Physics quiz question: concrete beam contraction

Physics 205A Quiz 7, fall semester 2019
Cuesta College, San Luis Obispo, CA

A concrete beam (linear expansion coefficient 9.8×10^–6 K^–1) is 12.2 m long at room temperature (293 K). In order to contract by 0.0010 m, its temperature should be decreased by:
(A) 1.2×10^–5 K.
(B) 8.2×10^–5 K.
(C) 0.38 K.
(D) 8.4 K.

Correct answer: (D)

The relation between the change in length ∆L due to a temperature change ∆T is given by:

α·∆T = ∆L/L,

such that:

∆T = ∆L/(α·L) = (–0.0010 m)/((9.8×10^–6 K^–1)·(12.2 m)) = –8.36400133824 K,

or to two significant figures, the decrease in temperature is 8.4 K or 8.4° C.

(Response (A) is L·α; response (B) is ∆L/L; response (C) is ∆L/(α·T₀).)

Sections 70854, 70855
Exam code: quiz07VlnC
(A) : 3 students
(B) : 8 students
(C) : 3 students
(D) : 37 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49

Physics quiz question: concrete vs. glued laminated wood beam contraction

Physics 205A Quiz 7, fall semester 2019
Cuesta College, San Luis Obispo, CA

"Finger joints in glue-lam beams, Polkky mill, Kuusamo2"
Eli Sagor
https://flic.kr/p/9xRT62

A concrete beam (linear expansion coefficient 9.8×10^–6 K^–1) and glued laminated wood beam (linear expansion coefficient 3.6×10^–6 K^–1[*]) have the same length at room temperature (293 K). If they both decrease in temperature by the same amount, the length of the concrete beam will be __________ the length of the wood beam. (A) shorter than.
(B) equal to.
(C) longer than.
(D) (Not enough information is given.)

[*] awc.org/pdf/codes-standards/publications/archives/lrfd/AWC-LRFD1996-Glulam-0203.pdf.

Correct answer: (A)

The relation between the change in length ∆L due to a temperature change ∆T is given by:

α_concrete·∆T = ∆L_concrete/L,

and similarly for the glued laminated beam:

α_wood·∆T = ∆L_wood/L,

where the original length L and the temperature change ∆T is the same for both the concrete and glued laminated beam. Solving for this common factor for both beams:

L·∆T = ∆L_concrete/α_concrete,

L·∆T = ∆L_wood/α_wood,

we can then set this common factor for both beams equal to each other:

L·∆T = L·∆T,

∆L_concrete/α_concrete = ∆L_wood/α_wood.

From inspection, since α_concrete > α_wood, then for the equality to hold, ∆L_concrete > ∆L_wood, and so the concrete beam would contract more, and as a result be shorter than the glued laminated beam.

Sections 70854, 70855
Exam code: quiz07VlnC
(A) : 18 students
(B) : 7 students
(C) : 26 students
(D) : 0 students

Success level: 35%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.05

Physics quiz archive: temperature, thermal equilibrium, heat transfers

Physics 205A Quiz 7, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855
Exam code: quiz07VlnC



Sections 70854, 70855 results

0- 6 :	* [low = 3]
7-12 :	**********
13-18 :	**************
19-24 :	******************* [mean = 18.9 +/- 6.2]
25-30 :	******* [high = 30]

Online reading assignment: temperature

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on temperature.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Temperature plays a big role in thermal stress with expansion or contraction. This can be used to our advantage or disadvantage."

"I understand that if the liquid expansion is greater than the container expansion, there will be overflow. Vice versa, there will be no overflow. Expansion occurs as a response to temperature change."

"Explaining a thermometer: temperature ultimately 'is' something greater than the feeling that something is hot or cold; rather, change in temperature is the expansion of materials. In the case of a thermometer, the red alcohol experiences a temperature increase expanding its volume filling up more of the glass indicating a temperature change."

"It totally didn't occur to me how objects expand depending on differences in temperature. It just isn't something that's on my mind daily, but now that I've read about it, it clearly makes sense. I understood the concept of the length of steel beams and how shorter beams would require a higher temperature to expand compared to longer ones."

"The more heat applied the greater an object will expand the size of the expansion is proportional to the size of the object. The same is true for chilling an object."

"That the forces needed to prevent a solid object from expanding must be strong enough to counteract any change in length that would occur due to a change in temperature. It makes sense to me that the change in forces can result in serious structural damage."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I do think I could use some extra examples covering linear thermal expansion and volume thermal expansion. These practice problems given were confusing to me."

"I had trouble understanding thermal stress and how it differs from normal stress. I was also confused by some of the equations for linear and volume thermal expansion."

"The linear and volume expansion formulas."

"I do not understand the concept behind why objects or fluids expand because of temperature change. Also, does heat mean expansion and cold mean shrink? Does it simply depend on the object?"

"I think I get the general concept of this, but I'm looking forward to the lecture and seeing how these equations will work out."

"Nothing was too crazy, just need to keep in mind how the equations work."

"The reading got more confusing as it went on. At the end, when it was discussing which time of day that the gas would be higher, I was not sure of the answer. "

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"The mathematical relationship between the coefficient of volume expansion and the coefficient of linear expansion is that the coefficient for volume expansion is three times as much as the coefficient of linear expansion."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	******************* [19]
the same.	**** [4]
a larger.	**** [4]
(Unsure/guessing/lost/help!)	* [1]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	************** [14]
equal to.	****** [6]
greater than.	****** [6]
(Unsure/guessing/lost/help!)	** [2]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	*********** [11]
equal to.	***** [5]
greater than.	************************ [24]
(Unsure/guessing/lost/help!)	****** [6]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [35%]
density: the cool gallon [76%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"Colder gasoline is more dense than warmer gasoline, so a cold gallon of gas contains more energy than a warm gallon of gas, even though they might cost the same."

"Chemically, cooling down allows for the molecules to slow and move closer together, allowing for the density to increase."

"When the gas is cooler it becomes denser and you actually end up with more molecules of gas per gallon."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"This class is going by so fast!"

"Just need to talk this over in class."

"I never knew they had to account for expansion when constructing sidewalks."

"I would love to go over the gasoline question a bit more."

"Why do objects expand and shrink with temperature change?" (The atoms and molecules inside move faster when hotter. But because of asymmetry of the spring-like interactions between the atoms and molecules, it is harder for them to move closer together (because of mutual repulsion) than it is for them to move farther apart, and so overall the object will expand.)

"Will we be experimenting with liquids during the next lab?" (Actually, we'll be finishing up with standing waves for the last lab.)

"Sad you didn't dress up as an astronaut again for Halloween this year :("

Physics quiz question: dimensional expansion of aluminum rod

Physics 205A Quiz 7, fall semester 2018
Cuesta College, San Luis Obispo, CA

An aluminum bar (linear expansion coefficient 2.3×10^–5 K^–1) has a length of 0.500 m, and a cross-sectional area of 4.0×10^–4 m² at room temperature (20.0° C). As the temperature of the bar is raised, its __________ will increase.
(A) length.
(B) cross-sectional area.
(C) (Both of the above choices.)
(D) (Neither of the above choices.)

Correct answer: (C)

The relation between the change in length (along any dimension) ∆L due to a temperature change ∆T is given by:

α·∆T = ∆L/L.

With a temperature increase, the length, width, and height of the bar will all proportionally expand, such that both the length and the cross-sectional area of the bar will increase.

Sections 70854, 70855
Exam code: quiz07PeA7
(A) : 25 students
(B) : 3 students
(C) : 22 students
(D) : 0 students

Success level: 44%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.13

Physics quiz archive: temperature, thermal equilibrium, heat transfers

Physics 205A Quiz 7, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz07PeA7



Sections 70854, 70855 results

0- 6 :	** [low = 6]
7-12 :	****
13-18 :	***********
19-24 :	********************** [mean = 20.8 +/- 6.0]
25-30 :	************ [high = 30]

Online reading assignment: temperature

Physics 205A, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on temperature.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"That the length of an object changes by an amount by a change in the amount of ΔL when the temperature changes by a ΔT. With linear expansion, when there is a hole in a piece of solid material, when heated the hole will expand along with the material."

"A shorter beam will require a greater increase in temperature to expand to the same of a longer beam based on the equation. If a liquid is in a container it may expand to a greater, less than, or equal to the coefficient of its container."

"The material-dependent linear expansion coefficient characterizes the response of the material to thermal stress. The shorter beam will require a greater increase in temperature to expand the same amount as the longer beam. If the liquid and the container both expand the same amount for the same increase in temperature then the liquid will still fill the container to the brim."

"The linear expansion of an object tells as how the object responds to thermal stress. I also learned that mercury and alcohol thermometers work because the volume of the liquids expand or contract as the temperature changes."

"The relationship between temperature and the effects it has on the molecules of materials. If the temperature increases, the molecules' vibrations speed up and the object/material expands. If the temperature decreases, then the molecules' vibrations slow down and the object/material shrinks."

"Thermal stress causes strain. Linear expansion and volume expansions are unitless."

"Temperature change is really just the measurement of the volume expansion of the liquid inside of a thermometer compared to the expansion of the thermometer."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I don't understand why the linear expansion coefficient is material dependent."

"Volume expansion--the water inside of a plastic bin. The water was at a lower level in the morning which means it contracted more than the plastic so I would assume it has a larger expansion coefficient?"

"The whole shorter beam needing more temperature change to increase the same length thing really messed me up for a second, because like shorter beam is less mass so like shouldn't it need less energy? But then somebody showed me the way that the equations work and it made sense."

"Volume expansion--I am not sure if it means that as the temperature rises, the volume increases of a substance. For instance, the alcohol in a thermostat rising as the temperature increases."

"How to understand when a coefficient for a solid is higher/lower than a liquid."

"How equations with ΔT can switch back and forth between Celsius and Kelvin units. That kind of tripped me up. I know that either can be used but I still found it a little confusing."

"I found the volume expansion kind of confusing when I first read about it. But after reading it over again I understand volume expansion and the equation for it."

"Everything makes sense."

"I did not get confused by any of this material."

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"Larger the linear expansion, the larger the volume expansion."

"Both coefficients are dependent on the type of material being measured. The coefficient of volumetric expansion is mathematically three times as much as the coefficient of linear expansion."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	***************************** [29]
the same.	**** [4]
a larger.	************ [12]
(Unsure/guessing/lost/help!)	*** [3]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	******************************* [31]
equal to.	*** [3]
greater than.	******* [7]
(Unsure/guessing/lost/help!)	******* [7]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	************* [13]
equal to.	**** [4]
greater than.	************************ [24]
(Unsure/guessing/lost/help!)	******* [7]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [25%]
density: the cool gallon [70%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"Colder gasoline is more dense than warmer gasoline, so another way to look at it is that a cold gallon of gas contains more energy than a warm gallon of gas."

"It's better to purchase a gallon of gasoline cool than when it is warm because gas is more dense when it is cool. Denser fluids have more mass so essentially when you fill your tank with cool gas you get more product for the same price per gallon."

"The hotter it is the more space between molecules. When cool the molecules move slowly when hot they move faster."

"I don't know--HELP!"

"If you buy gas when it is hot out you won't be able to put as much in your tank to make it full because it is hot and expanded. When it cools down, it will condense back its smaller form and you will have the same amount of gas but your tank won't be full?"

"I honestly don’t understand why it's better."

"Isn't mass and density the same?"

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Is the next midterm has only five questions?" (Yes, just like the previous midterm.)

"Please help with the gasoline question! thank you!"

"Please go over volume expansion coefficients."

"No questions today; this material seems to make sense."

"Would you rather live in an unexplored cave or in a treehouse in a remote forest?" (I choose treehouse.)

"How can fuel companies compensate for temperature-dependent volume changes of gas?" (They typically don't; so let the buyer beware.)

"I've been too focused on other classes and this totally slipped my mind."

Physics quiz question: expansion of aluminum rod

Physics 205A Quiz 7, fall semester 2017
Cuesta College, San Luis Obispo, CA

An aluminum bar (linear expansion coefficient 2.3×10^–5 K^–1) has a length of 1.0000 m at 20.0° C. It will have a length of 1.0001 m at:
(A) 4° C.
(B) 16° C.
(C) 20.4° C.
(D) 24° C.

Correct answer: (D)

The relation between the change in length ∆L due to a temperature change ∆T is given by:

α·∆T = ∆L/L,

such that with an increase in length of ∆L = +0.0001 m, then:

∆T = ∆L/(α·L) = (+0.0001 m)/((2.3×10^–5 K^–1)·(1 m)) = +4.347826087 K,

or to one significant figure, the change in temperature is +4 K or +4° C, and so the bar will stretch by 0.0001 m when the temperature is 20.0° C + 4° C = 24° C.

(Response (A) is ΔT; response (B) is 20.0° C – ΔT; response (C) is 20.0° C + (ΔT/10).)

Sections 70854, 70855
Exam code: quiz07Whu7
(A) : 6 students
(B) : 2 students
(C) : 12 students
(D) : 22 students

Success level: 52%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.59

Physics quiz archive: temperature, thermal equilibrium, heat transfers

Physics 205A Quiz 7, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz07Whu7


Sections 70854, 70855 results

0- 6 :
7-12 :	******* [low = 9]
13-18 :	*************
19-24 :	******************* [mean = 18.9 +/- 5.4]
25-30 :	*** [high = 27]

Online reading assignment: temperature

Physics 205A, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on temperature.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"The increase in any one dimension of a solid is called linear expansion. The volume of a normal material also increases as temperature increases, this is known as volume thermal expansion."

"The material-dependent linear expansion coefficient characterizes the response of the material to thermal stress."

"The material in the section relate to experiences in real life, such as liquid expanding when it is cooled and metals cooling and expanding."

"Solids and liquids expand with changes in temperature. A shorter length rod will expand less than a longer length when made of the same material and same change in temperature. ∆L is the change in length due to temperature."

"Thermal stress causes strain. A shorter beam will require a greater change in temperature to expand/contract the same distance as a longer beam."

"I learned that I need cooler gas to save money at the pump."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I don't fully understand volume expansion and feel that in some of the equations I would go go back and forth on what increases or decreases in volume."

"I found thermal stress and strain confusing. I could use further explanation on the equation."

"How you would calculate the amount of expansion that a metal undergoes by given the original length and the temperature?"

"I do not know how all of the equations relate to each other. I think I will have to review more before next class."

"Not as confusing as the last few subjects. Which is a relief for the end of semester. Still, I skimmed it because I'm studying for the quiz."

"Could you go over thermal stress? Maybe do an example problem, the one in the book was a little confusing."

"I didn't understand why the shorter beam will require a greater increase in temperature to expand the same amount as the longer beam."

"Thankfully due to my chemistry class this wasn't very confusing."

"I found most everything confusing from this reading and would benefit greatly from in class examples."

"I haven't gotten much into the reading yet, so it's all a little confusing right now."

"Nothing."

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"They have the same units, K^–1."

"No idea."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	*********************** [23]
the same.	**** [4]
a larger.	****** [6]
(Unsure/guessing/lost/help!)	* [1]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	********************** [22]
equal to.	***** [5]
greater than.	***** [5]
(Unsure/guessing/lost/help!)	** [2]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	************* [13]
equal to.	**** [4]
greater than.	************ [12]
(Unsure/guessing/lost/help!)	***** [5]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [38%]
density: the cool gallon [68%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"I don't know. Is it easier to handle? Maybe cheaper to move."

"The cooler gallon of gasoline would have more density and therefore should have more energy based in that gallon of gasoline."

"Because it has a greater density so the amount of energy within that gallon of gasoline is greater."

"The gasoline is more dense when it is cold and there for the volume is smaller. Although when it is warm the volume is bigger due to it being less dense. The volume might be more but the amount is still the same. Gas stations measure by volume therefore it is better to get gas when it is cold."

"Gasoline (and nearly all objects) expand and become less dense due to heat. Because of this it is more dense during a cool day. Since its density increases and since gas is bought in volume, you get more 'bang for your buck' when you buy on a cooler day."

"How can we figure out the gasoline question? We weren't given the properties of gasoline and how reactive it is at different temperatures."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Thank you for applying concepts to real-life situations."

"Does heat by itself change the atomic structure in solids?" (The space between atoms increases as atoms vibrate more at higher temperatures, because atoms repel each other at close distances, they will spend more time farther apart than closer together as they vibrate more.)

"We will soon be fluent in Greek." (Graecum est; non legitur.)

"Still really enjoying the class."

Physics final exam problem: USS Iowa passing through Panama Canal

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

"USS Iowa Pedro Miguel Locks"
National Archive #NN33300514 2005-06-30 PH1 JEFF HILTON
commons.wikimedia.org/wiki/File:USS_Iowa_Pedro_Miguel_Locks.jpg

One of the widest ships to pass through the Panama Canal was the USS Iowa, which has an outside width of 32.97 m. The narrowest portion of the Panama Canal is through the Pedro Miguel locks, which has an inside width of 33.53 m. Assume that the USS Iowa is entirely made of steel (coefficient of thermal expansion 12×10^–6 K^–1), the Pedro Miguel locks are entirely made of concrete (coefficient of thermal expansion 9.8×10^–6 K^–1), and that these widths were measured at 20° C. Determine whether or not it is plausible for this ship to still pass through the locks, if the ship and the canal are both at the highest reported temperature for this area of 39° C. [*][**][***][****]

[*] wki.pe/USS_Iowa_(BB-61).
[**] wki.pe/Panamax.
[***] engineeringtoolbox.com/linear-expansion-coefficients-d_95.html.
[****] wki.pe/Panama_City.

Solution and grading rubric:

• p:
  Correct. Determines/discusses:
  1. the expansion and/or new width of ship at the warmer temperature; and
  2. the expansion and/or new width of the locks at the warmer temperature; then
  3. compares either the relative difference in expansion, or the new expanded widths, and concludes that the expanded size of the ship will still fit within the expanded size of the locks.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at comparing linear thermal expansion of the ship and the locks.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than linear thermal expansion.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 28 students
r: 9 students
t: 1 student
v: 9 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student):

Physics quiz question: thermal contraction of lid and pot

Physics 205A Quiz 7, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Pot Lid"
Mike Shoup
flic.kr/p/bjbrwB

A tempered glass lid (linear expansion coefficient 3.3×10^–6 K^–1) fits exactly with no gaps on an aluminum pot (linear expansion coefficient 23×10^–6 K^–1) at room temperature (20° C). If both the lid and the pot decrease in temperature to 10° C, the lid will:
(A) have a gap all around it.
(B) still fit exactly.
(C) be squeezed by the pot.
(D) (Not enough information.)

Correct answer (highlight to unhide): (C)

The relation between the change ∆L of a linear dimension L (here, diameter) due to a temperature change ∆T is given by:

α·∆T = ∆L/L,

such that for the lid and the pot:

∆L_lid = L·α_glass·∆T,

∆L_pot = L·α_Al·∆T.

The original diameter of the lid and the pot at the initial temperature of 20° C is the same, and both lid and pot experience the same temperature decrease ∆T. Since the linear expansion coefficient for aluminum is greater than that of glass (α_Al > α_glass), then the diameter of the pot will contract more than the diameter of the lid (∆L_pot > ∆L_lid), such that the lid will be compressed by the pot.

Sections 70854, 70855, 73320
Exam code: quiz07p4sT
(A) : 11 students
(B) : 7 students
(C) : 34 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Physics quiz archive: temperature, thermal equilibrium, heat transfer

Physics 205A Quiz 7, fall semester 2016
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz07p4sT



Sections 70854, 70855, 73320 results

0- 6 :	* [low = 6]
7-12 :	*************
13-18 :	***************
19-24 :	*************** [mean = 18.5 +/- 6.6]
25-30 :	******** [high = 30]

Physics final exam question: thermal expansion of pendulum string

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

A Physics 205A student builds a simple pendulum using a string and a mass, and at a certain temperature it has a period of 1.50 s. As the temperature increases, determine whether the period will increase, decrease, or remain the same. Ignore friction/drag, and only consider the thermal expansion of the string. Explain your reasoning using the properties of simple harmonic motion and thermal expansion.

Solution and grading rubric:

• p:
  Correct. Discusses how the period of a simple pendulum depends on the gravitational acceleration constant (which does not change) and the string length (which expands due to the increase in temperature), such that the period will increase.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying thermal expansion to the simple pendulum parameters.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than applying thermal expansion to the simple pendulum parameters.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: final7rUk
p: 47 students
r: 1 students
t: 15 students
v: 6 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 5612):

Online reading assignment: temperature

Physics 205A, fall semester 2016
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on temperature.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understand how we've tied in stress to strain in solids to thermal stress changing an object's length. The material-dependent linear expansion coefficient characterizes the response of the material to thermal stress."

"When there is a change in temperature a material can expand lengthwise, so there needs to be a little 'give-and-take' room for materials to expand on contract."

"Different materials have different volume/length expansion coefficients, and that multiplied by change in temperature, you can thus get relative change in length or volume."

"When constructing buildings, it is important to take into account how much of a temperature change the area will go through because changes in temperature can cause strain."

"All elements have a coefficient that describes how their expansion/contraction rate is effected by changes in temperature. These coefficients can be used to compare the expansion of two compounds. Such as a thermometer and alcohol or a bucket and water."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I'm a little confused on why it says in solids, the material dependent thermal expansion coefficient for volume is three times the linear expansion coefficient. What is the linear expansion coefficient?"

"I don't really understand how the volume expansion coefficients come into play, I couldn't find the table for it in the book!"

"The difference about volume expansion β and linear expansion α."

"The examples for volume expansion were confusing. If you could go over them that would be great."

"I'm pretty good on this section I think. The example of the thermometer really helped. I was slightly confused about the 'overflow' part at first but I think I am okay on it now."

"I didn't find anything too confusing, but the expansion and contraction at different rates of a liquid inside a solid was a little confusing at first, but I'm pretty sure I understand it now."

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"Linear expansion is the coefficient α (material-dependent), and volume expansion β is 3 times this because the volume is being solved for."

"They are both in units of (°C^–1)."

"K^–1."

"I have no idea :-("

"I honestly do not know."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	*****************  [17]
the same.	*********  [9]
a larger.	************  [12]
(Unsure/guessing/lost/help!)	***  [3]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	******************  [18]
equal to.	*******  [7]
greater than.	****  [4]
(Unsure/guessing/lost/help!)	************  [12]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	***************  [15]
equal to.	** [2]
greater than.	************** [14]
(Unsure/guessing/lost/help!)	********** [10]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [34%]
density: the cool gallon [71%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"When the gallon of gasoline is warm it expands and becomes less dense. Thus you are getting less for your buck."

"When the gasoline is purchased in cool weather, the density is greater."

"Because the density of that 'cold' gallon of gas would take up less volume than a normal gallon of gas, you would be getting more gas since they give you the same volume of gas either way."

"Because it will take up less room in the gas tank. Since the warm gasoline has expanded more then the colder gasoline, it will take up more room with less material, indicating you're at a full tank, when you could have more if it was colder."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"A little clarification on linear thermal expansion would be helpful."

"I am confused with the gasoline problem and why temperature causes a difference."

"Wouldn't it be easier to keep the gas warmer or cooler so you could sell a precise amount?"

"I'm having trouble understanding why gas stations can't regulate temperature more accurately. Does it really make that much of a difference?" (For filling up your car, not very much. But for selling vast amounts of warm gas to millions of customers, yes, there is a significant profit in the total difference.)

"The examples for volume expansion were confusing. If you could go over them that would be great."

"Just the normal examples usually done in class will help me."

"Interested in going through the problems on this page briefly in class if there's time."