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Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.

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Liquids and solids expand with increasing temperature, because the kinetic energy of a body’s atoms and molecules increases. Explain why some materials shrink with increasing temperature.

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Problems&Exercises

The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35 . 0 º C size 12{"35" "." 0°C} {} . What will its height be on a day when the temperature falls to 10 . 0 º C size 12{–"10" "." 0°C} {} ? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

169.98 m

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How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15 º C size 12{"15"°C} {} ? Its original height is 321 m and you can assume it is made of steel.

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What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37 . 0 º C size 12{"37" "." 0°C} {} to 40 . 0 º C size 12{"40" "." 0°C} {} , assuming the mercury is unconstrained?

5 . 4 × 10 6 m size 12{5 "." 4 times "10" rSup { size 8{ - 6} } " m"} {}

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How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35 . 0 º C size 12{"35" "." 0°C} {} greater than when they were laid? Their original length is 10.0 m.

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You are looking to purchase a small piece of land in Hong Kong. The price is “only” $60,000 per square meter! The land title says the dimensions are 20 m × 30 m . size 12{"20"" m "` times "30 m" "." } {} By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was 20 º C size 12{"20"°C} {} above normal?

Because the area gets smaller, the price of the land DECREASES by ~ $ 17 , 000 . size 12{ "~" $"17","000" "." } {}

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Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1 . 00 º C . size 12{1 "." "00"°C "." } {} Note that this calculation is only approximate because ocean warming is not uniform with depth.

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Show that 60.0 L of gasoline originally at 15 . 0 º C size 12{"15" "." 0°C} {} will expand to 61.1 L when it warms to 35 . 0 º C, size 12{"35" "." 0°"C,"} {} as claimed in [link] .

V = V 0 + Δ V = V 0 ( 1 + β Δ T ) = ( 60 . 00 L ) 1 + 950 × 10 6 / º C 35 . 0 º C 15 . 0 º C = 61 . 1 L
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(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0 º C size 12{0°C} {} . What is their difference in length at 22 . 0 º C size 12{"22" "." 0°C} {} ? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

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(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5 . 00 º C, size 12{5 "." "00"°"C,"} {} how much will overflow when its temperature reaches 22 . 0 º C size 12{"22" "." 0°C} {} ? (b) How much less water would overflow under the same conditions?

(a) 9.35 mL

(b) 7.56 mL

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Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at 10 . C . size 12{"10" "." 0°C "." } {} What volume of radiator fluid will overflow when the radiator and fluid reach their 95 . C size 12{"95" "." 0°C} {} operating temperature, given that the fluid’s volume coefficient of expansion is β = 400 × 10 6 / º C size 12{β="400"´"10" rSup { size 8{ +- 6} } /°C} {} ? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than 95 . 0 º C . size 12{"95" "." 0°C "." } {}

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A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the 350 cm 3 size 12{"350"" cm" rSup { size 8{3} } } {} of coffee is in a 7.00-cm-diameter cup and decreases in temperature from 95 . 0 º C size 12{"95" "." 0°C} {} to 45 . 0 º C . size 12{"45" "." 0°C "." } {} (Most of the drop in level is actually due to escaping bubbles of air.)

0.832 mm

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(a) The density of water at 0 º C size 12{0°C} {} is very nearly 1000 kg/m 3 size 12{"1000"" kg/m" rSup { size 8{3} } } {} (it is actually 9 99 . 84 kg/m 3 size 12{9"99" "." "84 kg/m" rSup { size 8{3} } } {} ), whereas the density of ice at 0 º C size 12{0°C} {} is 9 17 kg/m 3 size 12{9"17 kg/m" rSup { size 8{3} } } {} . Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.) (b) What are the implications of this result for biological cells that are frozen?

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Show that β , size 12{β»3α,} {} by calculating the change in volume Δ V size 12{ΔV} {} of a cube with sides of length L . size 12{L "." } {}

We know how the length changes with temperature: Δ L = αL 0 Δ T size 12{ΔL=αL rSub { size 8{0} } ΔT} {} . Also we know that the volume of a cube is related to its length by V = L 3 size 12{V=L rSup { size 8{3} } } {} , so the final volume is then V = V 0 + Δ V = L 0 + Δ L 3 size 12{V=V rSub { size 8{0} } +ΔV= left (L rSub { size 8{0} } +ΔL right ) rSup { size 8{3} } } {} . Substituting for Δ L size 12{DL} {} gives

V = L 0 + αL 0 Δ T 3 = L 0 3 1 + α Δ T 3 . size 12{ V= left (L rSub { size 8{0} } +αL rSub { size 8{0} } ΔT right ) rSup { size 8{3} } =L rSub { size 8{0} rSup { size 8{3} } } left (1+αΔT right ) rSup { size 8{3} } "." } {}

Now, because α Δ T size 12{αΔT} {} is small, we can use the binomial expansion:

V L 0 3 1 + 3αΔT = L 0 3 + L 0 3 Δ T . size 12{V approx L rSub { size 8{0} } rSup { size 8{3} } left (1+3αΔT right )=L rSub { size 8{0} rSup { size 8{3} } } +3αL rSub { size 8{0} } rSup { size 8{3} } ΔT} {}

So writing the length terms in terms of volumes gives V = V 0 + Δ V V 0 + V 0 Δ T , size 12{V=V rSub { size 8{0} } +ΔV approx V rSub { size 8{0} } +3αV rSub { size 8{0} } ΔT,} {} and so

Δ V = βV 0 Δ T V 0 Δ T , or β . size 12{ΔV=βV rSub { size 8{0} } ΔT approx 3αV rSub { size 8{0} } ΔT,`"or"`β approx 3α} {}
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Questions & Answers

please I didn't not understand the concept of the physical therapy
John Reply
physiotherapy - it's a practice of exercising for healthy living.
Paul
what chapter is this?
Anderson
please I have probably with calculate please can you please and help me out
John Reply
Sure
Gift
What is Boyce law
Sly Reply
how to convert meter per second to kilometers per hour
grace Reply
Divide with 3.6
Mateo
multiply by (km/1000m) x (3600 s/h) -> 3.6
Muhammad
2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
Adarsh
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
Abdul
dimensions v²=u²+2at
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
Daniel Reply
How do you calculate precision
Sacky Reply
what module is that?
Fillemon
Chemisty 1A?
Fillemon
No it has something to do with measurements bro... What we did today in class
Sacky
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Fillemon
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
Sacky
I eat ass
Anderson
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
Fillemon
I'll eat your mom's ass with a side of tendies
Anderson
@Fillemon Nanwaapo
Anderson
lol, hush
Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
Because there's an equal number of negative and positive charges... objects are neutral in nature
NELSON
when a ball rolls on a smooth level ground,the motion of its centre is?
Mary Reply
what is electro magnetic field?
Mary
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
NELSON
Electromagnetic field is caused by moving electric charge
Muhammad
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh
what's the relationship btw displacement and position
Declan Reply
displacement is the change of position 8======✊=D 💦💦
Anderson
what is the meaning of elasticity
Pele Reply
is the ability of a material to or any object to expand to a limit point
king
this is about kinematics you bonk
Emi
what does emf/R mean
Eze Reply
What is work
Wisdom Reply
work is the product of force and perpendicular distance
DAVID
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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