The document describes an experiment to measure the coefficient of thermal expansion of copper, steel, and aluminum. Metal bars are heated using steam and their change in length is measured. The coefficients of linear expansion are calculated using the change in length, initial length, and change in temperature. Safety precautions are outlined as the experiment involves hot steam, water, and metal bars.
A 46 years old Lebanese Patient presented to my university dental clinic before tow months of COVID-19 pandemic having missing teeth, fracture roots, failed PFM bridge, multiple failed RCT and caries...
Treatment plan and clinical steps are presented in the above presentation, clinical treatment is postponed due to the pandemic.
hope you like it...
stay safe
A broad idea about Esthetic Crown objectives and their Indications along side with the drawbacks of SSC also the Classification of esthetic crowns plus the Pros and cons of each esthetic crown.
Tobacco negatively affects postoperative healing for almost all surgeries performed in the oral cavity. Tobacco, along with all its byproducts, is a peripheral vasoconstrictor, which means it constricts blood flow to the smaller blood vessels and raises blood pressure. It causes increased platelet adhesiveness, which, combined with constricted blood vessels, heightens the risk of these smaller blood vessels completely closing off.
Smoking can adversely affect the success of your implants and permanent damage to your tissues may be present even after quitting, but this doesn’t prevent you from being a candidate for this specialized procedure.
Dr rajat sachdeva has the skills to not only design a beautiful, personalized smile for you, but the experience to know when someone isn’t a good candidate and suggest an alternative treatment.
Dr Sachdeva’s Dental, Aesthetic And Implant Institute is one of the leading clinics in Delhi. So hurry up and come book an appointment with us at Ashok Vihar, Delhi which has state of the art clinic and all the latest and advanced equipments.
To book an appointment contact:
Dr. Rajat Sachdeva
Director & Mentor
Dr Sachdeva’s Dental Aesthetic And Implant Institute
I 101, Ashok Vihar Phase 1, Delhi- 110052
Contact us at
Phone : +919818894041,01142464041
Our Websites:
www.sachdevadentalcare.com
www.dentalimplantindia.co.in
www.dentalclinicindelhi.com
www.dentalcoursesdelhi.com
Facebook- dentalcoursesdelhi
Youtube- drrajatsachdeva
Linkedin- drrajatsachdeva
Slideshare- Dr Rajat Sachdeva
Twitter Page- drrajatsachdeva
Instagram page- surgicalmasterrajat
A 46 years old Lebanese Patient presented to my university dental clinic before tow months of COVID-19 pandemic having missing teeth, fracture roots, failed PFM bridge, multiple failed RCT and caries...
Treatment plan and clinical steps are presented in the above presentation, clinical treatment is postponed due to the pandemic.
hope you like it...
stay safe
A broad idea about Esthetic Crown objectives and their Indications along side with the drawbacks of SSC also the Classification of esthetic crowns plus the Pros and cons of each esthetic crown.
Tobacco negatively affects postoperative healing for almost all surgeries performed in the oral cavity. Tobacco, along with all its byproducts, is a peripheral vasoconstrictor, which means it constricts blood flow to the smaller blood vessels and raises blood pressure. It causes increased platelet adhesiveness, which, combined with constricted blood vessels, heightens the risk of these smaller blood vessels completely closing off.
Smoking can adversely affect the success of your implants and permanent damage to your tissues may be present even after quitting, but this doesn’t prevent you from being a candidate for this specialized procedure.
Dr rajat sachdeva has the skills to not only design a beautiful, personalized smile for you, but the experience to know when someone isn’t a good candidate and suggest an alternative treatment.
Dr Sachdeva’s Dental, Aesthetic And Implant Institute is one of the leading clinics in Delhi. So hurry up and come book an appointment with us at Ashok Vihar, Delhi which has state of the art clinic and all the latest and advanced equipments.
To book an appointment contact:
Dr. Rajat Sachdeva
Director & Mentor
Dr Sachdeva’s Dental Aesthetic And Implant Institute
I 101, Ashok Vihar Phase 1, Delhi- 110052
Contact us at
Phone : +919818894041,01142464041
Our Websites:
www.sachdevadentalcare.com
www.dentalimplantindia.co.in
www.dentalclinicindelhi.com
www.dentalcoursesdelhi.com
Facebook- dentalcoursesdelhi
Youtube- drrajatsachdeva
Linkedin- drrajatsachdeva
Slideshare- Dr Rajat Sachdeva
Twitter Page- drrajatsachdeva
Instagram page- surgicalmasterrajat
Inlays and onlays / implant dentistry course/ implant dentistry courseIndian dental academy
Indian Dental Academy: will be one of the most relevant and exciting training center with best faculty and flexible training programs for dental professionals who wish to advance in their dental practice,Offers certified courses in Dental implants,Orthodontics,Endodontics,Cosmetic Dentistry, Prosthetic Dentistry, Periodontics and General Dentistry.
A comprehensive lecture comparing the Types, Properties and Clinical applications of different types of artificial teeth used in denture making.
For more lectures on Dental materials follow Dr Rashid Lectures on Dental Materials on Facebook (dmbydrrashid)
Hi, I am Dr Komal Ghiya, a pediatric dentist by profession and I am here to upload some of my own presentations regarding dentistry for educational purposed for all the dental students, both undergraduates and postgraduates as well as dentists. I hope you like the presentation. All the best!
WorksheetPhysics I Thermal Expansion WorksheetClassUP1 LabNames.docxdunnramage
WorksheetPhysics I: Thermal Expansion WorksheetClass:UP1 LabNames:Zachary MannSection:Section 1Ashlynn HoltLab Group:Lab Group 15Alwleed AlmutairiAssignment Date:Tuesday, Nov 13answer key:numbersdataTable 1: Data and CalculationsLength (mm)ΔL (mm)Resistance at Room Temp. Rrm (Ω)Resistance when Heated Rhot (Ω)Room Temperature Trm ( C˚ )Heated Temperature Thot ( C˚ )Change in Temperature ΔT ( C˚ )Copper704.850.14111.006.56239572mSteel704.850.66105.406.74249470Aluminum704.851.25100.026.76259469Table 2: ResultsExperimental Thermal Coefficient α (1/C˚)Accepted Thermal Coefficient α (1/C˚)% Error (%)Copper2.717.684.66Steel13.313.51.48Aluminum25.723.49.83
ConclusionConclusion:
Thermal Expansion Apparatus 012-04394C
2
Accepted Values for Coefficient of
Thermal Expansion
Material a ( x10-6/∞C )
Copper 17.6
Steel 11.3 to 13.5
Aluminum 23.4
Changing Tubes
➤ Caution:
When changing tubes be careful
not to pull the wires off the
thermistor. The thumb-
screw must be com-
pletely removed
before the thermistor
can be lifted off the
threaded rod.
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item PASCO Part #
mod. Thermistor (100 kΩ) 150-03140
Al Tube Assy 003-04413
Cu Tube Assy 003-04412
Steel Tube Assy 003-04414
Foam Insulator 648-03100
Dial Gauge 620-050
Thermistor
Tube
Thumbscrew
012-04394C Thermal Expansion Apparatus
3
Introduction
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase. The added heat increases the average amplitude of vibration of
the atoms in the material which increases the average separation between the atoms.
Suppose an object of length L undergoes a temperature change of magnitude ∆T. If ∆T is
reasonably small, the change in length, ∆L, is generally proportional to L and ∆T. Stated
mathematically:
∆L = αL ∆T;
where α is called the coefficient of linear expansion for the material.
For materials that are not isotropic, such as an asymmetric crystal for example, a can have a
different value depending on the axis along which the expansion is measured.
a can also vary somewhat with temperature so that the degree of expansion depends not
only on the magnitude of the temperature change, but on the absolute temperature as well.
In this experiment, you will measure α for copper, aluminum, and steel. These metals are
isotropic so that a need only be measured along one dimension. Also, within the limits of
this experiment, a does not vary with temperature.
Procedure
➀ Measure L, the length of the copper tube at room temperature. Measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end
(see Figure 1). Record your results in Table 1.
➁ Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin
on the tube fits into the slot on the slotted mounting block and the bracket on the tube
presses against the spring arm of the dia.
Thermal Expansion Apparatus 012-04394C
2
Accepted Values for Coefficient of
Thermal Expansion
Material a ( x10-6/∞C )
Copper 17.6
Steel 11.3 to 13.5
Aluminum 23.4
Changing Tubes
➤ Caution:
When changing tubes be careful
not to pull the wires off the
thermistor. The thumb-
screw must be com-
pletely removed
before the thermistor
can be lifted off the
threaded rod.
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item PASCO Part #
mod. Thermistor (100 kΩ) 150-03140
Al Tube Assy 003-04413
Cu Tube Assy 003-04412
Steel Tube Assy 003-04414
Foam Insulator 648-03100
Dial Gauge 620-050
Thermistor
Tube
Thumbscrew
012-04394C Thermal Expansion Apparatus
3
Introduction
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase. The added heat increases the average amplitude of vibration of
the atoms in the material which increases the average separation between the atoms.
Suppose an object of length L undergoes a temperature change of magnitude ∆T. If ∆T is
reasonably small, the change in length, ∆L, is generally proportional to L and ∆T. Stated
mathematically:
∆L = αL ∆T;
where α is called the coefficient of linear expansion for the material.
For materials that are not isotropic, such as an asymmetric crystal for example, a can have a
different value depending on the axis along which the expansion is measured.
a can also vary somewhat with temperature so that the degree of expansion depends not
only on the magnitude of the temperature change, but on the absolute temperature as well.
In this experiment, you will measure α for copper, aluminum, and steel. These metals are
isotropic so that a need only be measured along one dimension. Also, within the limits of
this experiment, a does not vary with temperature.
Procedure
➀ Measure L, the length of the copper tube at room temperature. Measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end
(see Figure 1). Record your results in Table 1.
➁ Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin
on the tube fits into the slot on the slotted mounting block and the bracket on the tube
presses against the spring arm of the dial
gauge.
➤ NOTE: Slide or push the tube to one side of
the slide support. Drive the thumbscrew
against the pin until the tube can no longer be
moved. Use this as your reference point.
➂ Use one of the provided
thumbscrews to attach
the thermistor lug to the
threaded hole in the
middle of the copper
tube. The lug should be
aligned with the axis of
the tube, as shown in
Figure 2, so there is
maximum contact
L
Bracket on tube
Dial Gauge Spring Arm
Stainless steel pin
Figure 2 Equipment Setup (Top View)
Slotted bracket Thumbscrew
Figure 1 Measuring Tube Length
Experiment: Measuring the Coefficient of Linear
Expansion for Copper, Steel, and Aluminum
brucejohnson
H.
Inlays and onlays / implant dentistry course/ implant dentistry courseIndian dental academy
Indian Dental Academy: will be one of the most relevant and exciting training center with best faculty and flexible training programs for dental professionals who wish to advance in their dental practice,Offers certified courses in Dental implants,Orthodontics,Endodontics,Cosmetic Dentistry, Prosthetic Dentistry, Periodontics and General Dentistry.
A comprehensive lecture comparing the Types, Properties and Clinical applications of different types of artificial teeth used in denture making.
For more lectures on Dental materials follow Dr Rashid Lectures on Dental Materials on Facebook (dmbydrrashid)
Hi, I am Dr Komal Ghiya, a pediatric dentist by profession and I am here to upload some of my own presentations regarding dentistry for educational purposed for all the dental students, both undergraduates and postgraduates as well as dentists. I hope you like the presentation. All the best!
WorksheetPhysics I Thermal Expansion WorksheetClassUP1 LabNames.docxdunnramage
WorksheetPhysics I: Thermal Expansion WorksheetClass:UP1 LabNames:Zachary MannSection:Section 1Ashlynn HoltLab Group:Lab Group 15Alwleed AlmutairiAssignment Date:Tuesday, Nov 13answer key:numbersdataTable 1: Data and CalculationsLength (mm)ΔL (mm)Resistance at Room Temp. Rrm (Ω)Resistance when Heated Rhot (Ω)Room Temperature Trm ( C˚ )Heated Temperature Thot ( C˚ )Change in Temperature ΔT ( C˚ )Copper704.850.14111.006.56239572mSteel704.850.66105.406.74249470Aluminum704.851.25100.026.76259469Table 2: ResultsExperimental Thermal Coefficient α (1/C˚)Accepted Thermal Coefficient α (1/C˚)% Error (%)Copper2.717.684.66Steel13.313.51.48Aluminum25.723.49.83
ConclusionConclusion:
Thermal Expansion Apparatus 012-04394C
2
Accepted Values for Coefficient of
Thermal Expansion
Material a ( x10-6/∞C )
Copper 17.6
Steel 11.3 to 13.5
Aluminum 23.4
Changing Tubes
➤ Caution:
When changing tubes be careful
not to pull the wires off the
thermistor. The thumb-
screw must be com-
pletely removed
before the thermistor
can be lifted off the
threaded rod.
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item PASCO Part #
mod. Thermistor (100 kΩ) 150-03140
Al Tube Assy 003-04413
Cu Tube Assy 003-04412
Steel Tube Assy 003-04414
Foam Insulator 648-03100
Dial Gauge 620-050
Thermistor
Tube
Thumbscrew
012-04394C Thermal Expansion Apparatus
3
Introduction
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase. The added heat increases the average amplitude of vibration of
the atoms in the material which increases the average separation between the atoms.
Suppose an object of length L undergoes a temperature change of magnitude ∆T. If ∆T is
reasonably small, the change in length, ∆L, is generally proportional to L and ∆T. Stated
mathematically:
∆L = αL ∆T;
where α is called the coefficient of linear expansion for the material.
For materials that are not isotropic, such as an asymmetric crystal for example, a can have a
different value depending on the axis along which the expansion is measured.
a can also vary somewhat with temperature so that the degree of expansion depends not
only on the magnitude of the temperature change, but on the absolute temperature as well.
In this experiment, you will measure α for copper, aluminum, and steel. These metals are
isotropic so that a need only be measured along one dimension. Also, within the limits of
this experiment, a does not vary with temperature.
Procedure
➀ Measure L, the length of the copper tube at room temperature. Measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end
(see Figure 1). Record your results in Table 1.
➁ Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin
on the tube fits into the slot on the slotted mounting block and the bracket on the tube
presses against the spring arm of the dia.
Thermal Expansion Apparatus 012-04394C
2
Accepted Values for Coefficient of
Thermal Expansion
Material a ( x10-6/∞C )
Copper 17.6
Steel 11.3 to 13.5
Aluminum 23.4
Changing Tubes
➤ Caution:
When changing tubes be careful
not to pull the wires off the
thermistor. The thumb-
screw must be com-
pletely removed
before the thermistor
can be lifted off the
threaded rod.
Replacement Parts
The following parts can be ordered from
PASCO scientific.
Item PASCO Part #
mod. Thermistor (100 kΩ) 150-03140
Al Tube Assy 003-04413
Cu Tube Assy 003-04412
Steel Tube Assy 003-04414
Foam Insulator 648-03100
Dial Gauge 620-050
Thermistor
Tube
Thumbscrew
012-04394C Thermal Expansion Apparatus
3
Introduction
Most materials expand somewhat when heated through a temperature range that does not
produce a change in phase. The added heat increases the average amplitude of vibration of
the atoms in the material which increases the average separation between the atoms.
Suppose an object of length L undergoes a temperature change of magnitude ∆T. If ∆T is
reasonably small, the change in length, ∆L, is generally proportional to L and ∆T. Stated
mathematically:
∆L = αL ∆T;
where α is called the coefficient of linear expansion for the material.
For materials that are not isotropic, such as an asymmetric crystal for example, a can have a
different value depending on the axis along which the expansion is measured.
a can also vary somewhat with temperature so that the degree of expansion depends not
only on the magnitude of the temperature change, but on the absolute temperature as well.
In this experiment, you will measure α for copper, aluminum, and steel. These metals are
isotropic so that a need only be measured along one dimension. Also, within the limits of
this experiment, a does not vary with temperature.
Procedure
➀ Measure L, the length of the copper tube at room temperature. Measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end
(see Figure 1). Record your results in Table 1.
➁ Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin
on the tube fits into the slot on the slotted mounting block and the bracket on the tube
presses against the spring arm of the dial
gauge.
➤ NOTE: Slide or push the tube to one side of
the slide support. Drive the thumbscrew
against the pin until the tube can no longer be
moved. Use this as your reference point.
➂ Use one of the provided
thumbscrews to attach
the thermistor lug to the
threaded hole in the
middle of the copper
tube. The lug should be
aligned with the axis of
the tube, as shown in
Figure 2, so there is
maximum contact
L
Bracket on tube
Dial Gauge Spring Arm
Stainless steel pin
Figure 2 Equipment Setup (Top View)
Slotted bracket Thumbscrew
Figure 1 Measuring Tube Length
Experiment: Measuring the Coefficient of Linear
Expansion for Copper, Steel, and Aluminum
brucejohnson
H.
Experimental Investigation of Heat Transfer Using “Twisted Aluminium Tape”IJERA Editor
Heat exchanger has a wide industrial and engineering applications. Increasing the efficiency of heat exchanger will increase the overall performance of the unit. This paper is about increasing the heat transfer coefficient of heat exchanger by causing a turbulence in the liquid flow through the pipe. For causing the turbulence, liquid flow is subjected to a Twisted Aluminium Tape (TAT) which will increase the Reynolds number of flow. This will ensure heat transfer through the length of flow and thus there will be an increased heat transfer rate. The increased turbulence and higher shear caused by Twisted Aluminium Tape (TAT) will offer resistance to fouling also. KEY ]
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
Kseniya Leshchenko: Shared development support service model as the way to ma...Lviv Startup Club
Kseniya Leshchenko: Shared development support service model as the way to make small projects with small budgets profitable for the company (UA)
Kyiv PMDay 2024 Summer
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The Tata Group, a titan of Indian industry, is making waves with its advanced talks with Taiwanese chipmakers Powerchip Semiconductor Manufacturing Corporation (PSMC) and UMC Group. The goal? Establishing a cutting-edge semiconductor fabrication unit (fab) in Dholera, Gujarat. This isn’t just any project; it’s a potential game changer for India’s chipmaking aspirations and a boon for investors seeking promising residential projects in dholera sir.
Visit : https://www.avirahi.com/blog/tata-group-dials-taiwan-for-its-chipmaking-ambition-in-gujarats-dholera/
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
Memorandum Of Association Constitution of Company.pptseri bangash
www.seribangash.com
A Memorandum of Association (MOA) is a legal document that outlines the fundamental principles and objectives upon which a company operates. It serves as the company's charter or constitution and defines the scope of its activities. Here's a detailed note on the MOA:
Contents of Memorandum of Association:
Name Clause: This clause states the name of the company, which should end with words like "Limited" or "Ltd." for a public limited company and "Private Limited" or "Pvt. Ltd." for a private limited company.
https://seribangash.com/article-of-association-is-legal-doc-of-company/
Registered Office Clause: It specifies the location where the company's registered office is situated. This office is where all official communications and notices are sent.
Objective Clause: This clause delineates the main objectives for which the company is formed. It's important to define these objectives clearly, as the company cannot undertake activities beyond those mentioned in this clause.
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Liability Clause: It outlines the extent of liability of the company's members. In the case of companies limited by shares, the liability of members is limited to the amount unpaid on their shares. For companies limited by guarantee, members' liability is limited to the amount they undertake to contribute if the company is wound up.
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Capital Clause: This clause specifies the authorized capital of the company, i.e., the maximum amount of share capital the company is authorized to issue. It also mentions the division of this capital into shares and their respective nominal value.
Association Clause: It simply states that the subscribers wish to form a company and agree to become members of it, in accordance with the terms of the MOA.
Importance of Memorandum of Association:
Legal Requirement: The MOA is a legal requirement for the formation of a company. It must be filed with the Registrar of Companies during the incorporation process.
Constitutional Document: It serves as the company's constitutional document, defining its scope, powers, and limitations.
Protection of Members: It protects the interests of the company's members by clearly defining the objectives and limiting their liability.
External Communication: It provides clarity to external parties, such as investors, creditors, and regulatory authorities, regarding the company's objectives and powers.
https://seribangash.com/difference-public-and-private-company-law/
Binding Authority: The company and its members are bound by the provisions of the MOA. Any action taken beyond its scope may be considered ultra vires (beyond the powers) of the company and therefore void.
Amendment of MOA:
While the MOA lays down the company's fundamental principles, it is not entirely immutable. It can be amended, but only under specific circumstances and in compliance with legal procedures. Amendments typically require shareholder
Implicitly or explicitly all competing businesses employ a strategy to select a mix
of marketing resources. Formulating such competitive strategies fundamentally
involves recognizing relationships between elements of the marketing mix (e.g.,
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ENTREPRENEURSHIP TRAINING.ppt for graduating class (1).ppt
Measuring the coefficient of thermal expansion
1. EXPERIMENT T3
MEASURING THE COEFFICIENT OF THERMAL EXPANSION
OF COPPER, STEEL AND ALUMINIUM
Objectives
• To understand the concepts of heat exchange and thermal equilibrium
• To measure the coefficient of thermal expansion of copper, steel and aluminium
• To calculate the coefficients of volume expansion of copper, steel and aluminium.
SAFETY WARNING
In this experiment you will work with steam, hot water, and hot metal bars. Be careful not to
burn yourself when you touch an object. Do not open the steam generator, or touch the bars
when they’re hot!
Background
Most materials expand somewhat when heated through a temperature range that does not
produce melting or boiling. In a simple but useful atomic model of the material, the
temperature rise causes an increase of the amplitude of vibration of the atoms in the material,
which increases the average separation between the atoms, and the material expands as a
result.
It turns out that, provided the change in temperature isn’t too big, the amount by which the
material expands is directly proportional to the change in temperature. From the atomic model
you can infer that the expansion should also be directly proportional to the size of the object.
The constant of proportionality is called the coefficient of linear expansion (symbol: α) and
varies from material to material.
Not all materials expand to the same extent in different directions. Such materials are called
anisotropic, i.e. not (an) the same (iso) in all directions (tropic). In an asymmetric crystal for
example, α can have a different value depending on the axis along which the expansion is
measured. α can also vary somewhat with temperature so that the degree of expansion
depends not only on the magnitude of the temperature change, but on the absolute
temperature as well.
Now answer questions A1-A3 on the answer sheet
1
2. Experiment
In this experiment, you will measure α for copper, aluminium, and steel. These metals are
isotropic so that α need only be measured along one dimension. Also, within the limits of this
experiment, α does not vary with temperature.
The thermal expansion apparatus is shown in Figure 1. It allows you to make reasonably
accurate measurements of the coefficient of linear expansion for steel, copper, and aluminium
in a straightforward manner. The length of the bar is measured at room temperature, and again
when it has been heated up. By measuring the length at room temperature, the expansion, and
the temperature difference, you can work out the value of α.
To make the measurement, the tube is placed on the expansion base. The length of the tube is
measured at room temperature; the expansion is measured with a built-in dial gauge. Steam
from a steam generator (much like a kettle) is passed through the tube, and after a while the bar
reaches a certain constant temperature. You can monitor the temperature using a thermistor
attached to the centre of the tube. The resistance of the thermistor varies with temperature;
the relationship between temperature and resistance is known beforehand. Thus by monitoring
the resistance with a multimeter you can effectively monitor the temperature. Although the
relationship between temperature and resistance is not linear, a linear approximation can be
accurately used to interpolate between values listed in the table with an accuracy of
approximately ±0.2oC. If you wish to investigate the expansion of the metals at additional
temperatures, hot or cold water can be passed through the tubes.
Experimental set-up
Figure 1. Equipment set-up.
The thermistor that measures the tube temperature is embedded in the thermistor lug. Once
thermal equilibrium has been reached, the heat is highly uniform along the length of the tube.
The foam insulator is used to inhibit heat loss through the thermistor lug so the lug
temperature closely follows the tube temperature. The insulator does not have any
appreciable effect on the local temperature of the tube itself.
2
3. Procedure
1. To find L, the length of the copper tube at room temperature, measure from the inner edge
of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end.
Record your results as in Table A4.
2. Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin
on the tube fits into the slot on the mounting block and the bracket on the tube presses
against the spring arm of the dial gauge.
Figure 2. Mounting the tube.
NOTE: Slide or push the tube to one side of the slide support. Drive the thumbscrew
against the pin until the tube can no longer be moved. Use this as your reference point.
Attach the thermistor lug to the middle of the copper tube. The lug should be aligned with
the axis of the tube, as shown in Figure 2, so there is maximum contact between the lug and
the tube.
3. Place the foam insulator over the thermistor lug as shown in Figure 3.
4. Plug the leads of the multimeter into the banana plug connectors labelled THERMISTOR
in the centre of the expansion base and set the multimeter to measure resistance (Ω).
Figure 3. Thermistor lug.
5. Measure and record Rrm, the resistance of the thermistor at room temperature. Record this
value in the table A4.
3
4. 6. Use tubing to attach your steam generator to the end of the copper tube. Attach it to the
end farthest from the dial gauge.
7. Use a book or a block of wood to raise the end of the expansion base at which steam enters
the tube - a few centimetres is sufficient. This will allow any water that condenses in the
tube to drain out. Place a beaker under the other end of the tube to catch the draining
water.
8. Turn the outer casing of the dial gauge to align the zero point on the scale with the long
indicator needle. As the tube expands, the indicator needle will move in a anti-clockwise
direction.
9. Ensure there is enough water in the steam generator before switching it on. Once switched
on, do not remove the top. Turn on the steam generator. As steam begins to flow, watch
the dial gauge and the multimeter. When the thermistor resistance stabilises, record the
resistance (Rhot) as in Table A4. Also record the expansion of the tube length (∆L) as
indicated by the displacement of the indicator on the dial gauge. (Each increment on the
dial gauge is equivalent to 0.01 mm of tube expansion).
10.Repeat the experiment for the steel and aluminium tubes. Write down your results in table
A4.
11.If time permits, repeat the experiment, replacing the steam with cold water running through
the tube(s). Make sure the water is drained off properly! Complete
Caution: When changing tubes be careful not to pull the wires off the thermistor. The
thumbscrew must be completely removed before the thermistor can be lifted off the
threaded rod.
Now answer questions A4-A14 on the answer sheet
4
5. Mathematical notes
Equation 1 below defines the coefficient of linear expansion:
∆ L = α L0 ∆T (1)
Appendix: Useful Data
Table 1. Coefficient of Thermal Expansion
MATERIAL α (x10-6/oC)
Copper 16.5
Steel 11.7
Aluminium 23
5