physics 1401 semester exam review. 1.1 measurements vernier caliper micrometer photogate (millisec)

PHYSICS 1401

SEMESTER EXAM REVIEW

1.1 MeasurementsVernier caliper

%)100( valueltheoretica

valuealexperiment - valueltheoretica error %

Micrometer

Photogate (millisec)

1.2 Resultant and Equilibrant

2.4 Motion Graphs

2.4 Equations of Kinematics for Constant Acceleration

Equations of Kinematics for Constant Acceleration

POSITION, VELOCITY & ACCELERATION

tvvx o 21

221 attvx o

atvv o

axvv o 222

3.2 Equations of Kinematics in Two Dimensions

tavv xoxx tvvx xox 21

xavv xoxx 222 221 tatvx xox

3.2 Equations of Kinematics in Two Dimensions

tavv yoyy

221 tatvy yoy

tvvy yoy 21

yavv yoyy 222

3.3 Projectile Motion

Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80 m/s2.

2sm80.9ya

0xa

constant oxx vv


Objects falling in a vacuum will experience the same speed.

Galileo started experimenting totest the theories of otherscientists such as Aristotle.


Properties of Projectile Motion

1. Horizontal velocity stays constant.2. No vertical velocity when object is thrown horizontally

from the top of hill. 3. When object is launched from the ground, velocity

has horizontal and vertical components. 4. At the top of the trajectory, no vertical velocity, but

there is acceleration due to gravity. 5. The time for a projectile to reach the top is equal to

the time for it to go back to the ground. 6. The initial launching velocity is equal to the final

lvelocity just before it hits the ground.


y ay vy voy t-1050 m -9.80 m/s2 ? 0 m/s 14.6 s


y ay vy voy t? -9.80 m/s2 0 14 m/s


Example 7 The Time of Flight of a Kickoff

What is the time of flight between kickoff and landing?


y ay vy voy t0 -9.80 m/s2 14 m/s ?


y ay vy voy t0 -9.80 m/s2 14 m/s ?

221 tatvy yoy

2221 sm80.9sm140 tt

t2sm80.9sm1420

s 9.2t


Example 8 The Range of a Kickoff

Calculate the range R of the projectile.

m 49s 9.2sm17

221

tvtatvx oxxox

4.2 Newton’s First Law of Motion

An object continues in a state of restor in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force.

The net force is the vector sum of allof the forces acting on an object.

If the vector sum is equal to zero, then the system is in equilibrium.

4.2 Newton’s First Law of Motion

Inertia is the natural tendency of anobject to remain at rest in motion ata constant speed along a straight line.

The mass of an object is a quantitativemeasure of inertia.

SI Unit of Mass: kilogram (kg)

4.3 Newton’s Second Law of Motion

Newton’s Second Law

When a net external force acts on an objectof mass m, the acceleration that results is directly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.

m F

a

aF

m

4.3 Newton’s Second Law of Motion

SI Unit for Force

22 s

mkg

s

mkg

This combination of units is called a newton (N).

4.4 The Vector Nature of Newton’s Second Law

xx maFyy maF

The direction of force and acceleration vectorscan be taken into account by using x and ycomponents.

aF

m

is equivalent to

4.5 Newton’s Third Law of Motion

Newton’s Third Law of Motion

Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.

It involves TWO objects to form an action-reaction pair.

4.6 Types of Forces: An Overview

In nature there are two general types of forces,fundamental and nonfundamental.

Fundamental Forces

1. Gravitational force

2. Strong Nuclear force

3. Electroweak force

4.6 Types of Forces: An Overview

Examples of nonfundamental forces:

friction

tension in a rope

normal or support forces

4.7 The Gravitational Force

Newton’s Law of Universal Gravitation

Every particle in the universe exerts an attractive force on everyother particle.

He said gravity is universal.

The force that each exerts on the other is directed along the linejoining the particles.


For two particles that have masses m1 and m2 and are separated by a distance r, the force has a magnitude given by

221

r

mmGF

2211 kgmN10673.6 G


N 104.1

m 1.2

kg 25kg 12kgmN1067.6

8

22211

221

r

mmGF

4.9 Static and Kinetic Frictional Forces

When the two surfaces are not sliding across one anotherthe friction is called static friction.


The magnitude of the static frictional force can have any valuefrom zero up to a maximum value.

MAXss ff

NsMAXs Ff

10 s is called the coefficient of static friction.


Note that the magnitude of the frictional force doesNOT depend on the contact area of the surfaces.


Static friction opposes the impending relative motion betweentwo objects.

Kinetic friction opposes the relative sliding motion motions thatactually does occur.

Nkk Ff

10 k is called the coefficient of kinetic friction.

4.10 The Tension Force

Cables and ropes transmit forces through tension.

4.11 Equilibrium Application of Newton’s Laws of Motion

Definition of EquilibriumAn object is in equilibrium when it has zero acceleration.

0xF

0yF

4.12 Nonequilibrium Application of Newton’s Laws of Motion

xx maF

yy maF

When an object is accelerating, it is not in equilibrium.

5.1 Uniform Circular Motion

Let T be the time it takes for the object totravel once around the circle.

vr

T

2

r

5.2 Centripetal Acceleration

The direction of the centripetal acceleration is towards the center of the circle; in the same direction as the change in velocity.

r

vac

2

5.3 Centripetal Force

aF

m

m F

a

Recall Newton’s Second Law

When a net external force acts on an objectof mass m, the acceleration that results is directly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.

5.3 Centripetal Force

Thus, in uniform circular motion there must be a netforce to produce the centripetal acceleration.

The centripetal force is the name given to the net force required to keep an object moving on a circular path.

The direction of the centripetal force always points towardthe center of the circle and continually changes direction as the object moves.

r

vmmaF cc

2

5.7 Vertical Circular Motion

r

vmmgFN

21

1

r

vmmgFN

23

3

r

vmFN

22

2

r

vmFN

24

4

6.1 Work Done by a Constant Force

FsW J joule 1 mN 1


sFW cos1180cos

090cos

10cos


FssFW 0cos

FssFW 180cos

6.2 The Work-Energy Theorem and Kinetic Energy

THE WORK-ENERGY THEOREM

When a net external force does work on and object, the kineticenergy of the object changes according to

2212

f21

of KEKE omvmvW

6.3 Gravitational Potential Energy

sFW cos

fo hhmgW gravity


fo hhmgW gravity


fo mghmghW gravity

DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY

The gravitational potential energy PE is the energy that anobject of mass m has by virtue of its position relative to thesurface of the earth. That position is measured by the heighth of the object relative to an arbitrary zero level:

mghPE

J joule 1 mN 1


2212

f21W omvmv

fo hhmgW gravity

221

ofo mvhhmg

foo hhgv 2

sm40.8m 80.4m 20.1sm80.92 2 ov

6.4 Conservative Versus Nonconservative Forces

Version 1 A force is conservative when the work it doeson a moving object is independent of the path between theobject’s initial and final positions.

fo hhmgW gravity

6.4 Conservative Versus Nonconservative Forces

Version 2 A force is conservative when it does no work on an object moving around a closed path, starting andfinishing at the same point.

fo hh fo hhmgW gravity

6.5 The Conservation of Mechanical Energy

THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY

The total mechanical energy (E = KE + PE) of an objectremains constant as the object moves, provided that the network done by external nonconservative forces is zero.


of EE

2212

21

ooff mvmghmvmgh

2212

21

ooff vghvgh

6.7 Power

DEFINITION OF AVERAGE POWER

Average power is the rate at which work is done, and itis obtained by dividing the work by the time required to perform the work.

t

WP

Time

Work

(W)watt sjoule

6.7 Power

Time

energyin ChangeP

watts745.7 secondpoundsfoot 550 horsepower 1

vFP

6.8 Other Forms of Energy and the Conservation of Energy

THE PRINCIPLE OF CONSERVATION OF ENERGYEnergy can neither be created nor destroyed, but can only be converted from one form to another.

6.9 Work Done by a Variable Force

sFW cos

Constant Force

Variable Force

2211 coscos sFsFW

7.1 The Impulse-Momentum Theorem

There are many situations when the force on an object is not constant.


DEFINITION OF IMPULSE

The impulse of a force is the product of the averageforce and the time interval during which the force acts:

tFJ

Impulse is a vector quantity and has the same directionas the average force.

s)(N secondsnewton


tFJ


DEFINITION OF LINEAR MOMENTUM

The linear momentum of an object is the product of the object’s mass times its velocity:

vp

m

Linear momentum is a vector quantity and has the same direction as the velocity.

m/s)(kg ndmeter/secokilogram


t

of vva

aF

m

t

mm

of vvF

of vvF

mmt


of vvF

mmt

final momentum initial momentum

IMPULSE-MOMENTUM THEOREM

When a net force acts on an object, the impulse ofthis force is equal to the change in the momentumof the object

impulse

7.2 The Principle of Conservation of Linear Momentum

of PP

tforces external average of sum

If the sum of the external forces is zero, then

of PP

0 of PP

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

The total linear momentum of an isolated system is constant(conserved). An isolated system is one for which the sum ofthe average external forces acting on the system is zero.

7.3 Collisions in One Dimension

The total linear momentum is conserved when two objectscollide, provided they constitute an isolated system.

Elastic collision -- One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. Momentum and KE are constant.

Inelastic collision -- One in which the total kinetic energy of the system after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

Momentum is constant but not KE.

7.2 The Principle of Conservation of Linear Momentum

of PP

02211 ff vmvm

2

112 m

vmv ff

sm5.1

kg 88

sm5.2kg 542

fv

7.3 Perfectly Inelastic Collision

Momentum is conserved. Kinetic energy is NOT conserved.

7.5 Center of Mass

The center of mass is a point that represents the average location forthe total mass of a system.

21

2211

mm

xmxmxcm

7.5 Center of Mass

21

2211

mm

xmxmxcm

21

2211

mm

vmvmvcm

7.5 Center of Mass

21

2211

mm

vmvmvcm

In an isolated system, the total linear momentum does not change,therefore the velocity of the center of mass does not change.

7.5 Center of Mass

021

2211

mm

vmvmvcm

BEFORE

AFTER

0002.0

kg 54kg 88

sm5.2kg 54sm5.1kg 88

cmv

8.1 Rotational Motion and Angular Displacement

r

s

Radius

length Arcradians)(in

For a full revolution:

360rad 2 rad 22

r

r

8.1 Rotational Motion and Angular Displacement

rad 0349.0deg360

rad 2deg00.2

miles) (920 m1048.1

rad 0349.0m1023.46

7

rs

r

s

Radius

length Arcradians)(in

8.2 Angular Velocity and Angular Acceleration

DEFINITION OF AVERAGE ANGULAR VELOCITY

timeElapsed

ntdisplacemeAngular locity angular ve Average

ttt o

o

SI Unit of Angular Velocity: radian per second (rad/s)


Example 3 Gymnast on a High Bar

A gymnast on a high bar swings throughtwo revolutions in a time of 1.90 s.

Find the average angular velocityof the gymnast.


rad 6.12rev 1

rad 2rev 00.2

srad63.6s 90.1

rad 6.12


Changing angular velocity means that an angular acceleration is occurring.

DEFINITION OF AVERAGE ANGULAR ACCELERATION

ttt o

o

timeElapsed

locityangular vein Change on acceleratiangular Average

SI Unit of Angular acceleration: radian per second squared (rad/s2)

8.3 The Equations of Rotational Kinematics


Example 5 Blending with a Blender

The blades are whirling with an angular velocity of +375 rad/s whenthe “puree” button is pushed in.

When the “blend” button is pushed,the blades accelerate and reach agreater angular velocity after the blades have rotated through anangular displacement of +44.0 rad.

The angular acceleration has a constant value of +1740 rad/s2.

Find the final angular velocity of the blades.


θ α ω ωo t

+44.0 rad +1740 rad/s2 ? +375 rad/s

222 o

srad542rad0.44srad17402srad375

2

22

2

o

8.4 Angular Variables and Tangential Variables

velocityl tangentiaTv

speed l tangentiaTv


t

rt

r

t

svT

t

rad/s)in ( rvT


Tctotal aaa

Total acceleration is the vector sum of centripetal acceleration and tangential acceleration.


t

rt

rr

t

vva oToTT

0

to

)rad/sin ( 2raT


Example 6 A Helicopter Blade

A helicopter blade has an angular speed of 6.50 rev/s and anangular acceleration of 1.30 rev/s2.For point 1 on the blade, findthe magnitude of (a) thetangential speed and (b) thetangential acceleration.


srad 8.40rev 1

rad 2

s

rev 50.6

sm122srad8.40m 3.00 rvT


22 sm5.24srad17.8m 3.00 raT

22

srad 17.8rev 1

rad 2

s

rev 30.1

9.1 The Action of Forces and Torques on Rigid Objects

In pure translational motion, all points on anobject travel on parallel paths.

The most general motion is a combination oftranslation and rotation.


According to Newton’s second law, a net force causes anobject to have an acceleration.

What causes an object to have an angular acceleration?

TORQUE


DEFINITION OF TORQUE

Magnitude of Torque = (Magnitude of the force) x (Lever arm)

FDirection: The torque is positive when the force tends to produce a counterclockwise rotation about the axis.

SI Unit of Torque: newton x meter (N·m)


790 N

F

m106.355cos

2

mN 15

55cosm106.3N 720 2

9.2 Rigid Objects in Equilibrium

EQUILIBRIUM OF A RIGID BODY

A rigid body is in equilibrium if it has zero translationalacceleration and zero angular acceleration. In equilibrium,the sum of the externally applied forces is zero, and thesum of the externally applied torques is zero.

0 0yF0 xF


022 WWF

N 1480

m 1.40

m 90.3N 5302 F

22

WWF


021 WFFFy

0N 530N 14801 F

N 9501 F


Example 5 Bodybuilding

The arm is horizontal and weighs 31.0 N. The deltoid muscle can supply1840 N of force. What is the weight of the heaviest dumbbell he can hold?


0 Mddaa MWW

0.13sinm 150.0M


N 1.86

m 620.0

0.13sinm 150.0N 1840m 280.0N 0.31

d

Maad

MWW

9.3 Center of Gravity

When an object has a symmetrical shape and its weight is distributed uniformly, the center of gravity lies at its geometrical center.

9.3 Center of Gravity

21

2211

WW

xWxWxcg

9.6 Angular Momentum

DEFINITION OF ANGULAR MOMENTUM

The angular momentum L of a body rotating about a fixed axis is the product of the body’s moment of inertia and its angular velocity with respect to thataxis:

IL

Requirement: The angular speed mustbe expressed in rad/s.

SI Unit of Angular Momentum: kg·m2/s


PRINCIPLE OF CONSERVATION OF ANGULAR MOMENTUM

The angular momentum of a system remains constant (is conserved) if the net external torque acting on the system is zero.


Conceptual Example 14 A Spinning Skater

An ice skater is spinning with botharms and a leg outstretched. Shepulls her arms and leg inward andher spinning motion changesdramatically.

Use the principle of conservationof angular momentum to explainhow and why her spinning motionchanges.

10.1 The Ideal Spring and Simple Harmonic Motion

xkF Appliedx

spring constant

Units: N/m

10.1 The Ideal Spring and Simple Harmonic Motion

HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING

The restoring force on an ideal spring is xkFx

10.2 Simple Harmonic Motion and the Reference Circle

period T: the time required to complete one cycle

frequency f: the number of cycles per second (measured in Hz)

Tf

1

Tf

22

amplitude A: the maximum displacement

10.3 Energy and Simple Harmonic Motion

DEFINITION OF ELASTIC POTENTIAL ENERGY

The elastic potential energy is the energy that a springhas by virtue of being stretched or compressed. For anideal spring, the elastic potential energy is

221

elasticPE kx

SI Unit of Elastic Potential Energy: joule (J)


Example 8 Changing the Mass of a Simple Harmonic Oscillator

A 0.20-kg ball is attached to a vertical spring. The spring constantis 28 N/m. When released from rest, how far does the ball fallbefore being brought to a momentary stop by the spring?


of EE

2212

212

212

21

ooofff kymghmvkymghmv

oo mghkh 221

m 14.0

mN28

sm8.9kg 20.02

2

2

k

mgho

10.4 The Pendulum

Example 10 Keeping Time

Determine the length of a simple pendulum that willswing back and forth in simple harmonic motion with a period of 1.00 s.

2

2L

g

Tf

m 248.0

4

sm80.9s 00.1

4 2

22

2

2

gTL

2

2

4gT

L

Period of simple pendulum isg

LT

22

11.1 Mass Density

DEFINITION OF MASS DENSITY

The mass density of a substance is CONSTANT andis the mass of a substance divided by its volume:

V

m

SI Unit of Mass Density: kg/m3

11.1 Mass Density

11.2 Pressure

A

FP

SI Unit of Pressure: 1 N/m2 = 1Pa

Pascal

11.2 Pressure

Atmospheric Pressure at Sea Level: 1.013x105 Pa = 1 atmosphere

11.3 Pressure and Depth in a Static Fluid

VgAPAP 12

AhV

AhgAPAP 12

hgPP 12

11.3 Pressure and Depth in a Static Fluid

Pa 1055.1

m 50.5sm80.9mkg1000.1Pa 1001.15

233

pressure catmospheri

52

P

ghPP 12

11.4 Pressure Gauges

AB PPP 2

ghPPA 1

ghPP atm pressure gauge

2

absolute pressure

11.5 Pascal’s Principle

PASCAL’S PRINCIPLE

Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls.

11.5 Pascal’s Principle

m 012 gPP

1

1

2

2

A

F

A

F

1

212 A

AFF

11.6 Archimedes’ Principle

APPAPAPFB 1212

ghPP 12

ghAFB

hAV

gVFB

fluiddisplaced

of mass


ARCHIMEDES’ PRINCIPLE

Any fluid applies a buoyant force to an object that is partiallyor completely immersed in it; the magnitude of the buoyantforce equals the weight of the fluid that the object displaces:

fluid displaced

ofWeight

fluid

forcebuoyant of Magnitude

WFB


If the object is floating then the magnitude of the buoyant forceis equal to the magnitude of itsweight.

11.8 The Equation of Continuity

Incompressible fluid: 2211 vAvA

Volume flow rate Q: AvQ

11.9 Bernoulli’s Equation

The fluid accelerates toward the lower pressure regions.

According to the pressure-depthrelationship, the pressure is lowerat higher levels, provided the areaof the pipe does not change.


2222

11

212

1nc mgymvmgymvW

VPPAsPsFsFW 12


2222

11

212

112 mgymvmgymvVPP

2222

11

212

112 gyvgyvPP

BERNOULLI’S EQUATION

In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:

2222

121

212

11 gyvPgyvP

11.10 Applications of Bernoulli’s Equation

Conceptual Example 14 Tarpaulins and Bernoulli’s Equation

When the truck is stationary, the tarpaulin lies flat, but it bulges outwardwhen the truck is speeding downthe highway.

Account for this behavior.


Example 16 Efflux Speed

The tank is open to the atmosphere atthe top. Find an expression for the speed of the liquid leaving the pipe atthe bottom.


2222

121

212

11 gyvPgyvP

atmPPP 2102 v

hyy 12

ghv 212

1

ghv 21

12.1 Common Temperature Scales

Temperatures are reported in degreesCelsius or degrees Fahrenheit.

Temperatures changed, on theother hand, are reported in Celsius degrees or Fahrenheit degrees:

FC 5

9 1

AT SEA LEVEL

12.2 The Kelvin Temperature Scale

15.273 cTT

Kelvin temperature

AT SEA LEVEL

12.2 The Kelvin Temperature Scale

absolute zero point = -273.15oC

12.4 Linear Thermal Expansion

LINEAR THERMAL EXPANSION OF A SOLID

The length of an object changes when its temperature changes:

TLL o

coefficient of linear expansion

Common Unit for the Coefficient of Linear Expansion: 1C

C

1


THE BIMETALLIC STRIP

12.5 Volume Thermal Expansion

VOLUME THERMAL EXPANSION

The volume of an object changes when its temperature changes:

TVV o

coefficient of volume expansion

Common Unit for the Coefficient of Volume Expansion: 1C

C

1

12.5 Volume Thermal Expansion

Expansion of water.

The physics of burstingwater pipes.

12.6 Heat and Internal Energy

DEFINITION OF HEAT

Heat is energy that flows from a higher-temperature object to a lower-temperature object because of a difference in temperatures.

SI Unit of Heat: joule (J)

12.6 Heat and Internal Energy

The heat that flows from hot to cold originates in the internal energy ofthe hot substance.

It is not correct to say that a substancecontains heat.

13.1 Convection

CONVECTION

Convection is the process in which heat is carried from one placeto another by the bulk movement of a fluid.

convection currents

13.2 Conduction

CONDUCTION

Conduction is the process whereby heat is transferred directly througha material, with any bulk motion of the material playing no role in the transfer.

One mechanism for conduction occurs when the atoms or moleculesin a hotter part of the material vibrate or move with greater energy thanthose in a cooler part.

By means of collisions, the more energetic molecules pass on some oftheir energy to their less energetic neighbors.

Materials that conduct heat well are called thermal conductors, and thosethat conduct heat poorly are called thermal insulators.

13.2 Conduction

The amount of heat Q that is conducted through the bar depends on a number of factors:

1. The time during which conduction takes place.2. The temperature difference between the ends of the bar.3. The cross sectional area of the bar.4. The length of the bar.

13.3 Radiation

RADIATION

Radiation is the process in whichenergy is transferred by means ofelectromagnetic waves.

A material that is a good absorber is also a good emitter.

A material that absorbs completelyis called a perfect blackbody.

13.4 Applications

A thermos bottle minimizes heattransfer via conduction, convection,and radiation.

The space between the inner glass walls minimizes heat transfer by conduction and convection.

The silvered surfaces reflect radiatedheat back to the inside.

13.4 Applications

GREENHOUSE EFFECT-Depletion of the ozone layer is harmful to Earth-Harmful effects of technology and urbanization-Most heat transfer is by radiation.

14.1 Molecular Mass, the Mole, and Avogadro’s Number

One mole of a substance contains as manyparticles as there are atoms in 12 grams ofthe isotope cabron-12.

The number of atoms per mole is known asAvogadro’s number, NA.

123 mol10022.6 AN

AN

Nn

number ofmoles

number ofatoms

14.2 The Ideal Gas Law

An ideal gas is an idealized model for real gases that have sufficiently low densities.

The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively ELASTIC.

TP

At constant volume, the pressure isdirectly proportional to the temperature.


At constant temperature, the pressure is inversely proportional to the volume.

VP 1

The pressure is also proportionalto the amount of gas.

nP


THE IDEAL GAS LAW

The absolute pressure of an ideal gas is directly proportional to the Kelvintemperature and the number of moles of the gas and is inversely proportionalto the volume of the gas.

V

nRTP

nRTPV

KmolJ31.8 R


Consider a sample of an ideal gas that is taken from an initial to a finalstate, with the amount of the gas remaining constant.

nRTPV

i

ii

f

ff

T

VP

T

VP

constant nRT

PV


i

ii

f

ff

T

VP

T

VP

Constant T, constant n:iiff VPVP Boyle’s law

Constant P, constant n:

i

i

f

f

T

V

T

V Charles’ law

Constant V, constant n:

i

i

f

f

T

P

T

P Gay Lussac’s law

14.3 Kinetic Theory of Gases

The particles are in constant, randommotion, colliding with each otherand with the walls of the container.

Each collision changes the particle’s speed.

As a result, the atoms and molecules have different speeds.

14.3 Kinetic Theory of Gases

Tkmv Brms 232

21KE

THE INTERNAL ENERGY OF A MONATOMIC IDEAL GAS

nRTTkNU B 23

23

15.1 Thermodynamic Systems and Their Surroundings

Thermodynamics is the branch of physics that is built upon the fundamental laws that heat and work obey.

The collection of objects on which attention is being focused is called the system, while everything elsein the environment is called the surroundings.

Walls that permit heat flow are called diathermal walls,while walls that do not permit heat flow are calledadiabatic walls.

To understand thermodynamics, it is necessary to describe the state of a system.

15.2 The Zeroth Law of Thermodynamics

Two systems are said to be in thermal equilibrium if there is no heat flowbetween then when they are brought into contact.

Temperature is the indicator of thermal equilibrium in the sense that there is nonet flow of heat between two systems in thermal contact that have the sametemperature.

15.2 The Zeroth Law of Thermodynamics

THE ZEROTH LAW OF THERMODYNAMICS

Two systems individually in thermal equilibriumwith a third system are in thermal equilibriumwith each other.

15.3 The First Law of Thermodynamics

Suppose that a system gains heat Q and that is the only effect occurring.

Consistent with the law of conservation of energy, the internal energyof the system changes:

QUUU if

Heat is positive when the system gains heat and negative when the systemloses heat.


Thermodynamics is a conservation law; i.e. heat added to a system is usedby the system to increase its internal energy or to do work in expanding.

An increase in internal energy due to heat added to the system (positive) orwork done on the system (positive).

WQU

Work done on a system, according to this convention, would result in adecrease in volume:

)( VPW


THE FIRST LAW OF THERMODYNAMICS

Process Definition Result

Isothermal

Adiabatic

Isochoric or Isovolumetric

00 UT WQ

0Q WU

00 WV QU


Example 1 Positive and Negative Work

In part a, the system gains 1500J of heatand 2200J of work is done BY the system on its surroundings.

In part b, the system also gains 1500J of heat, but2200J of work is done ON the system.

In each case, determine the change in internal energyof the system.

15.4 Thermal Processes

An isobaric process is one that occurs atconstant pressure.

)( VPAsPFsW

Isobaric process: if VVPVPW )(

At constant pressure, if volume decreases,ΔV is negative, and work done is positive.


Example 3 Isobaric Expansion of Water

One gram of water is placed in the cylinder and the pressure is maintained at 2.0x105Pa. Thetemperature of the water is raised by 31oC. Thewater is in the liquid phase and expands by thesmall amount of 1.0x10-8m3.

Find the work done and the change in internal energy.


J0020.0m100.1Pa100.2 385

VPW

J 130J 0020.0J 130 WQU

J 130C 31CkgJ4186kg 0010.0 TmcQ


if VVPVPW )(


isochoric: constant volume

QWQU

0W


Example 4 Work and the Area Under a Pressure-Volume Graph

Determine the work for the process in which the pressure, volume, and temp-erature of a gas are changed along thestraight line in the figure.

The area under a pressure-volume graph isthe work for any kind of process.


Since the volume increases, the workis negative.

Estimate that there are 8.9 colored squares in the drawing.

J 180

m100.1Pa100.29.8 345

W

15.5 Thermal Processes Using an Ideal Gas

ISOTHERMAL EXPANSION OR COMPRESSION

Isothermalexpansion orcompression ofan ideal gas

i

f

V

VnRTW ln


Example 5 Isothermal Expansion of an Ideal Gas

Two moles of the monatomic gas argon expand isothermally at 298Kfrom and initial volume of 0.025m3 to a final volume of 0.050m3. Assumingthat argon is an ideal gas, find (a) the work done by the gas, (b) the change in internal energy of the gas, and (c) the heat supplied to the gas. ??


(a)

J 3400m 250.0

m 050.0lnK 298KmolJ31.8mol 0.2

ln

3

3

i

f

V

VnRTW

023

23 if nRTnRTU(b)

WQU (c)

J 3400WQ


(a)

(b)

J 700J 2200J 1500

WQU

J 3700J 2200J 1500

WQU


Example 2 An Ideal Gas

The temperature of three moles of a monatomic ideal gas is reduced from 540K to 350K as 5500J of heat flows into the gas.

Find (a) the change in internal energy and (b) the work done by the gas. ???

nRTU 23WQUUU if


J 7100K 540K 350KmolJ 31.8mol 0.323

23

23

if nRTnRTU

J 12600J 7100J 5500 UQW

(a)

(b)


A quasi-static process is one that occurs slowly enough that a uniformtemperature and pressure exist throughout all regions of the system at alltimes.

isobaric: constant pressure

isochoric: constant volume

isothermal: constant temperature

adiabatic: no transfer of heat

15.7 The Second Law of Thermodynamics

THE SECOND LAW OF THERMODYNAMICS: THE HEAT FLOW STATEMENT

Heat flows spontaneously from a substance at a higher temperature to a substanceat a lower temperature and does not flow spontaneously in the reverse direction.

The second law is a statement about the natural tendency of heat to flow from hot to cold, whereas the first law deals with energy conservationand focuses on both heat and work.

15.8 Heat Engines

A heat engine is any device that uses heat to perform work. It has three essential features.

1. Heat is supplied to the engine at a relatively high temperature from a place called the hot reservoir.

2. Part of the input heat is used to perform work by the working substance of the engine.

3. The remainder of the input heat is rejected to a place called the cold reservoir.

heatinput of magnitude HQ

heat rejected of magnitude CQ

done work theof magnitude W

15.8 Heat Engines

The efficiency of a heat engine is defined asthe ratio of the work done to the input heat:

HQ

We

If there are no other losses, then

CH QWQ

H

C

Q

Qe 1

15.8 Heat Engines

Example 6 An Automobile Engine

An automobile engine has an efficiency of 22.0% and produces 2510 J of work. How much heat is rejected by the engine?

HQ

We

CH QWQ

e

WQH

15.8 Heat Engines

CH QWQ

e

WQH

J 89001220.0

1J 2510

11

e

WWe

WQC

WQQ HC

15.9 Carnot’s Principle and the Carnot Engine

A reversible process is one in which both the system and the environment can be returned to exactly the states they were in before the process occurred.

CARNOT’S PRINCIPLE: AN ALTERNATIVE STATEMENT OF THE SECONDLAW OF THERMODYNAMICS

No irreversible engine operating between two reservoirs at constant temperaturescan have a greater efficiency than a reversible engine operating between the sametemperatures. Furthermore, all reversible engines operating between the sametemperatures have the same efficiency.

15.9 Carnot’s Principle and the Carnot Engine

The Carnot engine is useful as an idealizedmodel.

All of the heat input originates from a singletemperature, and all the rejected heat goesinto a cold reservoir at a single temperature.

Since the efficiency can only depend onthe reservoir temperatures, the ratio of heats can only depend on those temperatures.

H

C

H

C

T

T

Q

Qe 11

H

C

H

C

T

T

Q

Q

15.11 Entropy

Any irreversible process increases the entropy of the universe. 0universe S

THE SECOND LAW OF THERMODYNAMICS STATEDIN TERMS OF ENTROPY

The total entropy of the universe does not change when a reversible process occurs and increases when an irreversibleprocess occurs.

15.11 Entropy

Example 12 Energy Unavailable for Doing Work

Suppose that 1200 J of heat is used as input for an engine under two different conditions (as shown on the right).

Determine the maximum amount of work that can be obtainedfor each case.

H

C

T

Te 1carnot

HQ

We

15.11 Entropy

The maximum amount of work will be achieved when theengine is a Carnot Engine, where

(a) 77.0K 650

K 15011carnot

H

C

T

Te

J 920J 120077.0carnot HQeW

(b) 57.0K 350

K 15011carnot

H

C

T

Te

J 680J 120057.0carnot HQeW

The irreversible process of heat through the copperrod causes some energy to become unavailable.

15.12 The Third Law of Thermodynamics

THE THIRD LAW OF THERMODYNAMICS

It is not possible to lower the temperature of any system to absolute zero in a finite number of steps.

physics 1401 semester exam review. 1.1 measurements vernier caliper micrometer photogate (millisec)

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