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The First Law of Thermodynamics

Open System (Control Volume)

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First low of thermodynamics for open Systems

Reminder of an open System.Open system = Control volume

It is a properly selected region in space.

Mass and energy can cross its boundary.

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Control volume involves two main processes

Steady flow processes. Fluid flows through the control volume

steadily. Its properties are experiencing no

change with time at a fixed position.

Unsteady flow processes. Fluid properties are changing with time.

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Mass balance for steady flow processes

We already showed that for steady flow

Many engineering devices involve a single stream (one inlet and one exit only).

mm ei

21 mm

22211 VAVA or 1

5

Energy Balance for Steady-Flow Systems

2 21 1( ) ( )

2 2e e i iQ W m h V gz m h V gz

sysoutin EEE outin EE

in in i i out out e eQ W m Q W m

2 21 1( ) ( )

2 2in out in out e e i iQ Q W W m Pv u V gz m Pv u V gz

2 21 1( ) ( )

2 2e e i iQ W m Pv u V gz m Pv u V gz

0

, ,in in mass in out out mass outQ W E Q W E

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Let us look at some common steady flow devices

Only one in and one outMore than one inlet and exit

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For single stream steady flow devices, the 1st low becomes

ee

eeii

ii zgV

hmzgV

hmWQ22

22

Often the change in kinetic energy and potential energy is small.

ei i eQ W m h m h

ie hhwq Per unit mass

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Nozzles

A nozzle is a device that increases the velocity of a fluid at the expense of pressure

222111 AVAV

2

1

2

112 A

AVV

A1 A2

gasspeedlowfor

liquidsfor

21

21

12 VV

21 AA

9

A1 A2

Diffusers

A diffuser is a device that slows down the velocity of a fluid causing an increase in its pressure

12 VV

222111 AVAV

2

1

2

112 A

AVV

gasspeedlowfor

liquidsfor

21

21

21 AA

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Diffusers

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Nozzles and Diffusers (1st low analysis)

ieie

ie zzgVV

hhmWQ2

22

Is there work in this system?NOIs there heat transfer?

In fact, it depends on the problem!

Does the fluid change elevation?NO

2

022

ie

ie

VVhh

?m the to happened What:Q Ans: It is divided out

let us say: NO

12

22

22

ee

ii

Vh

Vh

How can you find the mass flow rate in a nozzle?

In a nozzle, enthalpy is converted into kinetic energy

torearrangedbecanwhich

222111 AVAVm

2

22

1

11

v

AV

v

AVm

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Example (4-9): Deceleration of Air in a Diffuser

Air at 10oC and 80 kpa enters the diffuser of a jet engine steadily with a velocity of 200 m/s. The inlet area of the diffuser is 0.4 m2. The air leaves the diffuser with a velocity that is very small compare to the inlet velocity.

Determine(1) The mass flow rate of the air and(2) The temperature of the air leaving the diffuser.

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Example (4-10): Acceleration of Steam in a Nozzle

Steam at 1.72 Mpa (250 psia) and 371C (700 F) steadily enters a nozzle whose inlet area is 0.019 m2 (0.2 ft2.) The mass flow rate of the steam through the nozzle is 4.54 kg/s (10 lbm/s) . Steam leaves the nozzle at 1.38 Mpa (200 psia) with a velocity of 274.3 m/s (900 ft/s). The heat losses from the nozzle per unit mass of the steam are estimated to be 2.8 KJ/kg (1.2 Btu/lbm). Determine:(a) the inlet velocity and (b) the exit temperature of the steam.

Answers: a) 41.0 m/s or 134.4 ft/s,b) 350 C or 661.9 F

Solution of Example: Acceleration of Steam in a Nozzle

Note that there is heat transfer (Q).So, you have to go back to the general form of the 1st low for single stream devices and get the following:

22

22e

ei

i

Vh

Vhq

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Turbines A turbine is a device that produces work at the expense of temperature and pressure.

As the fluid passes through the turbine, work is done against the blades, which are attached to a shaft. As a result, the shaft rotates, and the turbine produces work.

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18

19

20

CompressorsA compressor is a device that increases the pressure of a fluid by adding work to the system.

Work is supplied from an external source through a rotating shaft.

Compressor

Inlet

Exit

Win

21

22

23

24

ieie

ie zzgVV

hhmWQ2

22

Turbines and Compressors

Is there work in this system? Yes!

Is there heat transfer? Negligible because of insulation. Exception: Internal cooling in some compressors.

Does the fluid change elevation? NO

Does the kinetic energy change? Usually it can be ignored

)W(hhm ieW )kg/kJ(hhw ie

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Example (4-12): Power Generation by a Steam Turbine

The power output of an adiabatic steam turbine is 5 MW, and the inlet and the exit conditions of the steam are as indicated in the figure on the right.

a) Compare the magnitude of h, ke, and pe.

b) Determine the work done per unit mass of the steam flowing through the turbine.

c) Calculate the mass flow rate of the steam.

Answers: a) h = -885.9 kJ/kg,

ke = 14.95 kJ/kg, pe = -0.04 kJ/kg,

b) 871.0 kJ/kg, and c) 5.74 kg/s

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Throttling Valve

A throttling valve reduces the fluid pressure.

P1>P2

It is small device and thus the flow through it may be assumed adiabatic (q=0) since there is neither sufficient time nor large enough area for any effective heat transfer to occur.

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ieie

ie zzgVV

hhmWQ2

22

Throttling Valve

Is there work in this system? NO

Is there heat transfer? Usually it can be ignored

Does the fluid change elevation? NO

Does the fluid change velocity? Usually it can be ignored

0 e i e ih h h h

isenthalpic device

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What happens to the fluid temperature a cross throttling Valves ?

21 hh

222111 vpuvpu

Tuuvpvpif 121122

Tuuvpvpif 121122

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Throttling Valves (incompressible substance )

For incompressible substance (like water), is constant

21 vv 21 PP

risewillT

uuvpvp

121122

and222111 vpuvpu

For incompressible substance only!

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Throttling Valves (compressible substance: Vapor)Example (4-13): Expansion of Refrigerant-134a in a Refrigerator

Refrigerant-134a enters the capillary tube of a refrigerator as saturated liquid at 0.8 MPa and is throttled to a pressure of 0.12 MPa.

Determine the quality of the refrigerant at the final state and the temperature drop during this process. <Answers: 0.339, -53.69oC>

Solution of Example: Expansion of Refrigerant-134a in a Refrigerator

Notice that T2 <T1

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Throttling Valves (Compressible substance: an Ideal Gas) What happens if the gas is ideal? For ideal gases

h = Cp T But h = 0 So… T = 0 The inlet and outlet temperatures are the same!!!

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Mixing ChamberMixing two or more fluids is a common engineering process

The mixing chamber does not have to be a distinct “chamber.” An ordinary T-elbow, or a Y-elbow in a shower, for example, serves as the mixing chamber for the cold- and hot-water streams as shown in the figure (Left).

Mixing Chamber

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Mixing Chamber

ii

iiee

eegz

Vhmgz

Vhmnetnet WQ

22

22

We no longer have only one inlet and one exit stream

Is there any work done? No

Is there any heat transferred? No

Is there a velocity change? No

Is there an elevation change? No

iieehmhm0

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Mixing Chamber

Material Balance

Energy balance

eim m

321 mmm

Mixing ChamberMixing Chamber

i e eim h m h

332211 hmhmhm

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Example(4-14): Mixing of Hot and Cold Waters in a Shower

Consider an ordinary shower where hot water at 140oF is mixed with cold water at 50oF. If it is desired that a steady stream of warm water at 110oF be supplied, determine the ratio of the mass flow rates of the hot to cold water. Assume the heat losses from the mixing chamber to be negligible and the mixing to take place at a pressure of 20 psia.

<Answer: 2.0>

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Heat Exchanger

A heat exchanger is a device where two moving fluids exchange heat without mixing.

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Heat Exchangers

Your analysis approach will depend on how you define your system

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Heat Exchangers System (a): entire HX

Mass Balance Divide into two separate

streams with equal inlet and outlet flow rates

Energy balance Two inlets Two outlets

1 1 3 3 2 2 4 4m h m h m h m h

1 2 3 4,m m m m

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Heat Exchangers System (b): Single stream

Mass Balance Considering one single

stream with one inlet and one outlet flow rates

Energy balance One inlet One outlet Plus heat transfer

2 2 1 1Q m h m h

1 2m m

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Example: Cooling of Refrigerant-134a by Water

Refrigerant-134a is to be cooled by water in a condenser. The refrigerant enters the condenser with a mass flow rate of 6 kg/min at 1 MPa and 70oC and leaves at 35oC. The cooling water enters at 300 kPa and 15oC and leaves at 25oC. Neglecting any pressure drop, determine

(a) the mass flow rate of the cooling water required and (b) the heat transfer rate from the refrigerant to water.

<Answers: a) 0.486 kg/s, b) 20.35 kJ/s>