Energy, energy transfer, and general energy analysis

Chapter 3

Md. Mizanur Rahman MEng(Sweden), PhD (Finland), CEng Chartered Energy Engineer (EI, UK) Certified Energy Manager School of Mechanical Engineering Universiti Teknologi Malaysia Email: mizanur@mail.fkm.utm.my

INTRODUCTION

• As a result of the conversion of electric

energy consumed by the device to heat, the

room temperature will rise.

2

A refrigerator

operating with its

door open in a well-

sealed and well-

insulated room

A fan running in a

well-sealed and

well-insulated room

will raise the

temperature of air in

the room.

FORMS OF ENERGY • 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.

• Thermodynamics deals only with the change of the total energy.

• Macroscopic forms of energy: Those a system possesses as a whole with respect to some outside reference frame, such as kinetic and potential energies.

• Microscopic forms of energy: Relate to the molecular structure and molecular activity of a system

• Internal energy, U: The sum of all the microscopic forms of energy.

3

The macroscopic energy of an

object changes with velocity and

elevation.

• Kinetic energy, KE: The energy

that a system possesses as a result

of its motion relative to some

reference frame.

• Potential energy, PE: The energy

that a system possesses as a result

of its elevation in a gravitational

field.

4

Total energy

of a system

Energy of a system

per unit mass

Potential energy

per unit mass

Kinetic energy

per unit mass

Potential energy

Total energy

per unit mass

Kinetic energy

Mass flow rate

Energy flow rate

Some Physical Insight to Internal Energy

5

Sensible energy:

The portion of the

internal energy of

a system

associated with

the kinetic

energies of the

molecules.

• Latent energy: The internal energy associated with the phase of a system.

• Chemical energy: The internal energy associated with the atomic bonds in a molecule.

• Nuclear energy: The tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself.

6

Internal = Sensible + Latent + Chemical + Nuclear

Thermal = Sensible + Latent

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macroscopic kinetic energy:

organized, more useful

microscopic kinetic energy:

disorganized

• 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 or as

energy interactions.

• The dynamic forms of energy are

recognized at the system boundary

as they cross it, and they represent

the energy gained or lost by a

system during a process.

• The only two forms of energy

interactions associated with a

closed system are heat transfer

and work.

• The difference between heat transfer and work: An energy interaction is

heat transfer if its driving force is a temperature difference. Work is energy

transfer associated with force acting through a distance

Mechanical Energy

8

Mechanical energy: The form of energy that can be converted to

mechanical work completely and directly by an ideal mechanical device such as an ideal turbine.

Kinetic and potential energies: The familiar forms of mechanical energy.

Mechanical energy of a

flowing fluid per unit mass

Rate of mechanical

energy of a flowing fluid

Mechanical energy change of a fluid during incompressible flow per unit mass

Rate of mechanical energy change of a fluid during incompressible flow

ENERGY TRANSFER BY HEAT

9

Energy can cross the

boundaries of a closed system

in the form of heat and work.

Temperature difference is the driving

force for heat transfer. The larger the

temperature difference, the higher is the

rate of heat transfer.

Heat: The form of energy that is

transferred between two

systems (or a system and its

surroundings) by virtue of a

temperature difference.

10

Energy is

recognized

as heat

transfer only

as it crosses

the system

boundary.

During an adiabatic process, a system

exchanges no heat with its surroundings.

Heat transfer

per unit mass

Amount of heat transfer

when heat transfer rate

changes with time

Amount of heat transfer

when heat transfer rate

is constant

Historical Background on Heat

• Kinetic theory: Treats molecules as tiny balls that are in motion and thus possess kinetic energy.

• Heat: The energy associated with the random motion of atoms and molecules.

Heat transfer mechanisms:

• Conduction: 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: 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: The transfer of energy due to the emission of electromagnetic waves (or photons).

11

In the early nineteenth century, heat was

thought to be an invisible fluid called the

caloric that flowed from warmer bodies to

the cooler ones.

ENERGY TRANSFER BY WORK • Work: The energy transfer associated with a force acting through a distance.

– A rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions

• Formal sign convention: 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.

• Alternative to sign convention is to use the subscripts in and out to indicate direction. This is the primary approach in this text.

12

Specifying the directions

of heat and work.

Work done

per unit mass

Power is the

work done per

unit time (kW)

Heat vs. Work • 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).

13

Properties are point functions; but

heat and work are path functions

(their magnitudes depend on the

path followed). Properties are point functions

have exact differentials (d ).

Path

functions

have inexact

differentials ( )

Electrical Work

14

Electrical power in terms of resistance

R, current I, and potential difference V.

Electrical power

When potential difference

and current change with time

When potential difference

and current remain constant

MECHANICAL FORMS OF WORK • There are two requirements for a work interaction between a

system and its surroundings to exist:

– there must be a force acting on the boundary.

– the boundary must move.

15

The work done is proportional to the force

applied (F) and the distance traveled (s).

Work = Force Distance

When force is not constant

If there is no movement,

no work is done.

Spring Work

16

Elongation

of a spring

under the

influence of

a force.

When the length of the spring changes by

a differential amount dx under the influence

of a force F, the work done is

For linear elastic springs, the displacement

x is proportional to the force applied

k: spring constant (kN/m)

Substituting and integrating yield

x1 and x2: the initial and the final

displacements

The

displacement

of a linear

spring doubles

when the force

is doubled.

Shaft Work

17

A force F acting through

a moment arm r

generates a torque T

This force acts through a distance s

The power transmitted through the shaft

is the shaft work done per unit time

Shaft

work

MOVING BOUNDARY WORK

18

Moving boundary work (P dV work):

The expansion and compression work

in a piston-cylinder device.

The work associated

with a moving

boundary is called

boundary work. A gas does a

differential

amount of work

Wb as it forces

the piston to

move by a

differential

amount ds.

Quasi-equilibrium process:

A process during which the system

remains nearly in equilibrium at all

times.

Wb is positive for expansion

Wb is negative for compression

19

The area under the process

curve on a P-V diagram

represents the boundary work.

The boundary

work done

during a process

depends on the

path followed as

well as the end

states.

The net work done

during a cycle is the

difference between

the work done by

the system and the

work done on the

system.

20

Polytropic, Isothermal, and Isobaric processes

Schematic and

P-V diagram for

a polytropic

process.

For expansion and compression of ideal gases, relation between P and V is often PVn = C, where C and n are constants, n is also called as polytropic exponent. This type of process is called polytropic process. For isentropic process, n=γ, We also know for ideal gas eq. of state: PV=mRT, R is gas constant (kJ/kg-K)

Boundary work for polytropic process, 2

2 2 1 1

1 1b

PV PVW PdV

n

Boundary work for isothermal or constant temp. process,

Boundary work for isobaric or constant pressure process, 2

2 11

( )bW PdV P V V

Boundary work for isometric or constant volume process, 2

10bW PdV

or

22 2

1 1 2 21

1 1

ln lnb

V VW PdV PV PV

V V

Energy Balance

21

Energy Change of a System, ΔEsystem

22

The change in the total energy of a system during a process is the sum of the

changes in its internal, kinetic, and potential energies and can be expressed as

Example 1: A piston–cylinder device initially contains 0.4 m3 of air at 100 kPa and 80°C. The air is now compressed to 0.1 m3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process.

Solution:

It is an isothermal process, so we will use equation,

Here given, p1=100 kPa= 100x103 Pa, V1=0.4 m3, V2=0.1 m3,

So, boundary work Wb= 100x 103 x0.4 x ln(0.1/0.4) J= -55451 J= -55.451 kJ

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22 2

1 1 2 21

1 1

ln lnb

V VW PdV PV PV

V V

• Example 2: A piston–cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 120°C. The nitrogen is now expanded polytropically to a state of 100 kPa and 100°C. Determine the boundary work done during this process.

• Solution:

Here given, V1=0.07 m3, P1= 130 kPa, T1=120 ºC = (120+273) K= 393 K, P2=100 kPa, T2= 100 ºC= (100+273) K= 373 K, Wb= ?

The process is polytropic, so,

We also know for polytropic process, PVn=C, that means, P1V1n=P2V2n, so, n=ln(P1/P2)/ln(V2/V1)

For any ideal gas, we know, PV=mRT, here, R= gas constant= 0.2968 kJ/kg-K for Nitrogen

Therefore,

Done!

25

22 2 1 1

1 1b

PV PVW PdV

n

1 1

1

130 0.070.0780

0.2968 393

PVm kg

RT

22

2

0.078 0.2968 3730.0863 3

100

mRTV m

P

2 2 1 1 100 0.0863 130 0.071.86

1 1 1.248b

PV PVW kJ

n

ln(130 /100)1.248

ln(0.08637 / 0.07)n

Example 3: A piston–cylinder device initially contains 0.3 kg of steam at 1.0 MPa and 250 °C. Determine the boundary work if steam is expanded at constant pressure to 400 °C .

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0.3

Ex. 2

A piston-cylinder device contains 2 kg of superheated water at

200 kPa and 300 oC. The superheated water is now cooled at

constant pressure until the temperature drops to 200 oC.

i. Determine the boundary work done during this process [kJ].

ii. Sketch the process on pressure versus volume (P-V) diagram

clearly showing the states and the direction of the process.

Solution in next slide>

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28

Ex. 3

Air initially at 600 kPa and 250 oC is contained in a 0.30 m3 piston-

cylinder device. The air is now expanded slowly until the final pressure inside the cylinder is 200 kPa. The temperature of the air

remains constant during this process. Assume the air to be an ideal

gas with R = 0.287 kJ/kgK.

i. Determine the mass of the air in the cylinder (kg).

ii. Determine the boundary work done during this process (kJ).

iii. Sketch the process on pressure versus volume (P-V) diagram clearly showing the states and the direction of the process.

Solution in next slide >

29

30

Ex : A piston–cylinder device contains 0.10 kg of

air initially at 1 MPa and 250°C. The air is first

expanded isothermally to 500 kPa, then air is

compressed with constant volume to the initial

pressure. Determine the boundary work for each

process and the net-work done during the

processes.

Solution in next slide

31

• Example 4: A piston–cylinder device contains 0.05 m3 of a gas initially at 200 kPa. At this state, a linear spring that has a spring constant of 150 kN/m is touching the piston but exerting no force on it. Now heat is transferred to the gas, causing the piston to rise and to compress the spring until the volume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25 m2 , determine (a) the final pressure inside the cylinder, (b) the total work done by the gas, and (c) the fraction of this work done against the spring to compress it.

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34

Forms of energy Question- what is total energy of a system?

• The sum of all forms of the energy a system possesses is called total energy. In the absence of magnetic, electrical and surface tension effects, the total energy of a system consists of the kinetic, potential, and internal energies.

Question- what is mechanical energy? How does it differ from thermal energy? What are the forms of mechanical energy of a fluid stream?

• The mechanical energy is the form of energy that can be converted to mechanical work completely and directly by a mechanical device such as a propeller. It differs from thermal energy in that thermal energy cannot be converted to work directly and completely. The forms of mechanical energy of a fluid stream are kinetic, potential, and flow energies.

35

Energy transfer by heat and work • In what forms can energy cross the boundaries of a closed system?

• Energy can cross the boundaries of a closed system in two forms: heat and work.

• When is the energy crossing the boundaries of a closed system heat and when is it work?

• The form of energy that crosses the boundary of a closed system because of a temperature difference is heat; all other forms are work.

• What is an adiabatic process? What is an adiabatic system?

• An adiabatic process is a process during which there is no heat transfer. A system that does not exchange any heat with its surroundings is an adiabatic system.

36

Energy transfer by heat and work • A gas in a piston–cylinder device is compressed, and as a

result its temperature rises. Is this a heat or work interaction?

• It is a work interaction.

• A room is heated by an iron that is left plugged in. Is this a heat or work interaction? Take the entire room, including the iron, as the system.

• It is a work interaction

• A room is heated as a result of solar radiation coming in through the windows. Is this a heat or work interaction for the room?

• It is a heat interaction since it is due to the temperature difference between the sun and the room.

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38

Mechanical energy of a flowing fluid per unit mass

Rate of mechanical energy of a flowing fluid

Total energy of a system

Energy of a system per unit mass

• Example 5: Determine the total energy required to accelerate a 1300 kg car from 10 km/h to 60 km/h on an uphill road with a vertical rise of 40 m.

39

• Example 6: A person gets into an elevator at the lobby level of a hotel together with his 30-kg suitcase, and gets out at the 10th floor 35 m above. Determine the amount of energy consumed by the motor of the elevator that is now stored in the suitcase.

40

• Example 7: Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m3 /s at a location 90 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.

41

4–40 A piston–cylinder device initially contains 0.8 m3 of saturated water

vapor at 250 kPa. At this state, the piston is resting on a set of stops, and

the mass of the piston is such that a pressure of 300 kPa is required to

move it. Heat is now slowly transferred to the steam until the volume

doubles. Show the process on a P-v diagram with respect to saturation lines

and determine (a) the work done during this process, and (b) the total heat

transfer

4.10 example

A piston–cylinder device initially contains air at 150 kPa and 27°C. At this

state, the piston is resting on a pair of stops, as shown in Fig. 4–32, and the

enclosed volume is 400 L. The mass of the piston is such that a 350-kPa

pressure is required to move it. The air is now heated until its volume has

doubled. Determine (a) the final temperature, (b) the work done by the air

Test 1 14 October 2018 (Monday)

9-11 PM

DK5, P19

Syllabus for Test 1:

Chapter 1: Introduction and Basic concepts

Chapter 2: Properties of pure substances