Chapter 4 The First Law of T hermodynamics

Copyright (c) 2005 by John Wiley & Sons, Inc

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Thermodynamics: An Integrated Learning SystemP.S. Schmidt, O.A. Ezekoye, J.R. Howell and D.K. Baker

Chapter 4

The First Law of

Thermodynamics

Steam power still reigns on the Cumbres and Toltec

Scenic Railway in Colorado and New Mexico.

Chapter 4 The First Law of Thermodynamics

4. 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


4.1 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

systemboundary QOUT

WIN or WOUT

QIN

• Mass does not cross system boundary• Energy crosses system boundary.


4.2 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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4.2.1 Conservation of Mass

• Rate Basis

• Time Interval

• Useful Relations

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

– AX = cross-sectional flow area [m2 or 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 )

XAVm

v v

v

V


4.2.2 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

transfer is u + ke + pe + Pv = h + ke + pe per unit mass flow.


4.2.3 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

dtE 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)


4.3 Steady-State Steady-Flow Processes

• Steady-State (SS):

where ( )CV is any property of the system (e.g., m or E)

CVd0

dt

IN,OUTd0

dt

.

.. . .

• Steady-Flow (SF):

where ( )CV is any transfer across the system boundary (e.g., Q, W or m)



• 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



• SSSF Energy Balance

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

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

CVIN OUT

dEE E

dt

0, SS

N

IN IN IN,i i i i

I

i 1

N

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


4.3.1 Nozzles and Diffusers

• On next page, see a nozzle in a turbojet engine

A diffuser converts high speed, low pressure

flow to low speed, high pressure flow

A nozzle converts high pressure, low speed flow to low pressure,

high speed flow






• Common Assumptions– SSSF– No work or heat transfer– Neglect changes in pe

• Energy Balance: Crossing out terms assumed 0

INq0

INw0

h ke pe 0

IN

OUTq0

OUTw0

h ke pe

0

2 2

C CIN OUT

OUT

IN OUT h h2

h ke h kg 2g

e

v v


4.3.2 Throttling

• Throttling: Reduces Pressure• Common Assumptions:

– SSSF– No work or heat transfer– Neglect changes in pe and ke

• Energy Balance:

INq0

INw0

h ke 0

pe 0

IN

OUTq0

OUTw0

h ke 0

pe 0IN

OUOUT

Th h

ThrottlingValve

• Isenthalpic (h = constant) Process


4.3.3 Pumps, Fans, and Blowers

• Pumps: Pressurize or move liquids

• Fans & Blowers: Move air

OUT

OUT

OUT

m

T

P

INW

IN IN INm ,T ,P

Pump Schematic

• Common Assumptions:– SSSF– No heat transfer– Neglect changes in pe and ke

• Energy Balance for fan & blower

• Energy Balance for pump (assuming ICL)

IN OUT INw h h

IN OUT INw v P P


4.3.4 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)


4.3.4 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 OUTINQ

INE

OUTW m h ke pe OUT

OUTE

dEdt

0, SS

OUT IN OUT

OUT IN OUT

W m h h

Per unit mass flow w h h


4.3.4 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 turbojet

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

• Working Fluids– Gas– Vapor– Not Liquid (pump used)


4.3.4 Compressors

• Common assumptions for compressor:– SSSF– Adiabatic (q = 0)– Neglect kinetic and potential energies

• Compressor energy balance

INQ INW m h ke pe OUT OUTINQ W

INE

m h ke pe OUT

OUTE

dEdt

0, SS

IN OUT IN

IN OUT IN

W m h h

Per unit mass flow w h h


4.3.5 Heat Exchangers

• Allows heat transfer from one fluid to another without mixing

• Example: Car Radiator


4.3.5 Heat Exchangers in Steam Power Plant



4.3.5 Heat Exchangers

• Common Assumptions– SSSF– Externally adiabatic– Neglect kinetic and potential

energies

IN INQ W m h ke pe IN

OUT OUTQ 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


4.3.6 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


4.3.6 Mixing Devices



4.4 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

gzE Q W m h

2g g

1 gzE m u

2 g g

v

v

2 1t t t t

t


4.4.1 Uniform State Uniform Flow (USUF)

• Uniform State: All properties uniform across system at any instant in time

• Uniform Flow: All mass flow properties at each inlet and outlet are uniform across the stream

• Neglect kinetic and potential energies• Mass Balance:• Energy Balance:

IN OUT 2 1m m =m(t ) m(t )

2

1

t

IN IN IN IN OUT OUT OUT OUTt t

2 2

CV 2 CV 1c c c cCV,2 CV,1

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

gz gzE (t ) E (t )= m u m u

2g g 2g g

v v


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

2

c c

gz= m u

2g g

v

2

c cCV,2

gzm u

2g g

v

CV,

IN IN CV,2 CV,

1

1m h mu mu

IN 2 1m =m m

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Chapter 4 The First Law of T hermodynamics