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The First Law of Thermodynamics

Conservation of Energy

Energy Balance

= Energy transferred across system

boundary

ECV= Energy contained within system boundary

CVIN OUT

dEE E

dt

IN,OUTE

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Forms of Energy

Energy comes in a variety of forms

Potential

Mechanical Chemical Electrical

Internal Kinetic

Heat

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Closed Systems

Mass Balance

dmCV/dt = 0

mCV

= constant

Energy Balance

ECM= U + KE + PE

KE=mCMv2/2gC

PE = mCMzg/gC

CM CM 2 CM 1 IN IN OUT OUTE E (t ) - E (t ) Q W Q +W

system

boundary QOUT

WINor WOUT

QIN

Mass does not cross system boundary

Energy crosses system boundary.

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Open (Control Volume) Systems

Denote with CV subscript (e.g., mCV)

Mass and energy cross system boundary On the following slides,

Compare combustion in open and closed

systems See a gas turbine that is analyzed as an

open system

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Conservation of Mass

Rate Basis

Time Interval

Useful Relations

= Volumetric flow rate [m3/s or ft3/s]

AX

= cross-sectional flow area [m2or ft2]

CVIN OUT dmm m =

dt

2

1

t

IN OUT CV 1 CV 2

t=t[m (t)-m (t)] dt=m (t ) m (t )

XAV

mv v

v

V

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Flow Work and Enthalpy

Mass crossing system boundary

Carries energy u + ke + pe per unit mass flow Does flow work Pv per unit mass flow

Recall enthalpy, h = u + Pv

Total energy entering/leaving system due to mass

transferis u + ke + pe + Pv = h + ke + peper unit massflow.

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The First Law

IN IN IN,i i i i

CVOUT OUT OUT,j j j

CVIN OUT CV CV

IN,OUT

j

dEE E where E m ke pe

dt

E Q W m ke pe

o

u

h

Q W m h ke pe

dEQ W m h ke pe

dt

r

Change in energy for open system is sum of

Shaft work: Present if rotating shaft crosses boundary Boundary (PdV) work: Present if dVCV/dt 0

Heat Transfer

Energy transfer by mass transfer (u + ke + pe)

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Steady-State Steady-Flow Processes

Steady-State (SS):

where ( )CVis any property

of the system (e.g., m or E)

CVd 0dt

IN,OUTd

0dt

.

.. . .

Steady-Flow (SF):

where ( )CVis any transfer across the system

boundary (e.g., Q, W or m)

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Steady-State Steady-Flow Processes

Steady-State Steady-Flow (SSSF) = No changes

with time Mass Balance

If 1 stream (i.e., 1-inlet and 1-outlet)

N MCV

IN,i OUT,ji 1 j 1

dmm m

dt

0, SS

N M

IN,i OUT,ji 1 j 1

m m

IN OUTm m m

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Steady-State Steady-Flow Processes

SSSF Energy Balance

If 1 stream (i.e., 1-inlet and 1-outlet) and dividingby mass flow rate

IN IN OUT OUTIN OUTq w h ke pe q w h ke pe

CVIN OUT

dEE Edt

0, SS

N

IN IN IN,i i i i

I

i 1N

OUT OUT OUT,j

N O

j j j

U

j 1

T

Q W m h ke pe

Q W m h ke

E

pe

E

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Nozzles and Diffusers

On next page, see a nozzle in a turbojet engine

A diffuserconverts high

speed, low pressureflow to low speed, high

pressure flow

A nozzleconverts high

pressure, low speed

flow to low pressure,

high speed flow

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Nozzles and Diffusers

Common Assumptions

SSSF No work or heat transfer

Neglect changes in pe

Energy Balance: Crossing out terms assumed 0

INq 0

INw 0 h ke pe 0 INOUTq 0

OUTw 0

h ke pe

0

2 2

C CIN OUT

OUT

IN OUT h h

2h ke h k

g 2ge

v v

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Throttling

Throttling: Reduces Pressure

Common Assumptions: SSSF

No work or heat transfer

Neglect changes in pe and ke

Energy Balance:

INq 0

INw 0

h ke 0

pe 0IN

OUTq 0

OUTw 0 h ke 0 pe 0 INOU OUTT h h

ThrottlingValve

Isenthalpic (h = constant) Process

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Pumps, Fans, and Blowers

Pumps: Pressurize ormove liquids

Fans & Blowers: Moveair

OUT

OUT

OUT

m

TP

INW

IN IN INm ,T ,P

Pump Schematic

Common Assumptions:

SSSF

No heat transfer

Neglect changes in pe and ke

EnergyBalance for fan& blower

EnergyBalance for pump(assuming ICL)IN OUT INw h h

IN OUT INw v P P

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Turbines

Turbine: Enthalpy Shaft

work

Used in

Almost all power plants

Some propulsion systems (e.g.,

turbofan and turbojet engines) Working Fluid:

Liquids (e.g., hydro power

plants)

Vapors (e.g., steam power plants)

Gases (e.g., gas power plants)

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Turbines

Common assumptions for turbine:

SSSF

Adiabatic (q = 0)

Neglect kinetic and potential energies

Turbine energy balance (Single Stream)

IN INQ W m h ke pe OUTIN

Q

INE

OUTW m h ke pe OUT

OUTE

dE

dt

0, SS

OUT IN OUT

OUT IN OUT

W m h h

Perunit mass flow w h h

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Compressors

Compressor: Shaft work Increase pressure &

enthalpy of vapor or gas

Often like turbine run in reverse

Used in

Gas power plants (e.g., gas turbine engine)

Turbo propulsion systems (e.g., turbofan and turbojetengines).

Industry (e.g., supply high pressure gas)

Working Fluids

Gas

Vapor

Not Liquid (pump used)

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Compressors

Common assumptions for compressor:

SSSF

Adiabatic (q = 0)

Neglect kinetic and potential energies

Compressor energy balance

INQ INW m h ke pe OUT OUTIN

Q W

INE

m h ke pe OUT

OUTE

dE

dt

0, SS

IN OUT IN

IN OUT IN

W m h h

Perunit mass flow w h h

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H E h

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Heat Exchangers

Common Assumptions

SSSF Externallyadiabatic

Neglect kinetic and potential

energies

IN INQ W m h ke pe IN

OUT OUT

Q W

m h ke pe

OUT

dE

dt

COLD OUT,COLD IN,COLD HOT IN,

0,S

HOT COLD,

S

HOTm h h m h h

Energy Balance

Mi i D i

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Mixing Devices

Combine 2 or more streams

Common in industrial processes

Common assumptions

SSSF

Adiabatic

Neglect kinetic and potential energies

Energy Balance (Streams 1 & 2 mixing to form 3)

IN INQ W m h ke pe IN

OUT OUTQ W

m h ke pe

OUT

dE

dt

1 1 2 2 3

0, S

3

S

m h m h m h

T i t (U t d ) A l i

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Transient (Unsteady) Analysis

Typically open system not at steady state

Tank Filling

Tank Emptying

Mass Balance:

Energy Balance:

2

1

t

IN OUT CV 2 CV 1t

m - m dt m (t ) m (t )

2

1

t

IN OUT CV CVt

2

IN,OUTc c

2

CVc c

E E dt E E

gz

E Q W m h 2g g

1 gzE m u

2 g g

v

v

2 1t t t t

t

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T k Filli

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Tank Filling

Simplest USUF analysis:

No outlet flow

Assume adiabatic

Mass Balance:

Energy Balance:

IN INQ W

2

1

t

IN IN OUT OUT OUT OUTt t

m h - Q W m (t)(h (t)dt

2

c c

gz

= m u 2g g

v

2

c cCV,2

gz

m u 2g g

v

CV,

IN IN CV,2 CV,

1

1m h mu mu

IN 2 1m =m m