Final Exam Phys 220 - Purdue University

Lecture 15 – 1/30 Phys 220 Final Exam

Wednesday, August 6th 10:30 am – 12:30 pm

Phys 114

20 multiple choice problems (15 points each – 300 total)

75% will be from Chapters 10-16

25% from Chapters 1-9

Equation Sheet will be provided Practice Exam and Equation Sheet on course website

Students needing accommodations must contact me

by July 30th

Lecture 15 – 2/30 Phys 220

Physics Topics • Kinematics

• Forces, Torque, and Work

• Conservation of Energy

• Conservation of Momentum (Linear & Angular)

• Density and Pressure

• Harmonic Motion

• Traveling Waves

• Standing Waves – M10

• Heat and Temperature

• Ideal Gas Law

Lecture 15 – 3/30 Phys 220 Concepts – Chapter 12-13

• Intensity

▪ Watts/m2

• Sound Intensity Level

▪ Measured in decibels

• Waves on a String

▪ Mass Density (μ)

24 r

P

A

PI

Area

PowerIntensity

M

LFFv TT

L

M

0

10log)dB 10(I

I

Wave expands in all directions Area is typically surface area of sphere

Lecture 15 – 4/30 Phys 220 Standing Waves

• String fixed at both ends Pipe open (or closed) at both ends

▪ n = 1, 2, 3, 4, 5, …

•Pipe open at one end

▪ n = 1, 3, 5, 7, 9, …

• Speed of Sound (Section 13.1)

n = 1

n = 2

n = 3

n = 4

n

Ln

2

L

vnfn

2

n

Ln

4

L

vnf sound

n4

n = 1

n = 3

n = 5 m/s )20(6.0343 CTvsound

fundamental freq means n=1


• Beat Frequency

Frequency

21 fffbeat Period (T) 2

2

1

1

21

vv

ff

sound

source

sound

obs

sourceobs

v

v

v

v

ff

1

1

moving towards (f increases) + on top, – on bottom (1 + vobs/vsound ) on top

(1 – vsource/vsound) on bottom

moving away (f decreases) – on top, + on bottom (1 – vobs/vsound ) on top

(1 + vsource/vsound) on bottom

• Frequency for a wave stays constant

• Doppler Effect


A) Blue

B) Red

C) Neither

Which of the above arrows are pointing to antinodes for this standing wave?

A standing wave is shown on the left.

Question 1


A) It decreases by a factor of 2, which means v’=v0/2

B) It stays the same, which means v’=v0

C) It increases by a factor of 2 , which means v’=2*v0

D) It increases by a factor of 1.4 , which means v’=1.4*v0

What happens to the velocity of the wave on the string?

The tension on a string is increased by a factor of 2. (T’ = 2*T)

The string doesn’t change and thus has the same mass and length. M

LFv T

Question 2


Physics Topics

• Kinematics

• Forces, Torque, and Work

• Conservation of Energy

• Conservation of Momentum (Linear & Angular)

• Density and Pressure

• Harmonic Motion

• Traveling Waves

• Standing Waves

• Heat and Temperature


Temperature

• Not easy to give a simple definition for temperature

• Feel ▪ Hot

▪ Cold

• Measure ▪ Thermometer

▪ Temperature is related to energy of the system


Zeroth Law of Thermodynamics

• If two (or more) objects are in thermal equilibrium, they are at the same temperature.

• If two objects are in thermal equilibrium with a third, then the two are in equilibrium with each other.

▪ If TA = TC and TB = TC

▪ Then TA = TB

Lecture 15 – 11/30 Phys 220 Temperature Scales

• Three different scales are used

Lord Kelvin (1824 - 1907)

Anders Celsius (1701 - 1744)

Daniel G. Fahrenheit (1686 - 1736)

Lecture 15 – 12/30 Phys 220 Temperature Scales

• Note: 0 Kelvin (0 K) is “absolute zero”, meaning (almost) zero Kinetic Energy per molecule

325

9 CF TT

329

5 FC TT

15.273 KC TT

15.273 CK TT


Question 7

Two cups of coffee are heated to 100 degrees Fahrenheit. Cup 1 is then heated an additional 20 degrees Centigrade, cup 2 is heated an additional 20 Kelvin. Which cup of coffee is hotter?

A) One B) Two C) Same

K = C + 273

Lecture 15 – 14/30 Phys 220 Heat

• Definition: Flow of energy between two objects due to difference in temperature ▪ Note: similar to WORK

▪ Object does not “have” heat (it has heat energy)

• Heat flows from a system at higher temperature to one at lower temperature ▪ Hot to Cold

• Conservation of Energy ▪ Heat energy that “leaves” system 1

must equal heat energy that “enters” system 2


Heat

• Units:

▪ Joule (J)

▪ Calorie (Cal) – (Calorie is different unit than calorie)

» 1 calorie is the amount of heat needed to raise 1 g of water by 1 °C

• 1 Calorie = 1 kcal = 1000 cal = 4186 J = 4.186 kJ

• 1 cal = 4.186 J

• Sign convention:

▪ Heat added to the system: Q > 0 (positive heat)

▪ Heat removed from the system: Q < 0 (negative heat)


Heat and Mechanical Energy

• James Joule measured the “mechanical equivalent” of heat energy ▪ Used apparatus is similar

to the one shown

• As the mass fell, its potential energy rotated the paddle, raising the temperature of the liquid

• Joule could then relate the mechanical energy to the heat energy

Lecture 15 – 17/30 Phys 220 Heat Capacity and Specific Heat

• Heat Capacity = Q / T ▪ Shows how much heat is required to

change the T of object (system) ▪ Ratio of heat energy to change in T

• Specific Heat (c)

▪ Heat required to increase temperature depends on amount of material (m) and type of material

• Heat adds energy to object/system • IF there is no dissipation then:

▪ Heat increases internal energy: Q = ∆U ▪ Heat increases temperature: Q = m c ∆T

TcmQ

Tm

Qc


Exercise

After a grueling work out, you drink a liter of cold water (0 C). How many Calories does it take for your body to raise the water up to body temperature of 36 C?

A) 36 B) 360 C) 3,600 D) 36,000

1 liter = 1,000 grams of H20

1000 g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories

36,000 calories = 36 Calories!


Question

Suppose you have equal masses of aluminum and copper at the same initial temperature. You add 1000 J of heat to each of them. Which one ends up at the higher final temperature

A) aluminum

B) copper

C) the same

Substance c in J/(kg-C) aluminum 900 copper 387 iron 452 lead 128 human body 3500 water 4186 ice 2000 TcmQ

Lecture 15 – 20/30 Phys 220 Question

Two insulated buckets contain the same amount of water at room temperature. Two blocks of metal of the same mass, both at the same temperature, are warmer than the water in the buckets. One block is made of aluminum (c=0.9) and one is made of copper. You put the aluminum block into one bucket of water, and the copper (c=0.385) block into the other. After waiting a while you measure the temperature of the water in both buckets. Which is warmer?

A) The water in the bucket containing the aluminum block

B) The water in the bucket containing the copper block

C) The water in both buckets will be at the same temperature

Since aluminum has a higher specific heat than copper, you are adding more heat to the water when you dump the aluminum in the bucket (Q=mc∆T).

Lecture 15 – 21/30 Phys 220 Phase Transitions

• A phase transition occurs whenever a material is changed from one phase, such as the solid phase, to another phase, such as the liquid phase. ▪ Phase transitions occur at constant temperature.

▪ The latent heat of vaporization LV is the heat per unit mass that must flow to change the phase from liquid to gas or from gas to liquid.

• Fusion occurs when a liquid turns into a solid.

• Evaporation occurs when a liquid turns into a gas.

• Sublimation occurs when a solid changes directly to a gas without going into a liquid form.

Lecture 15 – 22/30 Phys 220 Latent Heat

• As you add heat to water, the temperature increases for a while, then it remains constant, despite the additional heat!

• Latent Heat (L) [J/kg] ▪ heat which must be added (or removed) for material to

change phase (liquid-gas).

T

Q added to water

water temp rises

water changes to steam (boils)

steam temp rises

100oC

Latent Heat

Substance Lf (J/kg) Lv (J/kg)

water 33.5 x 104 22.6 x 105

f=fusion v=vaporization

LmQ

Lecture 15 – 23/30 Phys 220 Phase Diagram

• Water

Lecture 15 – 24/30 Phys 220 Phase Diagram

• C02

Lecture 15 – 25/30 Phys 220 Boiling Point

Going from Lafayette to Denver the temperature at which water boils:

A) Increases B) Decreases C) Same

Lecture 15 – 26/30 Phys 220 Heating Ice

• What terms do you need to consider to calculate how much heat is required to take ice at –10 °C to steam at a final temperature of 120 °C ?

120 to100 steam,steam water to100 to0 water, water toice0 to20- ice,total QQQQQQ 120 to100 steam,steam water to100 to0 water, water toice0 to20- ice,total QQQQQQ

TcmLmTcmLmTcmQ steamvwaterfice total


Exercise

How much ice (at 0 °C) do you need to add to 0.5 kg of a water at 25 °C, to cool it down to 10 °C?

(L = 80 cal/g, c = 1 cal/g C)

calories 7500

)C 15)(Ccal/g 1)(kg 5.0(

TcmQ waterwaterwater

TcL

Qm

TcmLmQ

waterf

iceice

watericeficeice

grams 3.83

)C 10)(Ccal/g 1(Ccal/g 80

calories 7500

Lecture 15 – 28/30 Phys 220 Exercise

Ice cube trays are filled with 0.5 kg of water at 20 C and placed into the freezer. How much energy must be removed from the water to turn it into ice cubes at -5 C?

(L = 80 cal/g, cwater = 1 cal/g C, cice = 0.5 cal/g C)

Water going from 20 C to 0 C:

Water turning into ice at 0 C:

Ice going from 0 C to -5 C:

cal 000,10)C 20)(Ccal/g 1)(g 500(11 TcmQ waterwater

cal 000,40cal/g) 80)(g 500(2 fwater LmQ

cal 250,1)C 5)(Ccal/g 5.0)(g 500(23 TcmQ icewater

Total Heat Energy:

cal 250,51321 QQQQtotal

Lecture 15 – 29/30 Phys 220 Question

Which can absorb more energy from your soda, a “cooler” filled with water at 0 °C, or a cooler filled with ice at 0 °C ?

A) Water B) About Same C) Ice

T

Q added to water

ice temp rises

ice changes to water (melts)

water temp rises

0oC Latent Heat

Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas).

Lecture 15 – 30/30 Phys 220 Heat

• Heat energy transfers from the hot object to the cold object ▪ Energy is conserved

▪ Objects reach equilibrium

• Heat and Temperature ▪ Specific Heat

▪ No phase change

• Heat and Phase Transitions ▪ Heat of Fusion

» Melting

» Freezing

▪ Heat of Vaporization » Evaporation

» Condensation

TcmQ

fLmQ

vLmQ

Documents

Final Exam Phys 220 - Purdue University