Physics 7A -- Lecture 2 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg...

Physics 7A -- Lecture 2

Winter 2008

Physics 7A -- Lecture 2

Winter 2008

Prof. Robin D. Erbacher343 Phy/Geo Bldg

[email protected]

Prof. Robin D. Erbacher343 Phy/Geo Bldg

[email protected]

Physics 7A -A/BPhysics 7A -A/BPhysics 7A -A/BPhysics 7A -A/BThis course has two instructors:

Prof. Robin Erbacher (me) rderbacher @ucdavis Ruggero Tacchi (Lead DL Instructor) rtacchi @ucdavis

You are enrolled in one of two 7A classes. 7A-C/D has lectures on Tuesdays. We are independent courses but cover the same material, so you

can attend any review session. We have a common final exam.

The final exam is Tuesday March 18th, 10:30-12:30 If you know you cannot make the final, you should take 7A in

a different quarter. There are no make-up exams.

AnnouncementsAnnouncementsAnnouncementsAnnouncements

• Join this Class Session with your PRS clicker! (Practice run today, credit begins next time.)

• Quiz today! Lecture 1, DLMs 1&2. Must take it incorrect lecture time slot.

• Check Physics 7 website frequently for calendar &announcements. DL Instructors have PTA numbersfor adding this class. No Lecture next week!

• Turn off cell phones and pagers during lecture.

Models in Physics 7AModels in Physics 7AModels in Physics 7AModels in Physics 7A

• Three-phase model of matter

• Energy-interaction model

• Mass-spring oscillator

• Particle model of matter Particle model of bond energy Particle model of thermal energy

• Thermodynamics

• Ideal gas model

• Statistical model of thermodynamics

We started withthese two…

We introduce this one next(chapter 2)

Review: 3-Phase Model

Review: 3-Phase Model

Three Phase Model of MatterThree Phase Model of MatterThree Phase Model of MatterThree Phase Model of Matter

The basic idea


• Solid: Keeps its shape without a container.• Liquid: Takes the shape of the (bottom of) the container. Keeps its volume the same.• Gas: Takes the shape and volume of the container.

Example H2O

Graph of Ice to SteamGraph of Ice to SteamGraph of Ice to SteamGraph of Ice to Steam

• Tbp: Temperature at which a pure substance changes phase from liquid to gas (boiling point).• Tmp: Temperature at which a pure substance changes phase from solid to liquid (melting point).

Tbp

Tmp

Phase Changes - a recapPhase Changes - a recapPhase Changes - a recapPhase Changes - a recap

You take ice out of the freezer at -300C and place it in a sealed container and slowly heat it on the stove. You would find:

• the temperature of the ice rises,

• remains fixed at 00C for an extended time while it is a mixture of ice and water,

• the temperature rises again after it all melted,

• remains fixed at 1000C for an extended time while it is a mixture of liquid and gas,

• the temperature rises again after it is all gas (steam).


Q How do we change the phase of matter?

How do we change the temperature of matter?

A By adding or removing energy. Often this energy is transferred from, or to, the substance as heat, “Q”.

Example H2O

Heat CapacityHeat CapacityHeat CapacityHeat CapacityThe heat capacity, C, of a particular substance is defined as the amount of energy needed to raise the temperature of that sample by 1° C.

If energy (heat, Q) produces a change of temperature, T, then:

Heat capacity depends on the amount of a substance we have, since it will take more energy to change the temperature of a larger quantity of something.

It is thus called an extensive quantity, or dependent upon the quantity/mass of a substance (kg or mole).

Q = C TQ = C T

Heat capacity C – sort of the slope here of A, C, E

Heat of fusion Heat of vaporization

Q

€

C = Q

ΔT

Specific HeatSpecific HeatSpecific HeatSpecific HeatThe specific heat capacity, often simply called specific heat, is a particular number for a given substance and does not depend on quantity.

Specific heat is thus an intensive property.

The specific heat of water

is one calorie per gram

per degree Celsius.

The specific heat of water

is one calorie per gram

per degree Celsius.

SI units for heat capacity and specific heat:• heat capacity J/K• specific heat J/kg•K, or J/mol•K (molar specific heat)

Clicker QuestionClicker QuestionClicker QuestionClicker Question

You heat 1 L of water and raise its temperature by 100 C. (Water~1g/ml)

Question: If you add the same quantity of heat to 2 L of water, how much will the temperature rise?

a) Not enough information is given.

b) Twice as much.

c) Half as much.


You heat 1 L of water and raise its temperature by 100 C. (Water~1g/ml)

Question: If you add the same quantity of heat to 5 L of water, how much will the temperature rise?

• Not enough information is given.

• 20 C.

• 500 C.

An Aside on “calories”An Aside on “calories”An Aside on “calories”An Aside on “calories”

The scientific "calorie" is spelled with a lower-case "c".

One "calorie" = 4.184 Joules

The "dieter's" calorie is spelled with an upper-case "C".

One "Calorie" = 1000 calories

Definitions ReviewDefinitions ReviewDefinitions ReviewDefinitions ReviewHeat capacity - Extensive-How much energy it takes to change the temperature of this amount of pure substance (see parts A, C and E in graph).

Specific heat capacity (or specific heat) - Intrinsic-How much energy it takes to change the temperature per unit of pure substance (mass/mole) (parts A, C and E).

Heat of fusion - Intrinsic-How much energy it takes to melt all of the ice to water (see part B of graph).

Heat of vaporization - Intrinsic- How much energy it takes to boil all the water to steam (see part D of graph).

Energy Change Energy Change EEEnergy Change Energy Change EE

In our notation, we always have E = Efinal - Einitial .

E negative: Energy is released from the system. (“Neg. energy added.”)

E positive: Energy is put into the system. Be sure to select the correct sign for all energy transfers!

=> Note also: T is always Tf - Ti .


You put a red hot iron 1.0 kg mass into 1.0 L of cool water.

1) The increase in the water temperature is equal to the decrease in the iron’s temperature. True or False?


You put a red hot iron 1.0 kg mass into 1.0 L of cool water.

1) The increase in the water temperature is equal to the decrease in the iron’s temperature. True or False?

2) The iron and the water will both reach the same temperature.

True or False?

Energy Interaction Model

Energy Interaction Model

EquilibriumEquilibriumEquilibriumEquilibrium

The Zeroth law of thermodynamics says:

Since they are in thermal equilibrium with each other, there is no net energy exchanged among them.

If objects A and B are separately in thermal

equilibrium with a third object C, then A and B

are in thermal equilibrium with each other

If objects A and B are separately in thermal

equilibrium with a third object C, then A and B

are in thermal equilibrium with each other

EquilibriumEquilibriumEquilibriumEquilibriumThe Zeroth law of thermodynamics example:

• Let the third object C be the thermometer.• If the two readings are the same, then A and B are also in thermal equilibrium.

• Energy (heat) will not flow between A and B if put together.

More on HeatMore on HeatMore on HeatMore on Heat

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Starting definition of heat (to be revised much later):

Heat (Q) is the transfer of energy from a hot object to a cold object because the objects are at different temps.

If the two objects are at the same temperature, no heat flows between them.

Energy leaves hot objects in the form of heat.Energy enters cold objects in the form of heat.

Low temp High tempQ

Conservation of EnergyConservation of EnergyConservation of EnergyConservation of Energy• Energy is both a thing (quantity) and a process. You & I contain energy, as do the chairs you sit on and the air we breathe. • We cannot see it, but we can measure the transformation of energy (or change, E).

Conservation of EnergyEnergy cannot be created nor destroyed, simply

converted from one form to another.

Conservation of EnergyEnergy cannot be created nor destroyed, simply

converted from one form to another.

• If the energy of an object increases, something else must have given that object its energy.

• If it decreases, it has given its energy to something else.

• A transfer of energy is when one object gives energy to another.There are 2 types of energy transfers -- Heat and Work.

Energy SystemsEnergy SystemsEnergy SystemsEnergy Systems

Etherma

l

EbondEmovement

(KE)

Egravit

y

Eelectri

c

Esprin

g

There are many different types of energies called energy systems:

........

For each energy system, there is an indicator that tells us how that energy system can change:

Ethermal: indicator is temperatureEbond: indicator is the initial and final phases

Energy System ExpressionsEnergy System ExpressionsEnergy System ExpressionsEnergy System Expressions

•Ethermal = C T, Temperature is the indicator.

• Between phase changes, only thermalenergy changes.

• Ebond = |m H|, m is the indicator.

• At a physical phase change, only the bond-energy system changes. H is the heat of the particular phase change. m is the amount that changed phase.

• In a chemical reaction, there are several bond energy changes corresponding to diff. molecular species (reactants or products). Here H is the heat of formation for a particular species.

Etherma

l

Ebond

Energy Interaction Diagrams - Energy Interaction Diagrams - Closed SystemClosed System

Energy Interaction Diagrams - Energy Interaction Diagrams - Closed SystemClosed System

Ea Eb Ec

Conservation of EnergyThe total energy of a closed physical system must remain constant. So, the change of the energies of all energy systems associated with the physical system must sum to zero.

Change in closed system energy = ∆Ea + ∆ Eb + ∆ Ec = 0

Energy Interaction Diagrams - Energy Interaction Diagrams - Open SystemOpen System

Energy Interaction Diagrams - Energy Interaction Diagrams - Open SystemOpen System

Ea Eb Ec

Conservation of EnergyThe change of the energies of all systems associated with an open physical system must sum to the net energy added or removed. Energy is added or removed as Heat or Work.

Change in open system energy = ∆Ea + ∆ Eb + ∆ Ec

= (Energy added) - (Energy removed) = Q + W.

Energy added Energy removed

Example for Open SystemExample for Open SystemExample for Open SystemExample for Open System

Ea

Energy added = + 100 J

Suppose we have a system where 100J of heat comes in from the outside. Joe claims that the only energy system that changes is Ea and that Ea is negative (Ea decreases).

Can Joe be correct?1) Yes, its possible that he is correct.2) Yes, Joe is definitely correct.3) No way is Joe’s description correct.

Clicker!

Energy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsExample: Melting IceTi= 0°C Tf = room temperature

Tem

pera

ture

Energy of substance

solid

liquid

gas

l-g coexist

s-l coexist

Initial

TMP

TBP

Final

Energy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsExample: Melting Ice

Process 1: Ice at T=0ºC Water at T=0ºCProcess 2: Water at T=0ºC Water at room temperature

Tem

pera

ture

Energy of substance

solid

liquid

gas

l-g coexist

s-l coexist

Process 1Initial

TMP

TBP

Process 1Final /

Process 2Initial

Process 2Final


Process 1: Ice at T=0ºC Water at T=0ºC

Ice

∆T=0

∆Eth=0

Initial phase Solid, Final phase Liquid

Etherm

al

Ebond



Ice

∆T=0

∆Eth=0


Etherm

al

EbondHeat



Ice

∆T=0

∆Eth=0


∆Eth + ∆Ebond= Q+W

∆Ebond= Q

Etherm

al

EbondHeat


Process 2: Water at T=0ºC Water at room temperature

Ice

Initial phase Liquid, Final phase Liquid

Etherm

al

Ebond


Process 2: Water at T=0ºC Water at room temperature

Ice

Initial phase Liquid, Final phase Liquid

∆Ebond= 0

Etherm

al

Ebond

T

Heat

∆Eth + ∆Ebond= Q+W

∆Eth= Q


Ice

Initial phase Liquid, Final phase Solid

Etherm

al

Ebond

Freezing (Water at T=0°C Ice at T=0°C)

∆T=0

∆Eth=0

Heat

NOTE: Heat is released when bonds are formed! (In general E is negative)

EIM Algebra ReviewEIM Algebra ReviewEIM Algebra ReviewEIM Algebra Review• For a closed system:

(Is it clear why there’s no Q or W for a closed system?)

• For an open system:

(Q and W can be positive or negative, as can Es.)

€

E total = ΔE1 + ΔE 2 + ΔE 3 + ... = 0

€

E total = ΔE1 + ΔE 2 + ΔE 3 + ... = Q + W

Two New Energy Systems

Two New Energy Systems

Kinetic Energy System (KE)Kinetic Energy System (KE)Kinetic Energy System (KE)Kinetic Energy System (KE)

• Kinetic energy is simply Emoving.

• For translational energy, the indicator is speed; the faster an object moves, the more KE it has.

• There is a quantitative relationship between KE and speed:

• We discuss rotational KE later this quarter and in Physics 7B.

KEtrans = ½ m v2KEtrans = ½ m v2

Potential Energy System (PE)Potential Energy System (PE)Potential Energy System (PE)Potential Energy System (PE)

• Potential energy due to gravity: Eheight. (There are other

types of PE, such as PE in a spring, or chemical PE.)

• For gravitational PE, the indicator is height; a higher object (with respect to something else) has more PEgravity. Can we show this?

• The quantitative relationship between PE and height:

(g~10 m/s2 is the acceleration due to gravity on Earth.)

PEgravity = mghPEgravity = mgh

Conservation of EnergyConservation of EnergyConservation of EnergyConservation of Energy

PEgravity = KEtranslational

mgh = ½ m v2

Consider a simple pendulum:• At the height (peak) of the amplitude, the object is at rest. Egravity = mgh (define h above the low point)

• At the bottom of the motion, the object is moving quickly, and h=0. Etrans = ½ m v2

Conservation of Energy dictates that:

All of the PE goes into KE, and then back again!

Potential Energy: SpringsPotential Energy: SpringsPotential Energy: SpringsPotential Energy: Springs

• Springs contain energy when you stretch or compress them. We will use them a lot in Physics 7.

• The indicator is how much the spring is stretched or compressed, x, from its equilibrium (rest) state.

• k is a property of the spring, with units [k] = kg/s2.

• Much easier to stretch a spring a little bit than a lot!

PEspring = ½ kx2PEspring = ½ kx2

Next Time: More on Energy

Systems

Next Time: More on Energy

Systems

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Physics 7A -- Lecture 2 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg...

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