What is Linear expansion: Definition and 55 Discussions
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves. Substances which contract with increasing temperature are unusual, and only occur within limited temperature ranges (see examples below). The relative expansion (also called strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature. As energy in particles increases, they start moving faster and faster weakening the intermolecular forces between them, therefore expanding the substance.
So if I am understanding the question correctly, I need to find the change in temperature that causes one rights outer radii to be the same as another rings inner radii.
Now what I tried is two equations
change length_1= a_1*original length_inner * change in temp
change length_2= a_2*original...
Here I'm going to show all that I've understood -
1.
2.
3.
What I've attempted -
L = Lo (1+ α * ẟT)
ẟT = 150°C - 15°C = 135°C
(Steel) L = ẟL (1 + 11 * 10^-6 * 135)
(Copper) L = ẟL (1 + 17 * 10^-6 * 135)
This doesn't get me anywhere, obviously.
Am I supposed to understand from the...
Homework Statement
[/B]
Oceans cover 2/3 of the earth’s surface, with an average depth of 3.7 km. The average surface temperture is 17◦ C. Taking this temperature as representative of the entire ocean, and knowing that the coefficient of volume expansion for water at this temperature is β = 1.7...
Homework Statement
A rod of length ##L_o## is kept on a friction-less surface. The coefficient of linear expansion for the material of the rod is ##\alpha##. The the temperature of the rod is increased by ##\Delta T## the strain developed in the rod will be?
Homework Equations
$$ \Delta L=...
Homework Statement
http://i.imgur.com/swYr8aw.jpg
Homework Equations
delta L=LalphadeltaT
The Attempt at a Solution
sorry for s**ty handwriting look at #8[/B]
http://i.imgur.com/59Ew8vJ.jpg
edit:click the links please. The forum software cropped the quality of the photo.
Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...
ΔL=LαΔT
The concept is interesting and applying its formula isn't even tedious, but what are the real factors that determine α here? I understand that thermal expansion is a direct consequence of the average separation between atoms. And that the coefficient can be found through different...
Homework Statement
An automobile windshield has the dimensions 60cm by 150 cm. What minimum tolerance is needed in mm to prevent the windshield from breaking if the temperature changes by 200F (the linear expansion coefficient of glass is 9*10^-6 C-1)
Homework Equations
deltaL=alpha*Li*deltaT...
Homework Statement
An aluminium container (cylinder) is filled with glycerine. Glycerine has a volume expansion coefficient of 4.85 × 10^-4 (°C)-1. Aluminium has a linear expansion coefficient of 2.40 x 10^-5 (°C)-1. At a temperature of 20.00°C the scale on the side of the aluminium container...
Homework Statement
An object has a density of 1250 kg /m3 at 10◦C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25◦C?Homework Equations
V=βV0ΔT
V(T)=(1+β(Δt))V0
The Attempt at a Solution
How I got the answer is that I used...
An object has a density of 1250 kg m3 at 10◦C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25◦C?
I have tried using the equation ΔL=αL° ΔT but this equation has nothing to do with density.
the answer should be: 1248.6
Your...
A uniform rod of a length of 2.0 m at 5ºC has a coefficient of linear expansion of 5.0 × 10^-4 K^-1. How much longer is it when the temperature is 35ºC?
I want to know the procedure to solve this problem
This isn't hw, but I'm wondering how to solve it when it's K ^-1
Just trying to get some...
Homework Statement
A 25.0 g copper ring at 0°C has an inner diameter of D = 2.71585 cm. A hollow aluminum sphere at 88.0°C has a diameter of d = 2.72019 cm. The sphere is placed on top of the ring (see the figure), and the two are allowed to come to thermal equilibrium, with no heat lost to the...
Homework Statement
A clock based on a simple pendulum is situated outdoors in Anchorage, Alaska. The pendulum consists of a mass of 1.00kg that is hanging from a thin brass rod that is 2.000m long. The clock is calibrated perfectly during a summer day with an average temperature of 19.5°C...
Homework Statement
Measurements of XRay scattering from a metal are made. The bragg peaks are θ = 53° and 48° for temperatures of 300K and 1272K.
What is the linear expansion coefficient?
Homework Equations
linear expansion coef is given by (1/L)(dL/dT)
Bragg equation (differential...
An 8000kg aluminum flagpole 100m long is heated by the sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24*10-6 /°C. (The density of aluminum is 2.7*103 kg/m3 and 1 atm = 1.0*105 N/m2)
I know w=PΔV, and I know V at 10°C =...
Hi,
I was just wondering if it was possible to change the linear expansion (and expansion in volume as volume expansion is three times the linear expansion) of a certain material. The coefficient being;
a = (Final Length - Initial Length)/ (Initial length) * (ΔT)
Is it possible to...
Homework Statement
Original Length = 6.736 mm
Final Length = 7.802 mm
Initial Temp = 21.7 C
Final Temp = 99.5 C
Homework Equations
Coefficient = (Change in Length) / (Original Length * Change in Temperature)
The Attempt at a Solution
Change in Length = 7.802 - 6.736 = 1.066 mm...
Homework Statement
"A composit bar is made of two metals joined in series, with coefficients of linear thermal expansion 2.2E-5 and 0.9E-5 K^-1 respectively. The bar expands by 0.5% in length with a temperature rise of 500 K. Calculate the ratio of the initial lengths of the two metal...
Ok So I was told to think about what would happen if you tried measure something with a metal ruler or tape measure in an environment that would cause negative linear expansion; so the ruler gets smaller. How would the accuracy be affected if the tape measure/ ruler was calibrated at a greater...
Imagine we are at the center of a sphere of radius R containing a mass M.
The Beckenstein bound states that the entropy inside that sphere, S, must be given by the inequality:
\large S \leq \frac{2 \pi k c R M}{\hbar}.
In order to maximise the entropy we need to fill the sphere of radius R...
Homework Statement
A certain metal has a coefficient of linear expansion of 2.00 × 10-5 K-1. It has been kept in a laboratory oven at 325°C for a long time. It is now removed from the oven and placed in a freezer at -145°C. After it has reached freezer temperature, the percent change in its...
Homework Statement
The area of a copper plate is 0.1m^2. The coefficient of linear expansion (would be given in the problem). if the temperature increases from 22C to 100C, what is the new area of the copepr plate?
Homework Equations
L= LTá : but as alfa is linear Expansion coff...
Homework Statement
A weather balloon is designed to expand to a maximum radius of 26m hen in flight at its working altitude where the air pressure is .026 atm and the temperature is 229K
If the balloon is filled at atmospheric pressure and 434K, what is its radius at lift off...
Homework Statement
The question i need help on is question 6 part (c). I think I need to use the equation:
2. Equations used:
\DeltaL = \alphaL\DeltaT
Linear expansion of steel: 12x10 K^-1 (\alpha)
Density of steel: 7800
3. My attempted solution:
I tried substituting in the...
Hi there :)
At 19\circC, a rod is exactly 20.08 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 285\circC, where the rod now measures 20.18 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?
I used the...
Homework Statement
A highway is made of concrete slabs that are 15 m long at 20.0°C. (a) If the temperature range at the location of the highway is from -20.0°C to +40.0°C, what size expansion gap should be left (at 20.0°C) to prevent buckling of the highway? (b) How large are the gaps at...
Homework Statement
A girder made of steel. The length of the girder is 3.77 m. In the middle of the girder there is a fracture. The temperature rises 32° C.
Homework Equations
Find the height that the girder rises from the middle, if it is fixed at both ends. The linear expansion...
Homework Statement
A steel balk has a length of 50.485 m at the temperature of 5.0 oC.
Homework Equations
What would be the length of the balk at the temperature of -22 oC, when the coefficient of linear expansion (α ) is 0.000012 / oC?
The Attempt at a Solution
50.469m?
Lfinal-Linitial=a*Linitial*(Tfinal-Tinitial)
?
lets assume the linear expansion coefficient for sth is (0.0001) kelvin^-1, its (1) meter long and its at (10) kelvin.
now let's calculate its length when its at (20) kelvin in 2 different ways:
first way: L1-1 = 0.0001*1*10
so: Lfinal=1.001...
Hello. I have this easy question in linear expansion. Yeah, it's easy but I am really dumb in physics. Please help..
Homework Statement
Rod A which is 30 cm long, expands by 0.045 cm when heated from 0 degrees Celsius to 100 degrees Celsius. Rob B also 30 cm long expands by 0.075 cm for the...
Homework Statement
Steel rails for a train track are laid in a region subject to extremes of temperature. The distance from one juncture to the next is 5.4 m, and the cross-sectional area of the rails is 60 cm2. If the rails touch each other without buckling at the maximum temperature, 51...
Homework Statement
At 20° C, a rod is exactly 20.05 cm long on a steel ruler. Both the rod and the ruler are placed in an over at 250° C, where the rod now measure 20.11 cm on the same ruler. What is the coefficient of linear expansion for he material of which the rod is made?
Homework...
Homework Statement
"A round plug made of brass has a diameter of 87.53 mm at 20 C. The plug is to be fitted to a steel ring of inside diameter 87.43 mm. To what common temperature must they be brought in order to fit?"
The linear coefficient of expansion for brass:
\alpha_{b} = 18.7 \cdot...
Homework Statement
A glass tube of radius 0.80cm contains liquid mercury to a depth of 64.0cm at 12degrees. Find the depth of the mercury column at 100degrees. Assume that the linear expansion coefficient of the glass is 10x10^-6K-1 and the linear expansion coefficient of mercury is...
Hey guys, the following is a HW question I believe I am doing correctly but I'm not getting the correct answer, any input would be appreciated!
Q
uestion: A rod made from a particular alloy is heated from 27.5 °C to 127 °C. Its length increases by 9.13 x 10-4 m. The rod is then cooled from...
If a steel tower stands 300 m tall on an average day, 22 degrees C, how much taller is it on a hot day, 40 degrees C?
The coefficient of linear expansion for steel is 11 (10)^-6/degree C.
The equation for change in length of a material is (change in L) = L * α * (change in T)
I know...
Homework Statement
A brass plug is to be placed in a ring made of iron. At room temperature (20°C), the diameter of the plug is 8.749 cm and that of the inside of the ring is 8.739 cm. They must both be brought to what common temperature in order to fit?
It's a linear expansion problem...
Homework Statement
Two metre rulers made of metal of linear expansivity 25*10-6/degrees C are calibrated at 0 deg celsius.
One end of each of the metre rulers is fixed to a vertical wall and held side by side horizontally.
One of the meter rulers is maintained at 0 deg.C and the other at 100...
Homework Statement
Question: If the linear expansivity of aluminium is 24 x 10-6 K-1, how much does the aluminium expand during the heating?
Homework Equations
As far as additional information on the question goes;
An aluminium rod is heated from 15 degrees Celsius to 120 degrees Celsius. The...
Metal rod A is 0.300 m long expands by 6.50x10^-4 m when its temperature is increased by 100 degrees Celsius. Another rod made of different metal B and of the same length expands by 3.50x10^-4 m for the same increase in temperature. A third rod C, also 0.300 m long, is made up of pieces of the...
1.An aluminum rod and a copper rod have the same length of 100 cm at 5 degrees Celsius. At what temperature would one of the rods be 0.5mm longer than the other? Which rod is longer at such temperature?
how can i solve this? i have no idea.. help !
On a hot day where the temperature is 32 degrees celsius, the distance between two lamp posts on the road is 30m as measured by a metal tape whose coefficient of linear expansion is hypothetically 50 x 10^-6 /degree Celsius. If the tape gives its correct reading at 20 degrees celcius, what is...
Homework Statement
An automobile windshild has dimensions of 60 cm by 150 cm. What minimum tolerance in mm is needed to prevent the windshield from breaking if the temperature changes by 200 degrees Farenheight? (The linear expansion coeffecient of galss is 9 x 10^{}-6
(C)-1
Homework...
Given: The linear expansion coefficient of glass is 9 × 10−6 (◦C)−1. An automobile windshield has dimensions of 60 cm by 400 cm. What minimum spacing around the wind-shield is needed to prevent the windshield from breaking if the temperature changes by 150◦F? Answer in units of mm.
I...
Homework Statement
A steel ball bearing is encased in a Pyrex glass cube 1.0 cm on a side. At 390K , the ball bearing fits tightly inside the cube.
At what temperature will it have a clearance of 0.90pico meters all around?
Homework Equations
Coefficent of linear expansion...
linear expansion problem...urgent!
Homework Statement
A concrete highway is built of slabs 12m long (20 degrees C). How wide should the expansion cracks between the slabs be (at 15 C) to prevent buckling if the range of temperature is - 30 C to 43 C?
Homework Equations
change in...
at 20C a rod is exactly 20.05cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270C, where the rod now measures 20.11cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?
Homework Equations...
I have this multiple choice question:
Two thin strips of iron and zinc are riveted together to form a bimetallic strip that bends when heated. The iron is on the inside of the bend because:
(A) it has a higher coefficient of linear expansion
(B) it has a lower coefficient of linear...