Chapter 4Chapter 4 The First Law of The First Law of Thermodynamics:Thermodynamics:Control VolumesControl Volumes

4-1-1 Conservation of Mass principle

4-1 Thermodynamic analysis of 4-1 Thermodynamic analysis of Control VolumeControl Volume

CVei mmm

4-1-2 Conservation of Energy principle for Control Volume

The net energy change in energy of CV

Total energy crossing boundary

+ Total energy of mass entering CV=

-Total energy of mass leaving CV

4-1-3 Flow Work

PAF

FLW flow PAL PV

pvw flow

4-1-4 Total Energy of a Flowing Fluid

On a unit-mass basis, the energy stored in fluid: pekeue

gzue 2

2V

Considering the flow work, we have

pvw The total energy of a flowing fluid (denoted θ): epv

)( pekeupv

4-1-5 Enthalpy

Internal energy and flow work usually transferred at the same time in flowing fluid, so we define pvuh

Professor J. Kestin proposed in 1966 that the term θ be called methalpy (from metaenthalpy, which means beyond enthalpy)

pekeh

4-2 The Steady-Flow Process4-2 The Steady-Flow Process4-2-1 Definition of Steady-Flow ProcessA process during which a fluid flows

through a control volume steadily

4-2-2 Characteristics of Steady-Flow Process

1. No properties in the control volume change with time

2. No properties changes at the boundaries of the control volume with time

3. The heat and work interactions between a steady flow system and its surroundings do not change with time

4-2-3 Energy Equation of Steady-Flow ProcessFrom the above discussion we can

conclude that:

2. The net change in energy of CV is Zero

mmm ei .1

Energy Equation of Steady-Flow

Total energy crossing boundary per unit time

=

Total energy of mass leaving CV per unit time

-Total energy of mass entering CV per unit time

0)2

()2

(22

ee

eeii

ii gzhmgzhmWQVV

)2

()2

(22

ii

iiee

ee gzhmgzhmWQVV

mmm ie since

)2

()2

(22

ii

iee

e gzhmgzhmWQ VV

Using subscript 1and subscript 2 for denoting inlet and exit states

)](2

[ 12

21

22

12 zzghhmWQ

VV

)(2 12

21

22

12 zzghhwq

VV

Dividing the equation by m yields

wzghq

2

or2V

wzgpvuq

2

2V

Work

3-3 Some Steady-Flow Engineering 3-3 Some Steady-Flow Engineering devicesdevices

3-3-1 Nozzles and Diffusers

q = Δh + ΔV2 / 2 + gΔz + w

q = 0 Δz = 0 w = 0

212

2

1then hh V

)(2 21 hh V

3-3-2 Steam Turbine

from q = Δh + ΔV2 / 2 + gΔz + ws

if q = 0; Δc = 0; Δz = 0

then ws = -Δh

= h1 - h2

3-3-3 Throttling Valves

From q = Δh + ΔV2 / 2 + gΔz + ws

as q = 0; ws = 0; z = 0 ; ΔV2 / 2 =0

then Δh =0

That is h1 = h2

3-3-4 Mixing Chambers

From q = Δh + ΔV2 / 2 + gΔz + ws

as q = 0; ws = 0; z = 0 ; ΔV2 / 2 =0

then Δh =0

That is ∑hin = ∑ hexit

3-3-5 Heat exchangers

From q = Δh + ΔV2 / 2 + gΔz + ws

as q = 0; ws = 0; Δ z = 0;ΔV2 / 2 =0

Δh =0

That is ∑hin = ∑ hexit

3-4 Unsteady-Flow Processes3-4 Unsteady-Flow Processes3-4-1 Model

1. The net energy transferred to the system:

dQ ， e1dm1 ， p1v1dm1

2. The net energy transferred out of the system:

dWs ， e2dm2 ， p2v2dm2

3-4-2 Conversation of Energy

)()( 2222211111 dmvpdmedWdmvpdmedQdE

])2

1([ 11111

211 dmvpdmgzudQdE V

])2

1([ 11

2111111 dmgzdmvpdmudQdE V

])2

1([ 22222

222 dmvpdmgzudW V

])2

1([ 22

2222222 dmgzdmvpdmudW V

])2

1([ 11

2111 dmgzcdmhdQdE

1121122

222 )

2

1()

2

1( dmgzchdmgzchdWdEdQ s

])2

1([ 22

2222 dmgzcdmhdW

Divide dτ on each side

)2

1()

2

1( 1

21112

2222 gzchmgzchmW

EQ

)1( )2

1()

2

1( 1

21112

2222 gzchmgzchm

EWQ

3-5 Uniform-Flow Processes3-5 Uniform-Flow Processes

1. At any instant during the process, the state of control volume is uniform

2. The fluid properties may differ from one inlet or exit to another, but the fluid flow at an inlet or exit is uniform and steady

The end of this chapter

Thanks for your attention!