1. temperature&thermal expansion

8/6/2019 1. Temperature&Thermal Expansion

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Course Outline

This file is for exclusive use in my class Phy

WEEK

TOPIC HOUR

1st Course Orientation & Temperature & Thermal Expansion of Solids& Liquids

3

2nd Heat & Internal Energy, Specific Heat & Calorimetry , Latent Heat 33rd 1st Law of Thermodynamics, & Energy Transfer Mechanisms

(Long Test 1)3

4th Static Electricity (Coulombs law) 35th Electric Fields, Gausss Law & Electric Potential 36th Capacitance, Current & Resistance 37th Ohms Law & Simple DC Circuits (Long Test 2) 38th DC Circuits Analysis by Kirchhoffs Law 3

9th MIDTERM EXAMINATION WEEK 10th Magnetic Forces 311th Sources of Magnetic Fields 312th Motional Emf, Electromagnetic Induction , Motors & Generators

(Long Test 3)3

13thInductance & Transformers 3

14th Alternating Current Circuits 315th Fundamentals of Light, Reflection & Refraction, Dispersion (Long

Test 4)3

16th Mirrors & Lenses, Interference of light wave 317th Diffraction Patterns & Polarization of Light Waves 3

18th FINAL EXAMINATION WEEK


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y y

Course Orientation



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Course Objectives:At the end of the meeting, the student should be

able to:

1.Describe the concept of temperature and recognizeeach

temperature scale;2. Differentiate various scales of temperature &

convert fromone scale to another;

3. Recognize that for same temperature change,the amount

of thermal expansion depends on the type of material;

4. Determine by calculation the value of averagethermal

Temperature & Thermal Expansion of Solids&Liquids

This file is for exclusive use in my class Phy- -


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Temperature & Thermal Expansion of Solids &Liquids

SUB-TOPICS

What is temperature?

Zeroth Law of Thermodynamics

Scales of Measuring Temperature

Concept Map of Thermal Expansion

Linear, Area and Volume Expansion

Unusual Behavior of Water

Assessment

We often associate theconcept of temperature withhow hot or cold an objectfeels when we touch it.

However, our senses areunreliable and often mislead us.For example, if we remove ametal ice tray and a cardboardbox of vegetable from a freezer.Which object feels colder to thetouch?



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Two objects at different initial temperatures eventuallyreach some intermediate temperature when placed incontact with each other.

Mixing hot and cold water in a bathtub

Dropping an ice cube into a cup of hot coffee.

Definition:1.Thermal contact when two objects at

different temperatures exchanged energy betweenthem due to a temperature difference, even if they

are not in physical contact with each other.2.Thermal Equilibrium when two objects

would not exchange energy by heat or electromagnetic radiation if they were placed inthermal contact.



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Zeroth Law of Thermodynamics

If objects A and B are separately in thermal equilibrium with a thirdobject C, then A and B are in thermal equilibrium with each other.

Hence, how do we define temperature?

Temperature is the property that determines whether an object is inthermal equilibrium with other objects.

Temperature is a measure of the exchange of heat between twoobjects.



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Scales of Measuring Temperature1. Celsius Scale2. Fahrenheit Scale3. Kelvin Scale

On a day when the temperature reaches 50 F, what isthe temperature in degrees Celsius and in Kelvins?

A pan of water is heated from 25C to 80C. What is thechange in its temperature on the Kelvin scale and on the



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Change in Temperature The change between two temperatures is specified in

Celsius Degrees (C)

TK = TC = 5/9 TF


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The Physics of ThermographyRadiation emitted by an object can also be

used to indicate temperature. For low tomoderate temperatures, the radiation emittedis infrared.

Infrared camera registers the intensity of infrared radiation. It is then connected to acolor monitor that displays the differentinfrared intensities at different colors. This

thermal painting is called thermograph or thermogram. Thermography finds applicationin medicine, oceanography and meteorology


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Thermometric Properties

1. Dimensions for solid materials2. Pressure at constant volume for gas3. Volume at constant pressure for liquids4. Color 5. Resistance for conductors


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Thermal ExpansionA phenomenon describing the changes in the dimension

of a substance when temperature increases.



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Linear Expansion



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Materials /c Aluminum 24.0x10-6Brass/Bronze 18.8x10-6

Copper 16.8x10-6Glass (ordinary) 9.0x10-6Glass (pyrex) 3.2x10-6

Iron 11.4x10-6Lead 29.4x10-6

Invar (ni fe) Alloy 0.9x10-

Table of average expansioncoefficients for some metals



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Area & Volume ExpansionFORMULA V=Vo T

The constant characterizes

the volume expansionproperties of a particularmaterial (usually a fluid); it is

coefficient of volumeexpansion where =3 in solids, hence

A=2Ao TThis file is for exclusive use in my class Phy- -


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MATERIALS /(c)Alcohol, Ethyl 1.12x10-4Benzene 1.24x10-4

Acetone 1.50x10-4Glycerin 4.85x10-4Mercury 1.82x10-4Turpentine 9.00x10-4Gasoline 9.60x10-4Air2 at 0c 3.67x10-3

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coefficients for some liquid

materials



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Applications linear expansion has to be considered to minimize

sagging of wires in between post. in the concreting of highways, construction of

bridges and buildings, thermal expansion jointsmust compensate for dimensional changes thatoccur as temperature changes to avoid buckle-up

when electronic devices are in operation,temperature increases and this must beconsidered in the design

in the fabrication of materials for use in machineaccesories such as diameter of rods and rings



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Unusual behavior of waterLiquids generally increase in volume with increasing

temperature and have about ten times greater thanthose of solids. But cold water is an exception to this rule.As temperature of water increases from 0 to 4 C, water contracts and its density increases. Above 4 C, water expands with increasing temperature and so its density

decreases. The density of water, 1 g/cm3 (at 4 C), istherefore its maximum density.For example, during winter time, when atmospherictemperature drops from 7 C to 6 C, the surface water cools and consequently decreases in volume. Since it isdenser than the water below it, which has not cooled

and decreased in volume, it will sink and the warmer water from below is forced to the surface to be cooled.When the atmospheric temperature drops further andis between 4 C and 0 C, the surface water expandsas it cools becoming less dense than the water belowit. The mixing process stops and eventually the surfacewater freezes. As the water freezes, the ice remainson the surface because ice is less dense than water.This file is for exclusive use in my class Phy

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Assessment:

3. The Celsius equivalent of 200K isa. -73 C c. 73 Cb. 232 C d. 473 C

1. When energy is exchanged between 2 objects even if theyare not in physical contact, it is called

a. mental contact c. thermal contactb. mixture contact d. energy contact2. Two objects in thermal equilibrium with each other are

a. in physical contact c. at the same temperatureb. in thermal contact d. at different temperature

4. Lead melts at 626 F. The Celsius equivalent of this

temperature isa. 316 C c. 330Cb. 366 C d. 1069 C5. The temperature of an object increases by 50C . The

increase in itsabsolute temperature isa. 28 K c. 50 KThis file is for exclusive use in my class Phy


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Assessment:6. Fill the blank space with the given options. A material with anegative

coefficient of linear expansion ______________ whentemperature

is increased.a. increases linearly c. decreases linearlyb. is unaffected d. vanishes

7. For a solid, when its temperature is increased, theexpansion include its

a. length and width c. height and widthb. length and height d. 3 dimensions8. Ave. coefficient of linear expansion of aluminum is 24 x10-6/C, copper

has 19x10-6/C, and steel has 11 x10-6 /C. Theseindicates that for

same changes in temperature and same initial length, theincrease inlength for

a. steel is less than that of copper c. copper is less thanthat steel

b. aluminum is less than that of copper d. aluminum is less

9. If you purchased a 15.0 gal of gasoline when temperature is10 C, how

much gasoline will you have when temperature becomes 65

C? asoline= 9.6x 10-4 / C .This file is for exclusive use in my class Phy


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Assessment:10. A metal pot whose volume is 1000 cm3 at 20C has a

volume of 1006cm3 at 100 C. Calculate the coefficient of linear expansion of the

metal pot.a. 2.5 x 10 -5 / C c. 7.5 x 10 -5 / C

b. 4.2 x 10 -5 / C d. 0.0126 / CThese questions are of low and medium level of cognitivecomplexity to measure the learning of the students after thediscussion. When you score below 9 points , you shouldreview this topic and understand the concept and the useof temperature conversion and thermal expansion formulasbefore proceeding to solve questions/exercises of higher level of cognitive complexity.



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Sample Problems: (This problems belong to high cognitivecomplexity level)

#1. A brass ring of diameter 10.00 cm at 20C is heated andslipped over an aluminum rod of diameter 10.01 cm at 20C.Assuming the average of coefficients of linear expansion areconstant, to what temperature must this combination be cooled toseparate them? Is this attainable? ( al = 24 x 10-6 ,

brass = 19 x 10 -6 )

To conceptualize this problem, note that when the these twometals are cooled, both the diameter of the brass ring and thediameter of the aluminum rod will decrease. Since the coefficientof linear expansion of the aluminum is greater than that of thebrass, its change in diameter will be greater than that of the brassgiven the same change in temperature. Note also that in order toseparate these two metals, the change in diameter of thealuminum rod minus the change in diameter of the brass ring,

Dal - Dbrass = 0.01 cm. Hence we can write,This file is for exclusive use in my class Phy


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0.01 cm T = -------------------------------------------------[(24 x 10-6 /C)(10.01 cm) - ( 19 x 10 -6 /C)(10.00 cm)]

T = 199C , (note that Tf


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The stress on a steel beamA steel beam is used in the roadbed of a bridge.The beam is mounted between two concretesupports when the temperature is 23C, with noroom provided for thermal expansion. Whatcompressional stress must the concrete supportsapply to each end of the beam, if they are to keepthe beam from expanding when the temperaturerises to 42C? Assume that the distance betweenthe concrete supports does not change as thetemperature rises.



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Recall that compressional stress = F/A and the magnitude of the compressional force that the concrete supports exert oneach end of the steel beam is given by:F = YA ( L/Lo)

where Y is Youngs Modulus YA ( L/Lo)

Compressional stress = A = Y ( L/Lo)

Substituting Lo from the Lo in L = Lo ( T To)

(Y L)

Compressional stress = [ L/(T - To)] = Y (T-To)=(2.0x1011N/m2)[12x10-6(C] -1(42C - 23C)

= 4.6 x107N/m2 (Answer)



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References:sics, By Cutnell J., 7th ed, 2007, pp 360- 370sics for Scientist and Engrs. By Serway & Jewett, 7th ed. 2008 pp.sics for Scientist & Engrs. By Paul Tipler. 4th ed., 1990 pp. 541-549aums Outlines Applied Physics By Arthur Beiser 4th ed., 2004, pp.tube: Lec 32 8.01 Physics I: Classical Mechanics, MIT, Fall 1999

For 1st assignment, please refer to topic outline of Linear expansion uploaded in the yahoogroup [email protected]

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1. temperature&thermal expansion

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