ap physics b - thermodynamics (1)

8/6/2019 AP Physics B - Thermodynamics (1)

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Thermodynamics

AP Physics B


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Work done by a gas

Suppose you had a piston filled with aspecific amount of gas. As you addheat, the temperature rises andthus the volume of the gasexpands. The gas then applies aforce on the piston wall pushing it a

specific displacement. Thus it canbe said that a gas can do WORK.


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Work is the AREA of a P vs. V graph

positiveW

negativeW

V

V

VPW

on

by

!

!

!!(

!!(

(!

gastheONdoneisWork

gastheBYdoneisWork

The negative sign in the

equation for WORK is often

misunderstood. Since work done

BY a gas has a positive volume

change we must understand that

the gas itself is USING UP

ENERGY or in other words, it islosing energy, thus the negative

sign.

When work is done ON a gas the change in volume is negative. This cancels out

the negative sign in the equation. This makes sense as some EXTERNAL agent is

ADDING energy to the gas.


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Internal Energy ((U) and Heat Energy (Q)

All of the energy inside asystem is called INTERNALENERGY, (U.

When you add HEAT(Q), youare adding energy and theinternal energyINCREASES.

Both are measured in joules.

But when you add heat,there is usually an increasein temperature associatedwith the change.

0,0,

!(!(

o(o(

((

UTif

UTif

TUE


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First Law of Thermodynamics

The internal energy of a system tend to increase

when HEAT is added and work is done ON the

system.

byAdd

onAdd

WQUor

WQUWQU

!(

!(p!(

Suggests a CHANGE or subtraction

You are really adding a negative

here!The bottom line is that if you ADD heat then transfer work TO the gas,

the internal energy must obviously goup as you have MORE than

what you started with.


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Example continued

a) The gas is then

compressed at a constant

pressure of 2.0 atm from a

volume of 3.0 L to 1.0 L.

b) The gas is then heated

until its pressureincreases from 2.0 atm to

3.0 atm at a constant

volume.

!!(! )003.001(.102 5xVPWON -400 J

0since

0

!(

!(!

V

VPW


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Example continued

What is the NETWORK?

NET work is

the area inside

the shape.

600 J + -400 J = 200 J

Rule of thumb: If the systemrotates CW, the NET work is

positive.

If the system rotates CCW,

the NET work is negative.


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ExampleA series of thermodynamic processes is shown in the pV-diagram.

Inprocess ab 150 J of heat is added to the system, and inprocess bd , 600J of heat is added. Fill in the chart.

150

600

750

0

240

240

150 J

840 J

990 J

900

90 990 J900


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Thermodynamic Processes - IsothermalTo keep the temperature

constant both thepressure and volumechange to compensate.(Volume goes up,pressure goes down)

BOYLES LAW


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Thermodynamic Processes - IsobaricHeat is added to the gas

which increases theInternal Energy (U)Work is done by the gasas it changes in volume.

The path of an isobaricprocess is a horizontalline called an isobar.

U = Q - W can be used

since the WORK isPOSITIVE in this case


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Thermodynamic Processes - Adiabatic

ADIABATIC- (GREEK-adiabatos-

"impassable")

Inother words, NO

HEAT can leave orenter the system.


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In Summary


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Second Law of Thermodynamics

Heat will not flow spontaneously from a colder body toa warmer body AND heat energy cannot be

transformed completely into mechanical work.

The bottom line:1) Heat always flows from a hot body to a cold body

2) Nothing is 100% efficient


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EnginesHeat flows from a HOT

reservoir to a COLD

reservoir

CHoutput

CH

QQW

QWQ

!

!

QH = remove from, absorbs = hotQC= exhausts to, expels = cold


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Engine EfficiencyInorder to determine the

thermal efficiencyofan engine you have to

look at how much

ENERGY you get OUT

based on how muchyou energy you take IN.

Inother words:

H

C

H

CH

hotthermal Q

Q

Q

QQ

Q

W

e !

!! 1


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Rates of Energy UsageSo

metimes it isusef

ul to

express theenergy usage of an engine as a

RATE.

For example:

The RATE at which heat is absorbed!

The RATE at which heat is expelled.

The RATE at which WORK is DONE

P WERt

W

t

Q

t

Q

C

H

!


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Efficiency in terms of rates

t

Q

t

Q

P

e

P

t

Q

tQ

P

tQ

tW

Q

We

CH

H

HHH

thermal

!

!

pp!


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Is there an IDEAL engine model?Our goal is to figure out just how efficient

such a heat engine can be: whats the mostwork we canpossibly get for a given amount

of fuel?

The efficiency question was first posedand solvedby Sadi Carnot in 1820,

not long after steam engines had become efficient enough to begin replacingwater wheels, at that time the mainpower sources for industry. Not surprisingly,

perhaps, Carnot visualized the heat engine as a kind of water wheel in which

heat (the fluid) dropped from a high temperature to a low temperature,

losing potential energy which the engine turned into work done, just like a

water wheel.


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Carnot EfficiencyCarnot a believed that there was an

absolute zeroof temperature, fromwhich he figured out that on beingcooled to absolute zero, the fluid wouldgive upallits heat energy. Therefore, ifit falls only half way to absolute zerofrom its beginning temperature, it willgive up half its heat, and an engine

taking in heat at Tand shedding it at Twill be utilizing half the possible heat,and be 50% efficient. Picture a waterwheel that takes in water at the topof awaterfall, but lets it out halfwaydown. So, the efficiency of an idealengine operating between two

temperatures will be equal to thefractionof the temperature drop towardsabsolute zero that the heat undergoes.


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Carnot EfficiencyCarnot temperatures must be

expressed in KELVIN!!!!!!

The Carnot model has 4parts

An Isothermal Expansion

AnAdiabatic ExpansionAn Isothermal Compression

AnAdiabatic Compression

The PV diagram in a way shows us that the ratioof the heats are symbolic to

the ratioof the 2 temperatures


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ExampleThe efficiency of a Carnot engine is 30%. The engine absorbs 800

J of heat per cycle from a hot temperature reservoir at 500 K.Determine (a) the heat expelled per cycle and (b) the

temperature of the cold reservoir

!

!p!

!

!p!

!!p!

C

C

H

CC

C

CCH

H

T

T

T

Te

Q

QWQQW

WJ

W

Q

W

e

500130.01

800

80030.0240 J

560 J

350 K

ap physics b - thermodynamics (1)

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