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13.2 Thermal expansion of solids and liquids  (Page 2/10)

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Thermal expansion coefficients at 20 º C size 12{"20"°C} {} Values for liquids and gases are approximate.
Material Coefficient of linear expansion α ( 1 / º C ) size 12{α \( 1/°C \) } {} Coefficient of volume expansion β ( 1 / º C ) size 12{β \( 1/°C \) } {}
Solids
Aluminum 25 × 10 – 6 size 12{"25" times "10" rSup { size 8{–6} } } {} 75 × 10 – 6 size 12{"75"´"10" rSup { size 8{ +- 6} } } {}
Brass 19 × 10 – 6 size 12{"19" times "10" rSup { size 8{–6} } } {} 56 × 10 – 6 size 12{"56"´"10" rSup { size 8{ +- 6} } } {}
Copper 17 × 10 – 6 size 12{"17" times "10" rSup { size 8{–6} } } {} 51 × 10 – 6 size 12{"51" times "10" rSup { size 8{–6} } } {}
Gold 14 × 10 – 6 size 12{"14" times "10" rSup { size 8{–6} } } {} 42 × 10 – 6 size 12{"42" times "10" rSup { size 8{–6} } } {}
Iron or Steel 12 × 10 – 6 size 12{"12" times "10" rSup { size 8{–6} } } {} 35 × 10 – 6 size 12{"35" times "10" rSup { size 8{–6} } } {}
Invar (Nickel-iron alloy) 0 . 9 × 10 – 6 size 12{0 "." 9 times "10" rSup { size 8{–6} } } {} 2 . 7 × 10 – 6 size 12{2 "." 7 times "10" rSup { size 8{–6} } } {}
Lead 29 × 10 – 6 size 12{"29" times "10" rSup { size 8{–6} } } {} 87 × 10 – 6 size 12{"87" times "10" rSup { size 8{–6} } } {}
Silver 18 × 10 – 6 size 12{"18" times "10" rSup { size 8{–6} } } {} 54 × 10 – 6 size 12{"54" times "10" rSup { size 8{–6} } } {}
Glass (ordinary) 9 × 10 – 6 size 12{9 times "10" rSup { size 8{–6} } } {} 27 × 10 – 6 size 12{"27" times "10" rSup { size 8{–6} } } {}
Glass (Pyrex®) 3 × 10 – 6 size 12{3 times "10" rSup { size 8{–6} } } {} 9 × 10 – 6 size 12{9 times "10" rSup { size 8{–6} } } {}
Quartz 0 . 4 × 10 – 6 size 12{0 "." 4´"10" rSup { size 8{ +- 6} } } {} 1 × 10 – 6 size 12{1 times "10" rSup { size 8{–6} } } {}
Concrete, Brick ~ 12 × 10 – 6 size 12{ "~" "12"´"10" rSup { size 8{ +- 6} } } {} ~ 36 × 10 – 6 size 12{ "~" "36" times "10" rSup { size 8{–6} } } {}
Marble (average) 7 × 10 – 6 size 12{2 "." 5´"10" rSup { size 8{ +- 6} } } {} 2 . 1 × 10 – 5 size 12{7 "." 5 times "10" rSup { size 8{–6} } } {}
Liquids
Ether 1650 × 10 – 6 size 12{"1650" times "10" rSup { size 8{–6} } } {}
Ethyl alcohol 1100 × 10 – 6 size 12{"1100" times "10" rSup { size 8{–6} } } {}
Petrol 950 × 10 – 6 size 12{"950" times "10" rSup { size 8{–6} } } {}
Glycerin 500 × 10 – 6 size 12{"500" times "10" rSup { size 8{–6} } } {}
Mercury 180 × 10 – 6 size 12{"180" times "10" rSup { size 8{–6} } } {}
Water 210 × 10 – 6 size 12{"210" times "10" rSup { size 8{–6} } } {}
Gases
Air and most other gases at atmospheric pressure 3400 × 10 – 6 size 12{"3400" times "10" rSup { size 8{–6} } } {}

Calculating linear thermal expansion: the golden gate bridge

The main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from – 15 º C size 12{–"15"°C} {} to 40 º C size 12{"40"°C} {} . What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

Strategy

Use the equation for linear thermal expansion Δ L = αL Δ T size 12{ΔL=αL`ΔT} {} to calculate the change in length , Δ L size 12{ΔL} {} . Use the coefficient of linear expansion, α size 12{α} {} , for steel from [link] , and note that the change in temperature, Δ T size 12{ΔT} {} , is 55 º C size 12{"55"°C} {} .

Solution

Plug all of the known values into the equation to solve for Δ L size 12{ΔL} {} .

Δ L = αL Δ T = 12 × 10 − 6 º C 1275 m 55 º C = 0 . 84 m. size 12{ΔL=αLΔT= left ( { {"12" times "10" rSup { size 8{ - 6} } } over {°C} } right ) left ("1275 m" right ) left ("55"°C right )=0 "." "84 m"} {}

Discussion

Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.

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Thermal expansion in two and three dimensions

Objects expand in all dimensions, as illustrated in [link] . That is, their areas and volumes, as well as their lengths, increase with temperature. Holes also get larger with temperature. If you cut a hole in a metal plate, the remaining material will expand exactly as it would if the plug was still in place. The plug would get bigger, and so the hole must get bigger too. (Think of the ring of neighboring atoms or molecules on the wall of the hole as pushing each other farther apart as temperature increases. Obviously, the ring of neighbors must get slightly larger, so the hole gets slightly larger).

Thermal expansion in two dimensions

For small temperature changes, the change in area Δ A size 12{ΔA} {} is given by

Δ A = 2 αA Δ T , size 12{ΔA=2αAΔT} {}

where Δ A size 12{ΔA} {} is the change in area A size 12{A} {} , Δ T size 12{ΔT} {} is the change in temperature, and α size 12{α} {} is the coefficient of linear expansion, which varies slightly with temperature.

Part a shows the outline of a flat metal plate before and after expansion. After expansion, it has the same shape and ratio of dimensions as before, but it takes up a greater area. Part b shows the outline of a flat metal plate with a hole in it, before and after expansion. The hole expands. Part c shows the outline of a rectangular box before and after expansion. After expansion, the box has the same proportions as before expansion, but it has a greater volume.
In general, objects expand in all directions as temperature increases. In these drawings, the original boundaries of the objects are shown with solid lines, and the expanded boundaries with dashed lines. (a) Area increases because both length and width increase. The area of a circular plug also increases. (b) If the plug is removed, the hole it leaves becomes larger with increasing temperature, just as if the expanding plug were still in place. (c) Volume also increases, because all three dimensions increase.

Thermal expansion in three dimensions

The change in volume Δ V size 12{ΔV} {} is very nearly Δ V = 3 α V Δ T size 12{ΔV=3αVΔT} {} . This equation is usually written as

Δ V = βV Δ T , size 12{ΔV=βVΔT} {}

where β size 12{β} {} is the coefficient of volume expansion    and β ≈ 3α size 12{β approx 3α} {} . Note that the values of β size 12{β} {} in [link] are almost exactly equal to 3α size 12{3α} {} .

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
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how many start and codon
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what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
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Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
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pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
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Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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