EGR 334 Lecture 02 Work and Energy

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Chapter 2

Lecture 02:

Work and Energy



Today’s Objectives:

• Be able to distinguish between work and energy.• Be able to calculate Kinetic Energy• Be able to calculate Potential Energy• Be able to calculate Work done by an acting force• Be able to calculate Power

• Be able to calculate Work done by gases undergoing changesof state.• Be able to explain the concept of Internal Enegy

Reading Assignment:

Homework Assignment:

• Read Chap 2. Sections 1-5

From Chap 2: Problems 6, 20, 24, 32



Work, Heat, and Energy

Energy is conserved, but can be converted to different types

Ways to Transfer Energy Into or Out of A System

Work – transfers by applying a force and causing adisplacement of the point of application of the force.

Mechanical Waves – allow a disturbance to propagatethrough a medium.

Heat – is driven by a temperature difference between tworegions in space.

Matter Transfer – matter physically crosses the boundaryof the system, carrying energy with it.

Electrical Transmission – transfer is by electric current. Electromagnetic Radiation – energy is transferred byelectromagnetic waves

W = PE = KE = U

3Sec 2.1: Reviewing Mechanical Concepts of Energy



Thermodynamics “Work”

“Work is done by a system onits surroundings if the soleeffect on everything external

to the system could have been done by raising (ordropping) a weight.”

Physics definition of work is W = F sBut, in thermodynamics often we are working with

fluids (non-solids), so we need a broader definition.

4Sec 2.2: Broadening Our Understanding of Work



Joule’s Experiment (1845-Salford, England)

Joule dropped a known mass and measured the change intemperature of the water.

The experiment was conducted in the basement of his family’s brewery, where there was a constant ambient temperature.

The friction of the water molecules rubbing together caused thetemperature to increase.

5Sec 2.2: Broadening Our Understanding of Work

Joule’s Equipment - Manchester



Work Sign Convention

W > 0 : Work done BY the system

W < 0 : Work done ON the system

6Sec 2.2.1: Sign Convention

Sign is not inherently important, but this is the convention.

W < 0 : Work done ON the system

(System is compressed)

W > 0 : Work done BY the system

(System expands)

f

i

V

V PdV W



Power = Rate of Energy Transfer

Book’s convention: Dot above symbol represents the rate.

7Sec 2.2 .2: Power

The rate of work can be expressed as



Work Properties

Work is NOT a property of a system like V , T , or E .Work occurs when the system undergoes a process.

8Sec 2.2 : Work

A differential of a property is exact.

V

f

i

V

f iV

V dV V V The differential of work depends upon the path.

f

i

V

V W pdV



But, work depends on the process.

9Sec 2.2 : Work

For “Bobby” work

depends on the path,

since friction is a non-

conservative force.



So, we need to have a PV relationship for

the process.

10Sec 2.2 : Work

The process of changing volume is NOTnecessarily in equilibrium.

- He balloon popping, gas does not

instantly mix with air- Gas cylinder rupture, pressure inside ishigher then outside for some time, t

For this class, we will used an idealized process, that arecompletely reversible. We call this type of process

- quasi-equilbirium

- quasi-static



11Sec 2.2 : Work

Consider a box initially divided in half.

- Initially, one is filled with gas, the other a vacuum.

- The divider is then removed.

- The gas takes some time to fill the new volume.

During that time, there are different local values for Pin the volume. There is also likely some heat

generated, as the process is irreversible.

Non-quasi-static Process

V V V

Thermodynamics ≠ Kinetics



12Sec 2.2 : Work

Now we move the wall slowly, such that the gas is able to

adjust instantly. This is a reversible quasi-static process.

Quasi-static

V V V V

V V V V



Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W .

Process 1-2: Compression at constantpressure from p1=10 psi, V 1=4.0 ft3 to state 2

Process 2-3: Constant volume heating to state 3, where p3=50 psi

Process 3-1: Expansion to the initial state, during which the p-V relationship is pV = constant .

psi P

13

V

3 ft V

4

10

50



14

S d i O d di f



Energy

Physics energy typesKinetic Energy: Energy of objects in motion

Potential Energy: Energy of objects in a field (g,E,B)

Internal Energy

SpringChemical

Pressure

15Sec 2.3: Broadening Our Understanding of Energy

Pressure can be a form of energy if P > P atm

P atm

P Thus, the general energy

equation is

E PE KE U

6



Example Problem (2.37) A 10 V battery supplies a constant current of0.5 amp to a resistance for 30 min.

a) Determine the resistance, in ohms. b) For the battery, determine the amount

of energy transfer to work, in kJ.

16

Solution:



Example Problem (2.31)

Air contained within a piston-cylinder assembly is slowly heated. Asshown in Fig P2.31, during the process the pressure first varies linearly with volume and then remains constant. Determine the total work inkJ.

17

150

100

P (kPa)

V (m3)0.0700.0450.030

50

1

2 3

Solution:

8



End of Lecture 02

• Slides that follow show solutions to Exampleproblems.

18



Example (2.34): Air contained within a piston-cylinder assemblyundergoes three processes in series. Evaluate W.

Process 1-2: Compression at constant pressure from P1=10 psi, V1=4.0 ft3

to state 2

19

psi P

3 ft V 4

10

50

12

3

2

112 2 1

1 1 3 3 2 3

12 3 1

3

3 3

2

P

since:

:

104 0.8

50

V

V

W PdV V V

PV PV and V V

P then V V V

P

psiV ft ft

psi

Process 1-2: Isobaric Process

BTU ft psiW

f lb ft BTU

in

ft 92.548.010

778

1443

12 2

2

20




Process 2-3: Constant volume heating to state 3, where P3=50 psiProcess 3-1: Expansion to the initial state, during which the P-Vrelationship is PV = constant.

20

psi P

3 ft V

4

10

50

12

3

Process 2-3: Isovolumetric Process

002323

W V

21




Process 2-3: Constant volume heating to state 3, where P3=50 psiProcess 3-1: Expansion to the initial state, during which the P-Vrelationship is PV = constant.

21

psi P

3 ft V

4

10

50

12

3Process 3-1: Isothermic Process

3

11

3

1

3

lnC31 V

V V

V

V

V dV

V

C PdV W

23

3 2

14443

31 7780.810 4 ln

11.9

f

f t ft BTU

ft lb ft inW psi ft

BTU

3

1ln1131 V

V V P W

22



Example Problem (2.37) A 10 V battery supplies a constant current of0.5 amp to a resistance for 30 min.

a) Determine the resistance, in ohms. b) For the battery., determine the amount

of energy transfer to work, in kJ.

22

Solution: Electrical Work Principle

elec P VI elec elecW P t therefore: V = 10 V I = 0.5 A Δt =30 min

(10 )(0.5 ) 5elec

P VI V A W

60 1 / 1(5 )(30 min)

1 min 1 1000elec

s J s kJ W W

W J

then

0.15elec

W kJ

23



Example Problem (2.31)

Air contained within a piston-cylinder assembly is slowly heated. As shown inthe figure, during the process the pressure first varies linearly with volume

and then remains constant. Determine the total work in kJ.

23

150

100

P (kPa)

V (m3)0.0700.0450.030

50

1

2 3Solution: B

A

V

A B

V

W p dV

Conceptually, this representsthe area of the P-V plotunderneath the process lines.

2

1

1 2 _

V

PV trapezoid

V

W p dV A 3

2

2 3 _ rectangle

V

PV

V

W p dV A 31

(100 150)(0.045 0.030)2

kPa m 3(150)(0.070 0.045) kPa m

23 1 / 1

1.875 1.8751 1

kN m kJ kPa m kJ

kPa kN m

2

3 1 / 13.75 3.75

1 1

kN m kJ kPa m kJ

kPa kN m

1 3 1 2 2 3 1.875 3.75 5.625total W W W W kJ

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EGR 334 Lecture 02 Work and Energy