ENERGY

I am teaching Engineering Thermodynamics using the textbook by Cengel and Boles. A few figures in the slides are taken from that book, and most others are found online.

Similar figures can be found in many places.

I went through these slides in one 90-minute lecture. Zhigang Suo, Harvard University

System

• • • • • Experimental setup A fixed number of H 2 O molecules Cylinder Frictionless, perfectly sealed piston Weights Fire • • • System A system can be any part of the world.

Here the system is a fixed number of H The rest of the world is called the 2 O molecules in the cylinder.

surroundings

of the system. • • The system interacts with its surroundings Weights transfer energy to the system by

work

.

Fire transfers energy to the system by

heat

.

• • Closed system The system exchange energy with its surroundings.

The system does not exchange matter with its surroundings. • • • • Isolated system An isolated system does not interact with the rest of the world.

No exchange of matter. Seal the cylinder.

No exchange of energy. Jam the piston. Insulate the cylinder.

Do whatever necessary to prevent the rest of the world from affecting the system. 2

Energy

The world has many parts: stars, planets, animals, molecules, electrons, protons...

The parts move relative to one another, and interact with one another.

The motion and interaction carry energy. Energy is a fundamental concept. We don ’t know how to define energy in more fundamental concepts.

But we do know ways to measure and calculate energy. That is all that matters.

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Potential energy

When a mass

m

is lifted by a distance

z

, The energy increases by

mgz

.

We call this energy the

potential energy

.

z m

state 1

m

State 2 4

Kinetic energy

velocity v stationary

m

state 1

m

state 2 From the stationary state to a state of velocity v, the energy increases by 1 2

mv

2 We call this energy the

kinetic energy

.

5

Zero-sum game

1 2

mv

2 +

mgz

= constant h state 1 velocity = 0 height = 0 1 2

mv

2 -

mgh

= 0+0 state 2 state 1 state 2 velocity = v height = -h 6

Newton’s second law

a

=

dv dt v

=

dz ma

=

dt f f

= -

m dv dt

+

mg

= 0

mg z d m dt dv dt v

+

mgv

=

0

è 1 2

mv

2 +

mgz

ö 0 ø

1 2

mv

2 +

mgz

=

constant

mg 7

Vocabulary

• • • • Forms of energy (kinetic energy and potential energy) Conversion of energy from one form to another form.

Transfer of energy from one part of the system to another part.

Conservation of energy . When kinetic energy and potential energy convert to each other, their sum is fixed. Really?

8

Elastic energy

• • • • • • • • • Gradually add weights from different heights to pull the spring.

When the length of the spring is x, the amount of weights to maintain the length of the spring is F(x). When the length increases by dx the potential energy of the weights reduces by F(x)dx.

The total reduction of the potential energy of the weights is

x

ò ( )

dx

0 The same amount of energy is added to the spring as elastic energy.

The spring is a lattice of atoms. The elastic energy is stored in the stretched atom bonds.

How do I know? Gradually remove the weights to place them back to the original heights.

(Isolated system) = weights + spring. (energy of the system) = (potential energy of the weights) + (elastic energy of the spring) = constant Isolated system 9

Force, F

Force-length curve

Ideal spring Force, F loading

x

0 ò ( )

dx

Elongation, x loading unloading Elongation, x 10

Force-length curve

dissipative spring Force, F energy dissipated by the spring loading unloading Elongation, x 11

Force-length curve

dissipative spring (isolated system) = weights + spring + (insulated room) (potential energy of the weights) + (elastic energy of the spring) + (internal energy of the room) = constant Force, F energy dissipated by the spring loading unloading Elongation, x 12

A game-changing idea The principle of the conservation of energy A new zero-sum game

• • • • • • An isolated system has a fixed amount of energy.

What if energy of all known forms is not conserved?

Discover another form of energy to make energy conserve.

But what qualifies as a new form of energy?

Anything that can convert to a known form of energy .

Sounds like a self-fulfilling prophesy. It is.

My view on the principle of the conservation of energy follows, I believe, Feynman. Read his tale of “Dennis the Menace”. http://www.feynmanlectures.caltech.edu/I_04.html

The Feynman ’s Lectures ought to be required reading for all engineers. 13

Joule’s discovery

1 2

mv

2 +

mgz

decreases 14

Isolated system

Internal Energy

(isolated system) = fluid + paddle + weight (internal energy) + (kinetic energy) + (potential energy) = constant

U

+ 1 2

mv

2 +

mgh

= constant 15

Internal energy and molecular motion

Even when a tank of water is stationary at a macroscopic scale, water molecules undergo rapid and ceaseless motion. 16

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Electrical energy

(isolated system) = battery + bulb + (insulated room) (chemical energy of the battery) + (internal energy of the room) = constant Energy per unit time (power) going out the battery =

VI

Isolated system bulb current

I

conductor of negligible resistance voltage

V

battery 18

Convert chemical energy to electrical energy

lithium-ion battery wire Electron  electrode Lithium-ion  electrolyte electrode • Electrodes host lithium atoms.

• (lithium atom) = (lithium ion) + (electron) • Electrolyte conducts lithium ions.

• Wire conducts electrons.

Surface energy of liquid

• Molecules on surface have different energy from those in the interior.

• When the area of surface increases, more molecules come to the surface.

• The extra energy of the surface is proportional to the area of the surface: •

U

= s

s A

s s is the surface energy (per unit area).

dU

=

Fdx

2 s

s bdx

=

Fdx

2 s

s b

=

F

20

Convert energy from one form to another

kinetic potential light kinetic potential turbine rising object falling object solar sail seesaw light electrical chemical tribo luminescence generator hydro-electric photo electricity photo synthesis nuclear thermal friction falling object radiator electrical chemical nuclear motor electric pump light bulb electrical circuit charge battery radiator thermal explosion atomic bomb steam engine atomic bomb balloon chemo luminescence atomic bomb fire discharge battery chemical reaction nuclear power station thermo electricity atomic bomb chemical reaction fire nuclear reaction atomic bomb heat exchanger 21

Systems interact with the rest of the world in various ways

Open system Isolated system Closed system Thermal system Adiabatic system

Exchange matter

yes no no no no

Exchange energy by work

yes no yes no yes

Exchange energy by heat

yes no yes yes no 22

From isolated system to closed system

(Isolated system) = (weights) + (ideal spring) (closed system) =( ideal spring) •

Force

acting on the spring by the weights: F(x). •

work

done to the spring by the weights: F(x)dx.

• Change in the

elastic energy

of the spring: dU = F(x)dx. Isolated system closed system 23

Electrical Work

work per unit time (power) going out the battery =

VI

closed system bulb current

I

conductor of negligible resistance voltage

V

battery 24

Adiabatic work changes internal energy

Variations of Joule ’s experiment 25

Transfer energy to a closed system in two ways— heat and work

System = water thermal contact adiabatic contact • So far as water is concerned, the two ways of adding energy give the same result.

• Internal energy is a property of the closed system.

• Increase the internal energy of the closed system.

• Work and heat are not properties of the closed system.

• Thermal contact: transfer energy by heat.

• Adiabatic contact: transfer energy by work.

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THE FIRST LAW OF THERMODYNAMICS

• For all adiabatic processes between two states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process.

• Determine the change in internal energy by adiabatic process, D U = W.

• For a closed system, in general D U is not equal to W.

• The difference defines heat, D U = W + Q.

27

Mechanisms of transferring energy by

heat • • •

Conduction Convection Radiation

28

Yang, Stabler, Journal of Electronic Materials. 38, 1245 (2009) 29

What you need to know about energy

, The National Academies.

30

https://flowcharts.llnl.gov/

Summary

• Forms of energy.

• Convert energy from one form to another.

• Energy is additive.

• Transfer energy from one place to another.

• The energy of an isolated system is conserved.

• The internal energy of a closed system changes due to heat and work.

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