general energy analysis

Energy Energy Transfer and Energy, Energy Transfer, and General Energy Analysisgy y

Ref.1: Cengel & Boles, Chapter 2

ContentConcept of energy and its forms; internal energy heat and Concept of energy and its forms; internal energy, heat and terminologies associated with energy transfer by heatMechanisms of heat transfer: conduction convection and Mechanisms of heat transfer: conduction, convection, and radiation.Concept of work: e g electrical work and other forms of Concept of work: e.g. electrical work and other forms of mechanical workThe first law of thermodynamics:The first law of thermodynamics:Energy balances, and mechanisms of energy transfer to or from a system.

E i ffi i iEnergy conversion efficienciesImplications of energy conversions

© Swinburne University of Technology22

EnergyV i f Various forms: Thermal, Mechanical, Kinetic, Potential, Electric, Magnetic, Chemical, NuclearNuclearIn SI system in Joule (J) or kJsometime also express per unit mass; e = E/m (J/g)or per unit time (E flow rate) = J/s = Watt

Can be classified as: Macroscopic Those a system possesses as a whole with respect p y p pto some outside reference frame, e.g. PE, KEMicroscopic related to the molecular structures and activities


pInternal energy (U)

What is “Internal Energy” ?Sensible energy: The portion of the internal energy of a system associated with the kinetic

Ref.1

energies of the molecules.Latent energy: The internal energy associated with the phase of a system.Chemical energy: The internal energy associated with the atomic bonds in a molecule.Nuclear energy: The tremendous amount of energy associated with Ref.1

The internal energy of a system is the sum of all forms of the microscopic energies.

The various forms of

the strong bonds within the nucleus of the atom itself.

© Swinburne University of TechnologyInternal = Sensible + Latent + Chemical + Nuclear

Thermal = Sensible + LatentThe various forms of microscopic energies that make up sensible energy.

Consider a system moving with a velocity, v at an elevation Zrelative to the reference planerelative to the reference plane

GeneralSystem

CM rV

ZZ

We can define, the total energy E, that is: Ref plane (Z = 0)e, Z=0

The sum of all forms of energy that can exist within the system e.g. thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear

In simple mechanical system: E = sum of the internal energy (U), kinetic energy (KE), and potential energy (PE)


energy (PE)

Ki ti (KE) • Kinetic energy (KE) a result of the system's motion relative to an external relative to an external reference frame

• Potential energy (PE) a result of its elevation in a PE mgZ kJ( )esu t o ts e e at o agravitational field relative to the external reference frame

PE mgZ kJ= ( )

• Thus the total Energy E U KE PE kJ= + + ( )


on a unit mass basis

where e = E/m is the specific stored energy, and u = U/m is the specific internal energy.

If we are talking about the change in stored energyIf we are talking about the change in stored energy

∆ ∆ ∆ ∆E U KE PE kJ= + + ( )


I th f t ti l d t In the case of stationary closed systems: No change in KE and PE , ∆KE = ∆PE = 0

The change in the stored energy is identical to the change in internal energy for stationary systemsinternal energy for stationary systems

∆ ∆E U kJ= ( )∆ ∆E U kJ= ( )


How is energy transported across the boundary of a Energy TransportHow is energy transported across the boundary of a

general thermodynamic system ?

Closed systems (fixed mass systems) y ( y )Only in the form of heat or work

Open systems (control volumes) In the form of heat, work, and energy transported by the mass streams


Energy Transport by Heat and WorkH tHeat

energy transfer across a system boundary due to the gy y ytemperature difference between a system and its surroundings

WorkWorkenergy transfer associated with a force acting through a

di tdistance

Heat and work are energy transport mechanisms between a system and its surroundings


a system and its surroundings.

Similarities between heat and work:Th b th b d They are both boundary phenomena; i.e. recognized t th b d i

Surroundings

at the boundaries Systems possess energy, but

System(Energy)y p gy,

not heat or work W, Q

B th i t d ith t t t U lik Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state.Both are path functions, i.e., their magnitudes depends on the path followed during a process as well as the end


p g pstates

Heat and work are path dependent functions they have i t diff ti l (δ) i d δQ d δWinexact differentials (δ), i.e. expressed as δQ and δW

The following figure illustrates that properties (P, T, V, u, etc.) are point functions. However, heat and work are path functions.

700 kPa

100 kPa

© Swinburne University of Technology12120.01 m3 0.03 m3

The total heat transfer or work is obtained by adding the diff ti l t f h t (δQ) k (δW) l th differential amounts of heat (δQ) or work (δW) along the process path

2

121,

(not Q)along path

Q Qδ = ∆∫2

121,

(not )along path

W W Wδ = ∆∫

The integrals of δQ and δW are not Q2 – Q1 and W2 – W1


Sign Convention

Heat transfer to a system and k d b work done by a system are

positiveHeat transfer out of a system and work done to a system are negativeare negative


Energy Transfer by HeatE t f d t th T • Energy transfer due to the T difference between the system and its surroundings No heat transfer

heat heat

Surrounding, T = 25oC

and its surroundings• The net heat transferred to a

system is defined as: 25oC 15oC 5oC

Q Q Qnet in out= −∑∑

y

• Qin and Qout are the magnitudes of the heat transfer values• Often also represented in terms of heat transfer per unit mass of • Often also represented in terms of heat transfer per unit mass of

the system, q.Q


q Qm

= (J/g)

Adiabatic process process where there is no heat transfer across the

Q = 0

boundary (Q = 0), e.g. in perfectly insulated system

InsulationModes of heat transfer:

ConductionCo duct oConvection

© Swinburne University of Technology1616Radiation

ConductionConduction heat transfer is a Conduction heat transfer is a progressive transfer of energy from more energetic to less energetic

Ref.1

moleculesCan take place in solids, liquids or gases

Fourier's lawFourier s law

Q = heat flow per unit time (W)kt = thermal conductivity (W/m⋅K)A = area normal to heat flow (m2)

.


dT/dx = temperature gradient in the direction of heat flow (°C/m)

ConvectionConvection heat transfer is the mode of energy • Convection heat transfer is the mode of energy transfer between a solid surface and the adjacent fluid that is in motion

Combined effects of conduction and fluid motion Ref.1The rate of heat transfer by convection is

determined from Newton's law of cooling, expressed as

Q heat transfer rate (W).

Ref.1Q = heat transfer rate (W)A = heat transfer area (m2)h = convective heat transfer coefficient (W/m2⋅K)Ts = surface temperature (K)


s p ( )Tf = bulk fluid temperature away from the surface (K)

Th ti h t t f ffi i t (h) i The convective heat transfer coefficient (h) is an experimentally determined parameter

function of the surface geometry, the nature of the fluid motion, the properties of the fluid, and the bulk fluid , p p ,velocity

h W/m2⋅Kfree convection of gases 2-25free convection of liquids 50-100free convection of liquids 50 100forced convection of gases 25-250forced convection of liquids 50-20,000convection in boiling and condensation 2500 100 000


convection in boiling and condensation 2500-100,000

RadiationRadiative heat transfer is energy in Radiative heat transfer is energy in

transition from the surface of one body to the surface of another in the form of electromagnetic waves (photons)

Ref.1

Q = heat transfer per unit time (W)A = surface area for heat transfer (m2)

.A = surface area for heat transfer (m2)σ = Stefan-Boltzmann constant, 5.67x10-8 W/m2K4

ε = emissivity, 0 to 1Ts = absolute temperature of surface (K)


Tsurr = absolute temperature of surroundings (K)

Energy Transfer by WorkThe energy transfer associated with a force acting through a The energy transfer associated with a force acting through a

distance

a rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions

Of l d i f k d i f h Often also represented in terms of work done per unit mass of the system, w.


Mechanical forms of WorkEnergy expended by a force acting through a distanceEnergy expended by a force acting through a distance

Work = Force × Distanceexpressed as

when the force is not constant,

Symbol δ means that work is a path-dependent function and has an


y p pinexact differential

Other mechanical forms work Sh ft W kShaft Work

Consider a constant torque T h i li d h f f that is applied to a shaft, for a specified constant torque, the work done during n work done during n revolutions is determined as:

Power transmitted through the shaft (work done per unit time)


Other mechanical forms of workS i W kSpring WorkWhen the length of the spring changes by a differential amount dx under the influence of differential amount dx under the influence of a force F, the work done is

For linear elastic springs, the displacement x is proportional to the force applied.

where k = spring constant (kN/m)

Substituting and integrating yieldg g g y


Other mechanical forms work W k D El ti S lid BWork Done on Elastic Solid Bars

x

FF

σn = stress (unit, the same as pressure, N/m2)

Work Associated with the Stretching of a Liquid Film

Ref 1

σs = surface tension (energy required to extend a surface per unit area, J/m2)


Nonmechanical Forms of WorkElectrical work: The generalized force is the voltage (the electrical Electrical work: The generalized force is the voltage (the electrical potential) and the generalized displacement is the electrical charge.Power rate of electrical work done by yelectrons crossing a system boundary

The amount of electrical work done in a time period:

Magnetic work: The generalized force is the magnetic field strength and the generalized displacement is the total magnetic dipole moment. Electrical polarization work: The generalized force is the electric field strength and the generali ed displacement is the polari ation of the


strength and the generalized displacement is the polarization of the medium.

The First Law of ThermodynamicsC ti f E P i i lConservation of Energy Principle

E b ith t d d t d it Energy can be neither created nor destroyed; it can only change forms

Energy can cross the boundaries of a closed system in gy ythe form of heat or work Energy may cross a system boundary (control surface) Energy may cross a system boundary (control surface) of an open system by heat, work and mass transfer


PE1 = 10 kJKE1 = 0

mThe work (shaft)

(Adiabatic)

done on an adiabatic system is

equal to the increase in the

∆E = 8 kJ

PE2 = 7 kJ

∆z increase in the energy of the

system.Wsh,in = 8 kJ

E b

KE2 = 3 kJm

The work (Adiabatic)

Energy cannot be created or destroyed; it can only change forms.

The work (electrical) done on an adiabatic system is equal to

Win = 5 kJ

y g system is equal to the increase in the energy of the system.∆E = 5 kJ

Battery


yBattery

The First Law of Thermodynamics

The conservation of energy principle or the first law of The conservation of energy principle or the first law of thermodynamics is expressed as

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟⎠

⎞⎜⎜⎝

⎛system theofenergy

in total change Thesystem theleaving

energy system theentering

energy TotalTotal

E E E∆E E Ein out system− = ∆


The First Law of ThermodynamicsC id th f ll i t i l ti t f • Consider the following system moving relative to a reference plane r

V

EnergyinEnergyout

z

System CMr

V

Normally the total energy of a system is expressed as

Reference Plane, z = 0

Normally the total energy of a system is expressed as

E Internal energy Kinetic energy Potential energy= + + E U KE PE= + +

U = the sum of the energy contained within the molecules of the system


KE = the kinetic energy PE = the potential energy

The change in stored energy for the system isThe change in stored energy for the system is

∆ ∆ ∆ ∆E U KE PE= + +Thus conservation of energy principle, or the first law of thermodynamics for closed systems, is written as

in outE E U KE PE− = ∆ + ∆ + ∆

In the case of stationary system, i.e. v = 0 and has no change in elevation the equation reduces to

E E U∆© Swinburne University of Technology3131

in outE E U− = ∆

Mechanisms of Energy Transfer, Ein and EoutHow is energy transported across the boundary of a How is energy transported across the boundary of a

general thermodynamic system ?

Closed systems (fixed mass systems) y ( y )Only in the form of heat or work

Open systems (control volumes) In the form of heat, work, and energy transported by the mass streams


Mechanisms of Energy Transfer, Ein and EoutQ (Heat transfer)Q (Heat transfer)Energy transfer caused by a T difference between the system and its

di Q 0 f di b ti

W (Work)Energy transfer other than Q, e.g. i i i t t ti h ft tsurroundings. Q = 0 for adiabatic

systems

m (Mass flow)

rising piston, rotating shaft, etc.

( )The change of energy due to mass flow in or out of the system. This is equal to zero for closed systems. q y

Thus, the energy balance for a general system:

( ) ( )( )

in out in out in outE E Q Q W W

E E E

− = − + −

+ − = ∆


( ), ,mass in mass out systemE E E+ − = ∆

The energy balance can be expressed in a rate form:

For constant rates the total quantities during the time interval ∆tFor constant rates, the total quantities during the time interval ∆t are related to the quantities per unit time as

The energy balance may also be expressed in a per unit mass basis

and in differential forms


Cyclic ProcessF li th i iti l d fi l t t id ti l th For a cyclic process, the initial and final states are identical, thus

∆E = 0

The first law becomes:

Q W E∆net net cycle

net net

Q W E

Q W

− = ∆

=

In a cycle, the net change for any properties (point functions or exact differentials) is zero. However, the net work and heat transfer depend on the cycle path.


∆E = ∆U = ∆P = ∆T = ∆(any property) = 0

Energy Conversion EfficienciesEffi i ( ) i di t h ll i Efficiency (η) indicates how well an energy conversion or transfer process is accomplished

Desired ResultRequired Input

η =

Thermal efficiencyRatio of the net work output (the desired result) to the heat input

For a heat engine the desired result is the net work done (Wout – Win) and the inp t is the heat s pplied to make the c cle operate Q and the input is the heat supplied to make the cycle operate Qin.

η thnet outW

= , W W Wnet out out in, = −


η thinQ Q Qin net≠

Energy Conversion EfficienciesEffi i f h i l d iEfficiency of mechanical devices

Mechanical efficiency of pump and turbineMechanical efficiency of pump and turbine


Example

The mechanical efficiency of a fan is the ratio of the kinetic the ratio of the kinetic energy of air at the fan exit to the mechanical power input.

© Swinburne University of Technology38 Ref 1

Mechanical efficiency should not be confused with motor efficiency and generator efficiency

Pump efficiency

Generator efficiency

p y

Generator efficiency

Pump-Motor overall efficiency

Turbine-Generator overall efficiency

© Swinburne University of Technology

Combustion EfficiencyHeating value (HV) of the fuel: The amount of heat released when a unit Heating value (HV) of the fuel: The amount of heat released when a unit amount of fuel at room temperature is completely burned and the combustion products are cooled to the room temperature.

CombustionChamber

FuelCnHm

CO2H2ON2

Air

Q = HVReactantsProductsPP, TP

Combustion efficiency ratio of the actual heat transfer from the

Qout = HVTR, PR

Combustion efficiency ratio of the actual heat transfer from the combustion process to the heating value of the fuel

outQ


outcombustion

QHV

η =

Heating Value, HVLHV (lower heating value) the heating value when water appears as a LHV (lower heating value) the heating value when water appears as a gas in the products

LHV Q with H O in products=LHV is often used as the measure of energy per kg of fuel supplied to the gas turbine engine

2out vaporLHV Q with H O in products=

gas turbine engine

HHV (higher heating value) the heating value when water appears as HHV (higher heating value) the heating value when water appears as a liquid in the products

2 l dHHV Q with H O in products=HHV is often used as the measure of energy per kg of fuel supplied to the steam power cycle

2out liquidHHV Q with H O in products


Power Plant Overall Efficiency: y

, , ,

, ,

in cycle net cycle net electrical outputoverall

fuel fuel in cycle net cycle

Q W Wm HHV Q W

η⎛ ⎞⎛ ⎞⎛ ⎞

= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠

& & &

& && , ,

,

f f y y

overall combustion thermal generator

net electrical outputW

η η η η

η

⎝ ⎠⎝ ⎠⎝ ⎠=

&p

overallfuel fuelm HHV

η =&


Lighting Efficacy:Lighting Efficacy: Amount of Light in Lumens

Watts of Electricity ConsumedLighting Efficacy =

Type of lighting Efficacy, lumens/W

Ordinary Incandescent 6 - 20

Ordinary Fluorescent 40 - 60

Effi i f C ki A liEfficiency of a Cooking Appliance Effectiveness of Conversion of Electrical or chemical Energy to

Heat for Cooking

Useful Energy Transferred to FoodEnergy Consumed by Appliance

Cooking Efficiency =


Implications of energy conversion on the environmentThe conversion of energy from one form The conversion of energy from one form to another often affects the environment and the air we breathe in many ways.

Pollutants emitted during the combustion of fossil fuels are responsible for smog, acid rain, and green house effect:global warming global warming.

Improved energy efficiency energy Energy conversion Ref 1

Improved energy efficiency, energy conservation, and using renewable energy sources help minimize global

processes are often accompanied by environmental pollution.


energy sources help minimize global warming.

Implications of energy conversion on the environmentS t i bl Sustainable processes

SOCIAL

S i blBearableEquitable

SustainableENVIRONMENT

ECONOMIC ViableECONOMIC Viable


SummaryForms of energyForms of energy

Macroscopic = kinetic + potential Microscopic = Internal energy (sensible + latent + chemical + nuclear)

Energy transfer by heat Energy transfer by workM h i l f f kMechanical forms of workThe first law of thermodynamics

Energy balanceEnergy balanceEnergy change of a systemMechanisms of energy transfer (heat, work, mass flow)

E i ffi i iEnergy conversion efficienciesEfficiencies of mechanical and electrical devices (turbines, pumps)

Energy and environment


Energy and environment

Example 3

A fluid contained in a piston cylinder device receives 500 kJ of electrical workA fluid contained in a piston-cylinder device receives 500 kJ of electrical work as the gas expands against the piston and does 600 kJ of boundary work on the piston. What is the net work done by the fluid?

Wele =500 kJ Wb=600 kJ

( )net net bhW W W= +( )

( )( )

,

net net bother

net out in ele botherW W W W= − +

( )0 500 600100

net

net

W kJ kJW kJ

= − +

=


Example 4

A system receives 5 kJ of heat transfer and experiences a decrease in y penergy in the amount of 5 kJ. Determine the amount of work done by the system.

∆E= -5 kJQ 5 kJ W ?Qin =5 kJ Wout=?

System BoundaryBoundary

We apply the first law as

in out systemE E E− = ∆

5

5

in in

out out

t

E Q kJE W

E kJ

= ==

∆ = −

The work done by the system equals the energy input by heat plus the decrease in the energy of the working

( )

5

5 5

system

out in system

out

E kJ

E E E

W kJ

∆

= − ∆

= − −⎡ ⎤⎣ ⎦

decrease in the energy of the working fluid.


( )10

out

outW kJ⎣ ⎦

=

Example 5

A steam power plant operates on a thermodynamic cycle in which water circulates through a boiler turbine

net net cycle

t t

Q W EQ W

− = ∆

=circulates through a boiler, turbine, condenser, pump, and back to the boiler.

For each kilogram of steam (water)

net net

in out out in

out in out in

Q WQ Q W W

W Q Q W− = −

= − −For each kilogram of steam (water) flowing through the cycle, the cycle receives 2000 kJ of heat in the boiler, rejects 1500 kJ of heat to the

Let and

out in out in

W Qw qm m

w q q w

= =

= − +jenvironment in the condenser, and receives 5 kJ of work in the cycle pump. ( )2000 1500 5

out in out in

out

q qkJwkg

kJ

= − +

Determine the work done by the steam in the turbine, in kJ/kg.

505outkJwkg

=


Example 6

Air flows into an open system and carries energy at the rate of 300 kW. As the airAir flows into an open system and carries energy at the rate of 300 kW. As the air flows through the system it receives 600 kW of work and loses 100 kW of energy by heat transfer to the surroundings. If the system experiences no energy change as the air flows through it, how much energy does the air carry as it leaves the system, i kW?in kW?

System sketch:

Conservation of Energy:


Example 7

In example 2-5 the steam power plant received 2000 kJ/kg of heat, 5 kJ/kg of pumpIn example 2 5 the steam power plant received 2000 kJ/kg of heat, 5 kJ/kg of pump work, and produced 505 kJ/kg of turbine work. Determine the thermal efficiency for this cycle.

W it th th l ffi i it b iWe can write the thermal efficiency on a per unit mass basis as:

,net outth

wη =

( )505 5

thin

t i

qkJ

w w kg

η

−−

2000out in

in

w w kgkJqkg

= =

0.25 or 25%=


Example 8

A steam power plant receives 2000 kJ of heat per unit mass of steam flowing throughA steam power plant receives 2000 kJ of heat per unit mass of steam flowing through the steam generator when the steam flow rate is 100 kg/s. If the fuel supplied to the combustion chamber of the steam generator has a higher heating value of 40,000 kJ/kg of fuel and the combustion efficiency is 85%, determine the required fuel flow

t i k /rate, in kg/s.


general energy analysis

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