internally  reversible,  steady  state    flow  process.  (7  lectures)  
  • 3. Thermodynamics Study of heat and its interconversion to other kinds of energy Heat? Energy Energy transformation The principle of energy conservation Energy forms Chemical, mechanical, thermal, etc Systems that transform energy power plants refrigeration systems Internal combustion engine Fuel cells Rockets
  • 5. 5 System: A quantity of matter A system is a specific part of the universe that is of interest for study. Surroundings: ” Everything else” Concepts System boundary: Separates system from surroundings The boundary could be real or abstract. It is sometimes called control surface All types of interaction between system and surroundings occur through the boundary.
  • 6. 6 Example systems as defined by boundary Defining the system boundary will specify the types of interactions between system and surroundings
  • 7. 7 Types of system Closed system = Control mass No mass crosses boundary Energy can cross the boundary Control volume = open system Mass and energy exchange A gas in piston-cylinder assembly. example of a control volume ( open system. An automobile engine
  • 8. 8 Thermodynamics Classical StatisticalVs Macroscopic Temperature pressure, etc Overall behavior is a result of Microscpic Atoms, molecules molecular interactions Engineering thermodynamics Energy Total Energy = E E = U + KE + PE
  • 9. 9 Engineering thermodynamics Classical thermodynamics: Concerned with overall behavior of a system. Do not deal with the structure of matter at atomic, molecular or subatomic level. Objective: Evaluation important aspects of system behavior from observations of the overall system Applications: Chemical engineering in general and many others Statistical thermodynamics: The microscopic approach to thermodynamics. Objective: to characterize by statistical means the average behavior of particles making up a system. Applications: Lasers, plasma, high speed gas flows, chemical kinetics, cryogenics ( very low temperature ) and others
  • 10. 10 Thermodynamical concepts Property: Macroscopic characteristic of a system to which a numerical value can be assigned at a given time without knowledge of the previous behavior ( history) of the system. Ex. Mass, volume, energy, pressure and temperature If the value of a property for an overall system is the sum of its values for the parts into which the system is divided, it is called an Extensive property. Depend on the size or extent of the system. Ex. Mass, volume, energy, and several others Two types of properties: Extensive properties Intensive properties If the value for property is independent of the size or extent of the system it is called Intensive property. Ex. Temperature, density, ..
  • 11. 11 State: refers to the condition of a system as described by its properties. Steady state: A state in which the properties of the system do not change with time Process: Transition from one state to another. Thermodynamic cycle: a sequence of processes that begin and end at the same state. How many properties do you need to describe the state of a system? Thermodynamical concepts State 1 State 2 Process path : The succession of states during a process
  • 12. 12 Thermodynamical concepts P V (V1, P1) (V2, P2) Example of processes Gas
  • 13. 13 Process nomenclature Isothermal process A process that occurs under constant temperature conditions. example: melting of ice or evaporation of water Isobaric process A process that occurs under constant pressure conditions. example: melting of ice or evaporation of water Isometric or isochoric process A process that occurs under constant volume conditions. Adiabatic process A process that occurs with no heat transfer between the system and surroundings
  • 14. 14 A condition in which all the competing influences are in balance. Ex. Isolate a system and all its properties will go toward a uniform value Quasiequilibrium process: A process in which the departure from thermodynamic equilibrium is at most infinitesimal. i. e. a process that very close to equilibrium. Ex. The crystallization of glass. Glass is a quasi state of SiO2 but very slowly it goes toward the equilibrium state which is the crystalline state of it. Thermodynamical concepts Equilibrium Can a process take place when you have a state at equilibrium?
  • 15. 15 Phase: A quantity of matter that is homogenous throughout in both chemical composition and physical structure Ex. Air, homogenous liquid mixtures such as alcohol Pure Substance: A quantity of matter that is uniform and invariable in chemical composition. It can exist in more than one phase but its chemical composition must remain the same in all phases. Ex. Liquid water and water vapor Thermodynamical concepts
  • 16. 16 SI units SI units: Systéme International d’Unités or International System of unites. Legally accepted system in most countries. Quantity Dimensions Units symbol Mass M kilogram   kg Length   L meter m time t second s Quantity Dimensions Units symbol Name Velocity Lt-­‐1 m/s     Acceleration Lt-­‐2 m/s2     Force MLt-­‐2 kgm/s2 N newotons Pressure ML-­‐1t-­‐2 kg/ms2  (N/m2) Pa pascal Energy ML2t-­‐2 kgm2/s2  (Nm) J joule Power ML2t-­‐3 kgm2/s3  (J/s) W watt Primary dimensions Secondary dimensions
  • 17. 17 Density and Specific volume Continuum hypothesis: matter is described as distributed continuously throughout a region. ρ = lim V→ #V m V $ % & ' ( ) Density: When substances can be treated as continua, thus at any instant the density at a point is defined as. V´ is the smallest volume for which the matter can be considered as continuum Density or local mass per unit volume is an intensive property that might vary from point to point within a system. Specific volume: defined as the reciprocal of the density. m3/kg Intensive property that may vary from point to point. Specific molar volume: defined as the volume occupied by 1 mole of the substance. m3/kmol Intensive property that may vary from point to point. v = Mv
  • 18. 18 Pressure Pressure: from the continuum viewpoint, the concept of pressure at any point is defined as P = lim A→ "A Fnormal A # $ % & ' ( A´ is the smallest area at a point for which the matter can be considered as continuum The SI unit for pressure is Pascal (Pa) = 1 N/m2 Unit SI  unit 1  Pa 1  Pa 760  mmHg  (Torr) 1.0325x105Pa 1  atm 1.0325x105Pa 1  bar 105Pa
  • 19. Ordinary vacuum gauge △P = Patm - Pabs,2 19 Absolute vs Gage pressure Gage pressure: is the pressure measured with respect to the atmospheric pressure 0 Barometer reads atmospheric pressure Patm Ordinary vacuum gauge △P = Pabs,1 - Patm Patm Pabs,2 Pabs,1
  • 20. 20 h A V=A*h W = mg = ⍴Vg = ⍴gAh p = F/A = W/A = ⍴gh PT A B PA = PB PT = PA PB = Patm + ⍴gL PT = Patm + ⍴gL A Pressure measurement The gauge pressure is highly dependent on gravitational constant, so the gauge pressure on moon is completely different from that on Earth
  • 21. 21 Absolute vs Gage pressure Bourdon tube gage Manometer P – Patm = ρgL
  • 22. 22 Thermal equilibrium When changes in temperature, electrical resistance and all properties related to the energy of the bodies cease to exist, then the two bodies are in thermal equilibrium. Adiabatic process: a process with no thermal interaction with the surrounding. Temperature is the indication to see the thermal equilibrium. Isothermal process: a process in which the temperature of the system remains constant. Zeroth law of Thermodynamics When two bodies are in thermal equilibrium with a third body they are in thermal equilibrium. A C B Then A B
  • 23. 23 Temperature scale Kelvin scale: the absolute thermodynamical temperature scale that provides a continues definition of temperature. Denotes as K Celcius scale: uses the triple point of water as the standard fix point. The fix point is 273.16 K which is the 0 C.
  • 24. 24 Methodology for solving thermodynamics problems 1. Known: state briefly in your own words what is known. Careful reading. 2. Find: Identify the objective. What has to be determined. 3. Schematic and given data: draw a sketch of the system and determine which system is appropriate for the analysis. 4. Assumptions: list all simplifying assumptions and idealizations made to reduce it to one that is manageable. 5. Analysis: use the assumptions and idealizations, reduce the appropriate governing equations and relationships to forms that will provide the desired results.
  • 25. 25 Example Vacuum system IR spectrometer A wind turbine-electric generator is mounted atop a tower. As wind blows steadily across the turbine blades, electricity is generated. The electrical output of the generator is fed to storage battery. a) Considering only the wind turbine-electric generator as the system. Identify locations on the system boundary where system interacts with the surroundings. Describe changes occuring within the system with time. b) Repeat for a system that includes only the storage battery. Solution: Known: A wind turbine-electric generator provides electricity to a storage battery. Find: For a system of a) the wind turbine-electric generator b) the storage battery. Identify the locations where the system interacts with its surroundings, and describe the changes within the system with time.
  • 26. 26 Example Assumptions 1.In part (a) the system is the control volume shown by the dashed line. 2.In part (b) the system is closed system shown by dashed line 3.The wind is steady, i. e. blows at constant rate Analysis (a)1st interaction between the system and surroundings is the air crossing the boundary of the control volume. 2d interaction is the electrical current passing through the wires. In terms of macroscopic interaction this is not a mass transfer. The changes of the system with time is none existent since the system reaches a steady state by the steady blowing wing. The rotational speed of the blades are constant thus the electricity generation also. (b)There is no macroscopic mass transfer. The system is closed. As the battery is charged and chemical reactions occur within it, the temperature of the battery surface may increase and a heat transfer to the surrounding may occur.
  • 27. 27 Using specific volume and pressure 15 kg of carbon dioxide (CO2) gas is fed to a cylinder having a volume of 20 m3 and initially containing 15 kg of CO2 at a pressure of 10 bar. Later a pinhole develops and the gas slowly leaks from the cylinder. a)Determine the specific volume in m3/kg of the CO2 in the cylinder initially. Repeat for the CO2 after the addition of 15 kg. b)Plot the amount of CO2 that has leaked from the cylinder in kg versus the specific volume of the CO2 remaining in the cylinder. consider v ranging up to 1.0 m3/kg Solution: