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Engineering Thermodynamics _________________________________________________________ _ AAiT _____________________________________________________________________________________ Compiled by Yidnekachew M. Page 1 of 13 Chapter 3 Energy Transport by Heat, Work and Mass 3.1 Energy of a System Energy can be viewed as the ability to cause change. Energy can exist in numerous forms such as thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear, and their sum constitutes the total energy E of a system. The total energy of a system on a unit mass basis is denoted by e and is expressed as E e m ( / ) kJ kg (3.1) In thermodynamic analysis, energy can be group in to two forms: Macroscopic Microscopic Microscopic forms of energy are those related to the molecular structure of a system and the degree of the molecular activity, and they are independent of outside reference frames. The sum of all the microscopic forms of energy is called the internal energy of a system and is denoted by U. Example:- Latent energy Chemical energy Nuclear energy Sensible energy Internal energy A system associated with the kinetic energies of the molecules is called the sensible energy. The internal energy associated with the phase of a system is called the latent energy. The internal energy associated with the atomic bonds in a molecule is called chemical energy.

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EngineeringThermodynamics__________________________________________________________AAiT

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Chapter 3 Energy Transport by Heat, Work and Mass

3.1 Energy of a System

Energy can be viewed as the ability to cause change.

Energy can exist in numerous forms such as thermal, mechanical, kinetic, potential, electric,

magnetic, chemical, and nuclear, and their sum constitutes the total energy E of a system. The

total energy of a system on a unit mass basis is denoted by e and is expressed as

Eem

( / )kJ kg (3.1)

In thermodynamic analysis, energy can be group in to two forms:

Macroscopic

Microscopic

Microscopic forms of energy are those related to the molecular structure of a system and the

degree of the molecular activity, and they are independent of outside reference frames.

The sum of all the microscopic forms of energy is called the internal energy of a system and is

denoted by U.

Example:-

Latent energy

Chemical energy

Nuclear energy

Sensible energy

Internal energy

A system associated with the kinetic energies of the molecules is called the sensible energy.

The internal energy associated with the phase of a system is called the latent energy.

The internal energy associated with the atomic bonds in a molecule is called chemical

energy.

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The tremendous amount of energy associated with the strong bonds within the nucleus of

the atom itself is called nuclear energy.

The total energy of a system, can be contained or stored in a system, and thus can be viewed

as the static forms of energy.

The forms of energy not stored in a system can be viewed as the dynamic forms of energy.

The only two forms of energy interactions associated with a closed system are heat transfer

and work.

Macroscopic forms of energy are those a system possesses as a whole with respect to some outside

reference frame, such as kinetic and potential energies.

The energy that a system possesses as a result of its motion relative to some reference frame

is called kinetic energy (KE) and is expressed as

2

2VKE m ( )kJ (3.2)

Per unit mass 2

2Vke ( / )kJ kg (3.3)

The energy that a system possesses as a result of its elevation in a gravitational field is

called potential energy (PE) and is expressed as

PE mgz ( )kJ (3.4)

Per unit mass

pe gz ( )kJ (3.5)

The magnetic, electric, and surface tension effects are significant in some specialized cases only

and are usually ignored. In the absence of such effects, the total energy of a system consists of the

kinetic, potential, and internal energies and is expressed as

E U KE PE

2

2VE U m mgz ( )kJ (3.6)

Per unit mass

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e u ke pe 2

2Ve u gz ( / )kJ kg (3.7)

Most closed systems remain stationary during a process and thus experience no change in their

kinetic and potential energies.

Closed systems whose velocity and elevation of the center of gravity remain constant during a

process are frequently referred to as stationary systems. The change in the total energy E of a stationary system is identical to the change in its internal energy U.

3.2 Energy transport by heat and work Energy can cross the boundary of a closed system in two distinct forms: heat and work.

Figure 3.1 Energy can cross the boundaries of a closed system in the form of heat and work.

Energy transport by heat

Heat is defined as the form of energy that is transferred between two systems (or a system and its

surroundings) by virtue of a temperature difference.

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Figure 3.2 Heat transfer from hot surface to cold surface

That is, an energy interaction is heat only if it takes place because of a temperature difference.

Then it follows that there cannot be any heat transfer between two systems that are at the same

temperature.

A process during which there is no heat transfer is called an adiabatic process. The word adiabatic

comes from the Greek word adiabatos, which means not to be passed.

There are two ways a process can be adiabatic: Either the system is well insulated so that only a

negligible amount of heat can pass through the boundary, or both the system and the surroundings

are at the same temperature and therefore there is no driving force (temperature difference) for

heat transfer.

Figure 3.3 During an adiabatic process, a system exchanges no heat with its surroundings.

As a form of energy, heat has energy units, kJ being the most common one. The amount of heat

transferred during the process between two states (states 1 and 2) is denoted by Q12, or just Q. Heat

transfer per unit mass of a system is denoted q and is determined from

Qqm

( / )kJ kg (3.8)

Sometimes it is desirable to know the rate of heat transfer (the amount of heat transferred per unit

time) instead of the total heat transferred over some time interval.

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Figure 3.4 The relationships among q, Q, and Q .

The heat transfer rate is denoted , where the overdot stands for the time derivative, or per unit time. The heat transfer rate has the unit kJ/s, which is equivalent to kW. When varies with

time, the amount of heat transfer during a process is determined by integrating over the time

interval of the process:

2

1

t

tQ Qdt ( )kJ (3.9)

When remains constant during a process, this relation reduces to

Q Q t ( )kJ (3.10)

Where: 2 1t t t

Heat is transferred by three mechanisms: conduction, convection, and radiation. Conduction is the

transfer of energy from the more energetic particles of a substance to the adjacent less energetic

ones as a result of interaction between particles. Convection is the transfer of energy between a

solid surface and the adjacent fluid that is in motion, and it involves the combined effects of

conduction and fluid motion. Radiation is the transfer of energy due to the emission of

electromagnetic waves (or photons).

Energy Transport by Work

Work, like heat, is an energy interaction between a system and its surroundings. As mentioned

earlier, energy can cross the boundary of a closed system in the form of heat or work. Therefore,

If the energy crossing the boundary of a closed system is not heat, it must be work. Work is the

energy transfer associated with force acting through a distance.

Example:-

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A rising piston

A rotating shaft

Work is also a form of energy transferred like heat and, therefore, has energy units such as kJ. The

work done during a process between states 1 and 2 is denoted by W12, or simply W. The work done

per unit mass of a system is denoted by w and is expressed as

Wwm

( / )kJ kg (3.11)

The work done per unit time is called power and is denoted by . The unit of power is

kJ/s, or kW.

Heat and work are energy transfer mechanisms between a system and its surroundings, and there

are many similarities between them:

Both are recognized at the boundaries of a system as they cross the boundaries. That is,

both heat and work are boundary phenomena.

Systems possess energy, but not heat or work.

Both are associated with a process, not a state. Unlike properties, heat or work has no

meaning at a state.

Both are path functions (i.e., their magnitudes depend on the path followed during a process

as well as the end states).

Sign convention for energy transported by heat and work Heat and work are directional quantities, and thus the complete description of a heat or work

interaction requires the specification of both the magnitude and direction. One way of doing that

is to adopt a sign convention. The generally accepted formal sign convention for heat and work

interactions is as follows: heat transfer to a system and work done by a system are positive; heat

transfer from a system and work done on a system are negative. Another way is to use the

subscripts in and out to indicate direction

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Figure 3.5 Specifying the directions of heat and work.

Qin > 0 Heat transfer to a system (positive)

Qout < 0 Heat transfer from a system (negative)

Figure 3.6 Process from stage 1 to 2 Figure 3.7 Process from stage 1 to 2

W > 0 work done by the system (positive) Figure 3.6

W < 0 work done on the system (negative) Figure 3.7

Path functions have inexact differentials designated by the symbol . Therefore, a differential

amount of heat or work is represented by Q or W, respectively, instead of dQ or dW. Properties,

however, are point functions (i.e., they depend on the state only, and not on how a system reaches

that state), and they have exact differentials designated by the symbol d.

A small change in volume, for example, is represented by dv, and the total volume change during

a process between states 1 and 2 is

2

2 11dv v v v (3.12)

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Figure 3.8 Properties are point functions; but heat and work are path functions

The total work done during process 12, however, is

2

121W W ( )not W (3.13)

That is, the total work is obtained by following the process path and adding the differential amounts

of work ( W) done along the way. The integral of W is not W2 - W1 (i.e., the work at state 2 minus

work at state 1), which is meaningless since work is not a property and systems do not possess

work at a state.

3.3 Boundary work The work associated with a moving boundary is called boundary work. The expansion and

compression work is often called moving boundary work or simply boundary work.

Example:- pistoncylinder device.

Figure 3.9 The work associated with a moving boundary is called boundary work.

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In this section, we analyze the moving boundary work for a quasiequilibrium process, a process

during which the system remains nearly in equilibrium at all times. A quasi-equilibrium process,

Boundary work is done by the steam on the piston is calculated from figure 3.10.

Figure 3.10 The area under the process curve on a P-V diagram represents the boundary work.

2

1b bW W (3.14)

b sFW Fd Ads PdVA

(3.15)

2

1bW PdV (3.16)

This integral can be evaluated only if we know the functional relationship between P and v during

the process.

P= f (V) is simply the equation of the process path on a P-V diagram. The differential area dA is

equal to PdV. The total area A under the process curve 12 is obtained by adding these differential

areas:

2 2

1 1Area A dA PdV (3.17)

A comparison of this equation with the above (2

1bW PdV ), reveals that the area under the

process curve on a P-v diagram is equal, in magnitude, to the work done during a quasi-

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equilibrium expansion or compression process of a closed system. (On the P-v diagram, it

represents the boundary work done per unit mass.)

2

1bW PdV (3.18)

Some typical process

Boundary work at constant volume process

Figure 3.11 Schematic and P-V diagram for constant pressure process

If the volume is held constant, =0 and the boundary work equation becomes 2

10bW PdV (3.19)

Boundary work at constant pressure

Figure 3.12 Schematic and P-v diagram for constant pressure

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If the pressure is held constant the boundary work equation becomes. 2 2

2 11 1( )bW PdV P dV P V V (3.20)

Boundary work at constant temperature (Isothermal)

Figure 3.13 Schematic and P-V diagram for a polytropic process.

If the temperature of an ideal gas system held constant, then the equation of state provides the

pressure volume relation.

mRTPV

(3.21)

The boundary work is:

2

1bW PdV But

mRTPV

(3.22)

2

1bmRTW dV

V (3.23)

Let mRT C PV

2

1bdvW CV

(3.24)

2

1b

VW ClnV

(3.25)

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Substitute the value of C

2 21 1

1 1

lnbV VW mRTln PVV V

(3.25)

21 1

1

ln lnbVW PVV

(3.26)

Polytropic Process During actual expansion and compression processes of gases, pressure and volume are often

related by PVn = C. where n and C are constants

2

1bW PdV but PVn = C

1 12 2 1 2 2 1 11 1 1

nn

b

nV V PV PVCV dV Cn

Wn

(3.27)

Since 1 1 2 2n nC PV PV For an ideal gas (PV = mRT), this equation can also be written as

2 1( )1b

mR T TWn

1n (3.28)

For the special case of n = 1the system is isothermal process and the boundary work becomes

22

1

2

1 1ln nbW PdV CV d

VV

V PV (3.29)

Spring Work

When the length of the spring changes by a differential amount dx under the influence of a force

F, the work done is

Figure 3.14 Elongation of a spring under the influence of a force.

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springW Fdx (3.30)

But F kx

2 22 1

1 ( )2spring

W k x x (3.31)

3.4 Energy transferred by Mass Mass flow into and out of a system changes the energy content of the system. When mass enters a

control volume, the energy of the control volume increase because the entering mass carries some

energy with it. Likewise when some mass leaves the control volume, the energy contained within

the control volume decreases because some leaving mass takeout some energy within it.

Figure 3.14 The energy content of a control volume can be changed by mass flow