chapter 3 energy transfer by heat, work, and mass

CHAPTER

3

Energy Transfer byHeat, Work, and Mass

Heat Transfer

• Heat, means heat transfer.– Energy transfer driven by temperature difference– always hotter to cooler

• Adiabatic – no heat transfer– same as isothermal?

• Symbols used:– Q and q– Q

• Caloric?

Work

• Energy transfer not driven by a temperature difference. Examples– Rising piston– rotating shaft– electric wire crossing the system boundaries

• Symbols used:

• W and w

• W

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3-1

FIGURE 3-9Specifying the directions ofheat and work.

Formally:Qin and Wout

are positive,Qout and Win

are negative

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 3 Module 1 Slide 5Work

Heat and WorkHeat and Work

• Both heat and work are boundary phenomena.

• Systems possess energy, but not heat or work.

• Both are associated with a process, not a state.

• Both are path functions– Magnitudes depend on paths as well as end states



ProcessesProcesses

Process line, or pathProcess line, or path

State 1State 1

State 2State 2

P1

P3

P2



Electrical WorkElectrical Work

• We = VI

• so We = VIΔt if V and I are constant.



Mechanical WorkMechanical Work

sdFW

mm

F

sd

s



Work at a system Work at a system boundary...boundary...

There must be a force acting on the boundary.

The boundary must move.

Quasi – equilibrium processes,best case.


3-2

FIGURE 3-19A gas does a differential amount of work Wb as it forces the piston to move by a differential amount ds.



Work transfer at a boundaryWork transfer at a boundary

SystemSystemSurroundingsSurroundings

W > 0W > 0

W< 0W< 0

System BoundarySystem Boundary



Work of ExpansionWork of Expansion

2

1

x

xb pAdxW

ambientgas ppp



Work of Expansion: p-dV workWork of Expansion: p-dV work

2

1

bV

VpdVW

AdxdV )(Vpp



Evaluating a equilibrium Evaluating a equilibrium expansion processexpansion process

pp

V = AxV = AxVV11 VV22

pp11

pp22

)(Vpp


3-3

FIGURE 3-20The area under the process curve on a P-V diagram represents the boundary work.


3-4

FIGURE 3-22The net work done during a cycle is thedifference between the work done by thesystem and the work done on the system.


Chapter 3 Module 2 Slide 17Processes Involving Ideal Gases

PROCESSES PROCESSES INVOLVING INVOLVING IDEAL GASESIDEAL GASES



Polytropic processes...Polytropic processes...



The polytropic process: PVThe polytropic process: PVnn=Const.=Const.

VV

p State 1

State 2



AssumptionsAssumptions

• Changes in KE and PE Changes in KE and PE are zeroare zero

• Quasistatic processQuasistatic process

• Polytropic processPolytropic process

• Ideal gasIdeal gas



Expression for work:Expression for work:

2

1

2

1

)(

,21

V

V

V

Vby

dVVP

PdVW

Process equation:Process equation:

nn PVCVP 111



Evaluating the integral:Evaluating the integral:

n

VPVP

dVV

CW

V

V nby

11122

1,21

2

1

Note that n cannot equal one, which is the general case.Note that n cannot equal one, which is the general case.



For the special case when n = 1:For the special case when n = 1:

1

211

1,21

ln

2

1

V

VVP

dVV

CW

V

Vby



Polytropic processesPolytropic processes

p p

VV11 VV22 V V

TT11

TT2 2

Isothermal Process Isothermal Process (n = 1) (n = 1)

n > 1 n > 1

pp11

pp22

pp22



Alternative expressions for WAlternative expressions for W1-21-2

1,ln

1,1

1

221

1221

nV

VmRTW

nTTn

mRW



Constant pressure Constant pressure processes...processes...



Constant pressure processConstant pressure process

• Consider as a limiting case of the general Consider as a limiting case of the general polytropic process.polytropic process.

• P = ConstantP = Constant

• Evaluation of the work integralEvaluation of the work integral

)( 1231

2

1

VVPPdVWV

V



Constant pressure, constant temperatureConstant pressure, constant temperatureand polytropic processes:and polytropic processes:

1

2

1n

1n

PP

VV

P = ConstantP = Constant(n = 0)(n = 0)Isobaric processIsobaric process



Shaft WorkShaft Work

• Work = F∙d– Replace force with torque, T

– Replace distance with angle rotated = 2πn• where n is number of rotations

• Wsh = T(2πn) or

• Wsh = T(2πn) where n is frequency in Hz

chapter 3 energy transfer by heat, work, and mass

Documents

work heat

work work transfer

work work of expansion

work mechanical work

boundary work

work energy transfer

net work

work electrical work