Lecture 3 Thermodynamics

8/3/2019 Lecture 3 Thermodynamics

http://slidepdf.com/reader/full/lecture-3-thermodynamics 1/48

Lecture_ 3 Energy Transfer by

Heat, Work, and Mass



Processes

Process line, or path

State 1

State 2

P1

P 3

P 2



Interactions

Ma

System f( P k , k =1...N)=0

Surroundings

Mass Flow

Mass FlowWork

Heat



Mechanical work flow

Motor Electrical Power

System

Boundary

Work Flow

The turning fan

represents the

result of a mechanical work

transfer.



Energy Transfer

• Energy transfer to/from closed systems – Heat (Q)

– Work (W )

• Energy transfer to/from open systems (control

volumes)

– Heat (Q)

– Work (W )

– Mass flow )( m



3-1

FIGURE 3-9 Specifying thedirections of

heat and work.



Heat

• Heat (Q) is the transfer of energy due to atemperature difference

– a system w/o heat transfer is an adiabatic system

– SI units: kJ

• Heat rate, (kJ/s or kW)

• Heat per unit mass, q = Q/m

• Sign convention:

– Q > 0: heat transferred to system from surroundings – Q < 0: heat transferred from system to surroundings

Q



Heat Transfer Modes

• Conduction – transfer of heat through a material due to random molecular

or atomic motion; most important in solids

• Radiation

– transfer of heat due to emission of electromagnetic waves,usually between surfaces separated by a gas or vacuum

• Convection

– transfer of heat between a solid surface and fluid due to

combined mechanisms of i) fluid conduction at surface; ii)

fluid flow within boundary layer



Conduction Heat Transfer

• Fourier’s law of conduction:

dx

dT kAQcond



Convection Heat Transfer

• Newton’s law of “cooling”, or convection:

)( f sconv T T hAQ



Radiation Heat Transfer

• Stefan-Boltzmann law of radiation (between a

small surface A of emissivity e and large

surroundings):

44

surr srad T T AQ e



Work

• Work (W ) is the energy transfer associated with aforce acting through a distance:

• Work rate or power

• Work per unit mass, w = W/m

• Sign convention

– W > 0: work done by system on surroundings

– W < 0: work done on system by surroundings

(kJ) sd F W

kW)or(kJ/s V F W



Work

dsdt ds

dsdV m

dt dV msd F

V d V V

ds

sd F d W d s



Work

KE W

V V m

msd F W s

s

2121

21

22

21

2

2

2

1



Work

m

gm

F s

sd F d W d s



Work

PE KE

ssgmKE sd F s

s

2121

1221

2

1



Types of Work

• Moving boundary (compression/expansion) work • Shaft work

• Spring work

• Electrical work

• Other forms; work associated with: – Acceleration

– Gravity

– Polarization

– Magnetization

– Solid deformation

– Liquid film stretching



Moving Boundary Work• Associated with a volume change of a fluid system

(aka compression-expansion work)

2

1

2

1

2

1

PdV W

PAdxFdxW

b

x

x

x

x

FIGURE 3-19 A gas does adifferential amountof work dW b as it

forces the piston tomove by adifferential amountd s.



3-3

FIGURE 3-20 The area underthe processcurve on a P-V

diagramrepresents theboundary work.



Moving Boundary Work, cont.

• Expansion: dV > 0, W b > 0

• Compression: dV < 0, W b < 0

• Work processes on P-V diagram:

curvesbetweenarea

)(curve1-2underarea

(-)curve2-1underarea

exp

1

221,exp

2

112,

W W W

PdV W W

PdV W W

compcycle

b

bcomp



Moving Boundary Work, cont.

• Special cases:

1) if V = constant, W b = 0

2) if P = constant, W b = P(V 2-V 1)

3) if PV n = constant (known as a polytropic process),

)1( ln

)1( 1

1

211

1122

nV

V V PW

nn

V PV PW

b

b



3-4

FIGURE 3-22 The net workdone during acycle is thedifferencebetween thework done bythesystem and the

work done onthe system.



Shaft Work

• Associated with a rotating shaft

unit time)persrev' ( 2

s)revolutionof no. ( 2

thenconstant, if

torque)( 2

1

2

1

nnW

nnW

d Frd W

sh

sh

sh



Spring Work

• Associated with the extension or compression of aspring; if spring is linear, then force obeys Hooke’s

law,

2

1

2

221

2

1

andconstant)spring(

x xk

kxdxW

k kxF

sp

sp



Electrical Work

• Associated with the motion of electrons due to an

electromotive force

V

V

V V

I W

I t I

N

N sd E N

sd F W

e

e

current)(

voltage)(

charge)electric( 2

1

2

1



Evaluating work at a

boundary...



Note: P gas > P ambient

Direction of Motion

x

X p ambient

The gas is the system for analysis.

Force balance at the boundary on the

piston, where the boundary deforms.

p gas



)0,0,( xF F

c

ambient gas x

g

gm

A p pF

X

P ambient

P gas

dx

The net force on

the piston.



Total work done

dxF W xd

dx

g

gm A p A pW

x

x

x

x c

ambgas

2

1

2

1

d



p ambient

p gas > p ambient

X

dxg

gm A p A pW x

x

x

x c

ambgas

2

1

2

1

d

Component of work due

to expansion of the gasWork to raise

the piston



Work of Expansion

2

1

x

x

e pAdxW

ambiengas p p p



Work of Expansion: p-dV work

2

1

V

V

e pdV W

AdxdV )(V p p



Evaluating a equilibrium expansion process

p

V = AxV 1 V 2

p1

p 2

)(V p p

n egra or



n egra ora quasistatic process

p

V = AxV 1 V 2

p1

p 2

pAdx pdV W e d



Conservation of Mass

• “Mass can neither be created nor destroyed” – mass and energy can be converted to each other

according to Einstein’s E=mc2, but this effect is

negligible except for nuclear reactions)

• For closed systems, this principle imposes m =constant since mass cannot cross the system

boundary

• For control volumes, the mass entering andleaving the system may be different and must be

accounted for



Key concepts and terms

Equilibrium process

Kinetic energy

Path-dependent workQuasistatic process

Work at a system boundary

Work transferWork of expansion



Mass and Volume Flow Rates

• Mass flow rate: fluid mass conveyed per unit time[kg/s]

where V n = velocity normal to area [m/s] = fluid density [kg/m3]

A = cross-sectional area [m2]

A ndAm V

Mass and Volume Flow Rates, cont.



Mass and Volume Flow Rates, cont.

• For most pipe flows, = constant and the average

velocity (V ) is used:

• Volume flow rate is given by

v

Am

Am ave

V

V

or

v

V V m

AV

then

V

)(V



Conservation of Mass Principle - Control

Volume

• Net mass transfer during a process is equal to thenet change in total mass of the system during that

process

where i = inlet, e = exit, 1 = initial state, 2 = final state

• in rate form:

• In fluid mechanics, this is often referred to as the

continuity equation

systemei mmmm )( 12

dt

dm

mm

system

ei



FIGURE 3-48 Schematic forflow work.

Steady-Flow Processes



Steady Flow Processes

• Steady-flow or steady-state – a condition where allfluid and flow properties, heat rates, and work

rates do not change with time.

– mathematically:

– applied to mass balance:

0dt d

0dt

dmsystem

Steady-Flow Processes, cont.



Steady Flow Processes, cont.

• Conservation of mass during a steady-flow process:

• If control volume is single-stream (i.e., one inlet, one

exit), then

ei mm

2

22

1

11

21

orv

AV

v

AV

mmm



Incompressible Flow

• If = constant, then the mass flow is consideredincompressible

– for steady-flow:

– for single-stream, steady-flow:

ei V V

2211

21

or

V V A A

V V

Total Energy of a Flowing Fluid



Total Energy of a Flowing Fluid

• A flowing fluid contains internal, kinetic, and

potential energies:

• Fluid entering or leaving a control volume has an

additional form of energy known as flow energy,

which represents the work required to “push” the

fluid across a boundary:

gzue

gzum E

2

21

2

21 or ,)(

V

V

mPvPV W flow energyflow



3-6

FIGURE 3-51

The total energyconsists of three partsfor a nonflowing fluidand four parts for aflowing fluid.



Total Energy of a Flowing Fluid, cont.

• The total energy of a flowing fluid (on a unit-mass

basis, ) becomes

• Using the definition of enthalpy (h),

Pvgzu 2

21 V

gzh 2

21 V



Energy Transport by Mass

• Amount of energy transport:

• Rate of energy transport:

)(2

21 gzhmm E

mass V

)( 221 gzhmm E mass V



FIGURE 3-58

The absorption ofradiation incident on

an opaque surfaceof absorptivity .

Lecture 3 Thermodynamics

Documents

Transcript of Lecture 3 Thermodynamics