LF Thermal Expansion

Course OutlineWEEKS TOPICS HOURS

1st & 2nd Course Orientation & Temperature & Thermal Expansion of Solids & Liquids

6

3rd Heat & Internal Energy, Specific Heat & Calorimetry , Latent Heat 3

4th First Law of Thermodynamics, & Energy Transfer Mechanisms(Long Test 1)

3

5th Static Electricity (Coulomb’s law) 3

6th Electric Fields (Gauss’s law) 3

7th Capacitance, Current & Resistance 3

8th Ohm’s Law and Simple DC Circuits(Long Test 2)

3

9th DC Circuits Analysis by Kirchhoff’s Law 3

10th MIDTERM EXAMINATION WEEK 3

11th Magnetic Forces 3

12th Sources of Magnetic Fields 3

13th Motional Emf, Electromagnetic Induction , Motors & Generators(Long Test 3)

3

14th Inductance & Transformers 3

15th Alternating Current Circuits 3

16th Fundamentals of Light, Reflection & Refraction, Dispersion(Long Test 4)

3

17th Mirrors & Lenses, Interference of light wave 3

18th FINAL EXAMINATION WEEK 3

Phy 271-NEU-CET by LDH

Course Orientation


New Era UniversityCollege of Engineering & Technology

PHYSICS 271

Temperature and Thermal

Expansion


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

1. Describe the concept of temperature and identify each temperature scale;2. Identify which material expands more given the same changes in temperature 3. Identify the important role of thermal expansion in various practical applications.4. Determine by calculation the effect of temperature change

to the length, area and volume of the material and how this change in dimension and/or volume affect the system when more than one material is involved;5. Differentiate various scales of temperature by converting

one scale to another.

Temperature & Thermal Expansion of Solids &Liquids


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 the concept of temperature with how hot or cold an object feels when we touch it.

However, our senses are unreliable and often mislead us. For example, if we remove a metal ice tray and a cardboard box of vegetable from a freezer. Which object feels colder to the touch?


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 between them 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 in thermal

contact.


Two objects at different initial temperatures eventually reach some intermediate temperature when placed in contact with each other.

Zeroth Law of Thermodynamics

Hence, how do we define temperature?

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

Temperature is a measure of the exchange of heat between two objects.


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.

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

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

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


Change in Temperature The change between two temperatures is specified in

“Celsius Degrees” (C°)

Δ TK = Δ TC° = 5/9 Δ TF°


The Physics of Thermography

Radiation emitted by an object can also be used to indicate temperature. For low to moderate temperatures, the radiation emitted is infrared.

Infrared camera registers the intensity of infrared radiation. It is then connected to a color monitor that displays the different infrared intensities at different colors. This “thermal painting” is called thermograph or thermogram. Thermography finds application in medicine, oceanography and meteorology


Thermometric Properties

1.Dimensions for solid materials2.Pressure at constant volume for gas3.Volume at constant pressure for liquids4.Color5.Resistance for conductors


Thermal ExpansionA phenomenon describing the changes in the dimension of a substance when temperature increases.


Linear Expansion


Linear expansion equation


The change in the length of the rod due to change in temperature is

ΔL = αLoΔT equation 1 L – Lo = αLoΔT L = αLoΔT + Lo L = Lo(αΔT + 1)

where:α = average coefficient of linear expansion

Solving for α in equation 1 gives ΔL α = ------ LoΔT

LoΔL

Materials α/c°Aluminum 24.0x10-6 Brass/Bronze 18.8x10-6 Copper 16.8x10-6 Glass (ordinary) 9.0x10-6 Glass (pyrex) 3.2x10-6 Iron 11.4x10-6

Lead 29.4x10-6 Invar (ni fe) Alloy 0.9x10-6 Concrete 12.0x10-6 Steel 13.4x10-6

Table of average expansion coefficients for some metals


Area & Volume ExpansionFORMULA ∆V=βVo ∆T

The constant β characterizes the volume expansion properties of a

particular material (usually a fluid); it is coefficient of volume expansion

where β=3α in solids, hence∆A=2αAo ∆T∆V=3αVo ∆T


MATERIALS β /(°c)Alcohol, Ethyl 1.12x10-4

Benzene 1.24x10-4

Acetone 1.50x10-4

Glycerin 4.85x10-4

Mercury 1.82x10-4

Turpentine 9.00x10-4

Gasoline 9.60x10-4

Air2 at 0°c 3.67x10-3

Helium 3.665x10-3

Table of average expansion coefficients for some liquid materials


Lossen a jar lid

Pour hot water into the lid of a tightly closed glassjar will loosen the lid since metal expands more thanglass.


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 joints must compensate for dimensional changes that occur as temperature changes to avoid “buckle-up”• when electronic devices are in operation, temperature increases and this must be considered in the design • in the fabrication of materials for use in machine accesories such as diameter of rods and rings


Unusual behavior of waterLiquids generally increase in volume with increasing temperature and have β about ten times greater than those of solids. But cold water is an exception to this rule.

As temperature of water increases from 0 to 4 ºC, water contracts and its density increases. Above 4 ºC, water expands with increasing temperature and so its density decreases. The density of water, 1 g/cm3 (at 4 ºC), is therefore its maximum density.

For example, during winter time, when atmospheric temperature drops from 7 ºC to 6 ºC, the surface water cools and consequently decreases in volume. Since it is denser 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 and is between 4 ºC and 0 ºC, the surface water expands as it cools becoming less dense than the water below it. The mixing process stops and eventually the surface water freezes. As the water freezes, the ice remains on the surface because ice is less dense than water. The ice continues to build up at the surface while water near the bottom remains at 4 ºC.


Assessment:1. When two objects are in thermal equilibrium with each other, they are

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

2. The Celsius equivalent of 200K is a. -73 °C c. 73 °C b. 232 °C d. 473 °C

3. Ave. coefficient of linear expansion of aluminum is 24 x10-6 /C°, copper has 19x10-6/C°, and steel has 11 x10-6 /C°. These indicates that for same changes in temperature and same initial length, the increase in length for a. steel is less than that of copper c. copper is less than that steel b. aluminum is less than that of copper d. aluminum is less than that of

steel

4. If you purchased a 15.0 gal of gasoline when temperature is 10 °C, how much gasoline will you have when temperature becomes 65 °C? (βgasoline= 9.6x 10-4 / C°). a. 0.79 gal c. 15.79 gal b. 14.2 gal d. 16.08 gal


Assessment:5. Lead melts at 626 °F. The Celsius equivalent of this temperature is

a. 316 °C c. 330°C b. 366 °C d. 1069 °C

7. A metal pot whose volume is 1000 cm3 at 20°C has a volume of 1006 cm3 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 / °C

8. A steel bridge is 500 m long at 0°C. By how much does it expand when the temperature becomes 35 °C? The coefficient of linear expansion of steel is 1.2 x 10-5 /°C. a. 21 m c. 21 cm b. 0.21 cm d. 2.1 m

6. For a solid, when it’s temperature is increased, the expansion include its a. length and width c. height and width b. length and height d. 3 dimensions


Assessment:

11. A glass flask whose volume is 1000 cm3 at 0.0 ° C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55 ° C, 8.95 cm3 of of mercury overflow. If the coefficient of volume expasion of mercury is 18.0 x 10-5/K, compute the coefficient of volume expansion of glass a. 1.7 x10-5/° C c. 2.7 x10-5/° C b. 5.1 x10-5/° C d. 3.1 x10-5/° C12. A surveyor uses a steel measuring tape that is exactly 50 m long at a temperature of 20 ° C. What is its length on a hot summer day when the temperature is 35 ° C? a. 50.9 m c. 9 cm b. 9.0 mm d. 50.009 m

9. The following are thermometric properties of a substance EXCEPT a. dimensions c. pressure b. color d. energy

10. Ethyl alcohol freezes at -114°C. The Fahrenheit equivalent of this temperature is a. 237 °F c. 95°F b. -321 °F d. -173 °F


Assessment:13. Fill the blank space with the given options. A material with a negative coefficient of linear expansion ______________ when temperature is increased. a. increases linearly c. decreases linearly b. is unaffected d. vanishes

14. The temperature of an object increases by 50°C . The increase in its absolute temperature is a. 28 K c. 50 K b. 90 K d. 323 K

15. A glass flask with volume 200 cm3 is filled to the brim with mercury at 20 ° C. How much mercury overlows when the temperature of the system is raised to 100 ° C? The coefficient of linear expansion of the glass is 0.40 x 10-5 /K a. 0.19 cm3 c.2.9 cm3

b. 2.7 cm3 d. 3.09 cm316. The Humber Bridge in England has the world’s longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0°C to 18.0 °C a. 0.43 m c. 0.24 m b. 0.34 m d. 0.42 m


Assessment:

These questions are of low and medium level of cognitive complexity to measure the learning of the students after the discussion. When you score below 12 points, you should review this topic and understand the concept and the use of temperature conversion and thermal expansion formulas before proceeding to solve questions/exercises of higher level of cognitive complexity.


Sample Problems: (This problems belong to high cognitive complexity level)#1. A brass ring of diameter 10.00 cm at 20°C is heated and

slipped over an aluminum rod of diameter 10.01 cm at 20°C. Assuming the average of coefficients of linear expansion are constant, to what temperature must this combination be cooled to separate them? Is this attainable? ( αal = 24 x 10-6 ,

αbrass = 19 x 10 -6 )

To conceptualize this problem, note that when the these two metals are cooled, both the diameter of the brass ring and the diameter of the aluminum rod will decrease. Since the coefficient of linear expansion of the aluminum is greater than that of the brass, its change in diameter will be greater than that of the brass given the same change in temperature. Note also that in order to separate these two metals, the change in diameter of the aluminum rod minus the change in diameter of the brass ring, ΔDal - ΔDbrass = 0.01 cm. Hence we can write,


0.01 cmΔT = ------------------------------------------------- [(24 x 10-6 /Cº)(10.01 cm) - ( 19 x 10 -6 /Cº)(10.00 cm)]ΔT = 199Cº , (note that Tf<TI , since temperature was decreased and ΔT must be a negative number or we can also write ΔT = Ti – Tf)

(αDoΔT) al - (αDoΔT) brass = 0.01 cm.ΔT [(αDo) al - (αDo) brass ] = 0.01 cm.ΔT [(24x10-6/Cº)(10.01cm)-(19 x10-6)(10.00

cm)]=0.01cm

ΔT = Ti – Tf

Tf = Ti - ΔT Tf = 20 ºC - 199 ºC Tf = - 179 ºC, this is attainable since when converted to

Kelvin, this gives Tf = - 179 + 273 Tf = 94K (answer)


The stress on a steel beamA steel beam is used in the roadbed of a bridge. The beam is mounted between two concrete supports when the temperature is 23°C, with no room provided for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the beam from expanding when the temperature rises to 42°C? Assume that the distance between the concrete supports does not change as the temperature rises.


Recall that compressional stress = F/A and the magnitude of the compressional force that the concrete supports exert on each end of the steel beam is given by:

F = YA ( ΔL/Lo)where Y is Young’s Modulus

YA ( ΔL/Lo) Compressional stress = A = Y ( ΔL/Lo)

Substituting Lo from the Lo in ΔL = α Lo ( T –To)

(Y ΔL)

Compressional stress = [Δ L/α(T - To)] = Y α(T-To) =(2.0x1011N/m2)[12x10-6(C°] -1(42°C - 23°C) = 4.6 x107N/m2 (Answer)


References:

1.Physics, By Cutnell J., 7th ed, 2007, pp 360- 3702.Physics for Scientist and Engrs. By Serway & Jewett, 7th ed. 2008 pp. 581-5943.Physics for Scientist & Engrs. By Paul Tipler. 4th ed., 1990 pp. 541-549,633-6364.Schaum’s Outlines Applied Physics By Arthur Beiser 4th ed., 2004, pp. 213-2325.You 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 uni portal www.vle.neu.edu.ph

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LF Thermal Expansion

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