ap physics b - thermodynamics

8/2/2019 AP Physics B - Thermodynamics

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Thermodynamics

AP Physics B


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Work done by a gasSuppose you had a piston filled with a

specific 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 aspecific 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 theequation for WORK is oftenmisunderstood. Since work doneBY a gas has a positive volumechange we must understand thatthe gas itself is USING UPENERGY or in other words, it islosing energy, thus the negativesign.

When work is done ON a gas the change in volume is negative. This cancels outthe negative sign in the equation. This makes sense as some EXTERNAL agent isADDING 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), you

are 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,

UTifUTif

TU


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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 thesystem.

byAdd

onAdd

WQUor

WQUWQU

Suggests a CHANGE or subtraction

You are really adding a negativehere!

The bottom line is that if you ADD heat then transfer work TO the gas,the internal energy must obviously go up as you have MORE thanwhat you started with.


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ExampleSketch a PV diagram and find

the work done by the gasduring the following stages.

(a) A gas is expanded from avolume of 1.0 L to 3.0 L at a

constant pressure of 3.0atm.

(b) The gas is then cooled at a

constant volume until thepressure falls to 2.0 atm

)001.0003.0(103 5xVPWBY

600 J

0since

0

V

VPW


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Example continued

a) The gas is thencompressed at a constantpressure of 2.0 atm from avolume of 3.0 L to 1.0 L.

b) The gas is then heated

until its pressureincreases from 2.0 atm to3.0 atm at a constantvolume.

)003.001(.102 5xVPWON -400 J

0since

0

V

VPW


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Example continued

What is the NETWORK?NET work isthe area insidethe shape.

600 J + -400 J = 200 J

Rule of thumb: If the systemrotates CW, the NET work ispositive.

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.

In process 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 usedsince the WORK isPOSITIVE in this case


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Thermodynamic Processes - Isovolumetric


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Thermodynamic Processes - Adiabatic

ADIABATIC- (GREEK-

adiabatos-"impassable")

In other words, NOHEAT 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 to

a 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 body2) Nothing is 100% efficient


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EnginesHeat flows from a HOTreservoir to a COLDreservoir

CHoutput

CH

QQW

QWQ

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


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Engine EfficiencyIn order to determine the

thermal efficiencyofan engine you have tolook at how muchENERGY you get OUT

based on how muchyou energy you take IN.In other words:

H

C

H

CH

hotthermal Q

Q

Q

QQ

Q

W

e

1


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Rates of Energy UsageSometimes it is useful to express the

energy usage of an engine as aRATE.

For example:

The RATE at which heat is absorbed!

The RATE at which heat is expelled.

The RATE at which WORK is DONE

POWERt

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


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Carnot EfficiencyCarnot a believed that there was an

absolute zero of temperature, fromwhich he figured out that on beingcooled to absolute zero, the fluid wouldgive up allits 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 top of awaterfall, but lets it out halfwaydown. So, the efficiency of an idealengine operating between two

temperatures will be equal to thefraction of 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 4 partsAn Isothermal Expansion

An Adiabatic ExpansionAn Isothermal CompressionAn Adiabatic Compression

The PV diagram in a way shows us that the ratio of the heats are symbolic tothe ratio of the 2 temperatures


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ExampleA particular engine has a power output of 5000 W and an

efficiency of 25%. If the engine expels 8000 J of heat in each

cycle, find (a) the heat absorbed in each cycle and (b) the timefor each cycle

tt

W

t

WP

W

QWQQW

QJQ

Qe

Q

QeWP

HCH

Hc

H

H

C

5000

8000

8000

8000

125.025.0

15000

10,667 J

2667 J

0.53 s


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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) thetemperature of the cold reservoir

C

C

H

CC

C

CCH

H

T

TTTe

Q

QWQQW

WJ

W

Q

W

e

500130.01

800

80030.0240 J

560 J

350 K

ap physics b - thermodynamics

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