Expansion Definition and 1000 Threads

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.

View More On Wikipedia.org
Recent contents Top users
  1. I

    Finding the Limit of a Sequence with Taylor Expansion and Exponentials

    Homework Statement Let ##x_n## be the solution to the equation ##\left( 1+\frac{1}{n} \right)^{n+x} = e## Calculate ##\lim_{n\to \infty} x_n## Homework Equations N/A The Attempt at a Solution Since ##\lim_{n \to \infty} \left(1+ \frac{1}{n} \right) = e## that tells me that ##\lim_{n\to...
  2. Jorrie

    Insights Approximate LCDM Expansion in Simplified Math - Comments

    Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math Continue reading the Original PF Insights Post.
  3. O

    Big Bang Expansion Creates Planets?

    If I understand what the BB Theory proposes, all the universe was originally confined to the size of something very small, like a dot or an atom. This small dot or atom or whatever was said to explode, although some say there was no explosion in the sense of a bomb going off, but would be more...
  4. A

    Comparing Coefficients of Thermal Expansion in Solid Rods

    Homework Statement the difference in length between an aluminium rod and a copper rof at 0 degreeC is 2cm. If they have the same difference in length at any temperature difference, what are the length of the 2 rods at 0 degreeC.? Al - expansivity = 20*10^-4 K^-1 Cu- expansivity= 15*10^-6 K^-1...
  5. B

    Confused - Pressure in a canister?

    A manufacturer quotes a standard CO2 canister contains 16g of CO2 at a volume of 20cm^3. So I need to calculate the pressure in the canister... Using ideal gas law P = nRT/V n = 0.364mol (16 of co2) R = 8.314 J/Kmol (universal gas constant) T = 294k (gas is at room temp 21 deg C) V = 20cm3...
  6. ComaBerenices

    Proportions and other Stuff about Expansion

    I'm not too well read in cosmology, but I know the universe is presumed to be homogeneous in space but not in time, therefore the curvature of the universe can essentially be calculated under one mean. I just have a few questions about how the universe expands and whether some proportions are...
  7. G

    Does space expansion affect the rate of time?

    Time can have 2 different connotations. One is inherent to an entity in spacetime by itself, say a lonely radioactive atom. It may decay or it may not decay, independently of what's going on around it. But another involves interactions between particles, for example "it takes 60 seconds for...
  8. ognik

    MHB Simplifying Binomial Expansion for Relativistic Velocity Sum

    Hi, given the sum of 2 relativistic velocities $ \frac{w}{c} = \frac{\frac{u}{c}+\frac{v}{c}}{1+\frac{uv}{c^2}}$ and setting $ \frac{u}{c}= \frac{v}{c} = (1-\alpha)$, find $ \frac{w}{c} $ in powers of $ \alpha $ through $ {\alpha}^{3} $ I used a binomial expansion to get a tidy intermediate...
  9. P

    Gimbal Joint analysis (Thermal expansion)

    Good day, I am currently developing a thermal expansion analysis of a pipe line, I need to validate if the current installed Gimbal joints will withstand those conditions. These gimbal joints just allow angular movement. Is there any software or method that can help me as reference for this...
  10. **Mariam**

    Calculating linear expansion of windshield 60cm*150cm

    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...
  11. ognik

    MHB Prove L'Hopitals rule using Taylors expansion

    I'm given that $ \frac{f\left({x}_{o}\right)}{g\left({x}_{o}\right)} =\frac{0}{0} $ and asked to show that: $ \lim_{{x}\to{{x}_{0}}}\frac{f\left({x}\right)}{g\left({x}\right)} = \lim_{{x}\to{{x}_{0}}} \frac{f^{'} \left({x}\right)}{g^{'}\left({x}\right)} $ This should be easy, but I suspect...
  12. S

    Why is the internal energy change of free expansion 0?

    ΔU=q-w and in a free expansion w=0 and Free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. Does this mean that free expansion is an isolated system? Meaning the walls of the container are adiabatic in which no heat can enter the system and so q=0...
  13. ognik

    MHB Find average from a Taylor's expansion

    The question is: Expand a function $ {\phi}(x, y, z) $ by Taylor’s expansion. Evaluate $ \overline{\phi} $ the average value of $ {\phi} $, averaged over a small cube of side $ l $ centered on the origin and show that the Laplacian of  is a measure of deviation of  $ {\phi} $ from (0, 0...
  14. Berenices

    Are Universal Oscillations Causing Changes in Cosmological Expansion?

    Hey all, I was reading up on some discoveries made in cosmology. http://iopscience.iop.org/1538-3881/149/4/137/ This could easily be due to observational error, but I was wondering whether something such as this is possible in our current models of expansion and dark energy without having to...
  15. CjCastro

    Photons and Space-Time Expansion

    Hello all! I apologize if this question has been asked already, anyways I have a conceptual question, let me see if I can explain it properly. So we know that the universe is expanding at a rapid rate, very rapid in fact, space and time itself is expanding; and we also know the maximum speed...
  16. Berenices

    How Does the Expansion of the Universe look?

    Hey all, I was reading a webpage which I found rather confusing: http://www.dailygalaxy.com/my_weblog/2015/06/todays-galaxy-insight-the-lonely-galaxies.html The problem I found with this is that the guy (who is a famous theoretical physicist) is stating that because the objects will be traveling...
  17. S

    Cosmological Expansion: Is There a Limit?

    is there any limit to cosmological expansion?
  18. G

    Isn't space expansion logically required?

    If spacetime is a single entity, shouldn't it be simply logical that space expands? We know that spacetime is one single entity, there is no space AND time, but just spacetime. As we move towards the future, more time gets 'created', the more we get into the future away from the Big Bang, the...
  19. kinbeat

    Comp Sci How to Implement Laplace Expansion in Fortran for Matrix Determinants?

    Hi, I'm dealing with an exam problem (which i have 8 days to solve, with no outside help limitations), which is to write a fortran95 program that solves linear systems. the first part asks to find the determinant of a NxN matrix with the laplace expansion, implementing it as a recursive...
  20. A

    Thermal Expansion of piano wire

    I'd like to setup an Excel spreadsheet to demonstrate the expected change in string frequency due to small changes in temperature. How should I go about doing this? This is the data from the piano that I can gather: -string length -string diameter -string area -string/partial frequency How do...
  21. R

    What force is needed to overcome expansion?

    As I understand it gravitationally bound objects don’t move apart with expansion. So I was wondering, assuming constant acceleration of expansion, what is the minimum gravitational force required to keep objects from moving apart?
  22. A

    Does universe expansion separate photons, traveling parallel?

    I understand that the force of gravity prevents galaxies from expanding, as space increases. However, I question if universal expansion separates photons (electromagnetism), as they are traveling along parallel paths (Would the normal distance between them increase over time)? Thank you.
  23. Feeble Wonk

    Spatial Expansion Interpretation with Quantum Graphity Model

    The way the Quantum Graphity model has been explained to me is that I should picture "space" as being represented by the quantum graph, with points in the graph being nodes of communication/interaction between various fields. So, as space expands, do the points become farther apart, separated by...
  24. V

    A layman's guide to the accelerating expansion of space

    I am writing this thread because I have too often had to explain this and I basically wanted to have a resource available to direct folks to, and, frankly, the Wikipedia topics on this are pretty vague on the explanation. Any questions, comments, or corrections are greatly appreciated. So, here...
  25. Jimster41

    Does expansion a(t) affect QM probability density?

    I'm picturing a comoving particle, meaning at rest with respect to CMB? Does expansion affect the probability density, density current? I can't see how it wouldn't? But then it seems like there would have to be a uniform negative probability density current everywhere.
  26. Shafat Hasan

    Speed and / or expansion rate of the Universe?

    Is it true that the universe itself expands faster than c = 3 × 10^8 m/s at some places / areas / points. I have heard it but wasn't able to confirm. Because outside of the the universe, there ain't anything as far as we understand and hence the universe should not have to follow any law as...
  27. F

    What is the role of dark energy in the expansion of the universe?

    If we look at our own solar system, our sun is pushing gasses outwards as solar winds. Our Galaxy has what around 100 billion stars? All which most likely follow suit expelling their own atmospheres outwards as solar winds. The ratio of stars being born to stars dying is something like 350:1...
  28. Q

    Coeff. of Linear Exp. of glass from vol expansion of content

    Homework Statement The coefficient of volume expansion of olive oil is 0.68 × 10-3 K-1. A 1-liter glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25 C°. As a result, 0.0167 liters of...
  29. G

    Could energy be extracted from spacetime expansion?

    Purely theoretically, could it be possible to extract energy from spacetime's expansion? Like, say, imagine two celestial bodies far away enough so that they are not bound enough by gravity, they get farther away from each other due to spacetime expansion. We tie them to each other with a rope...
  30. A

    Cumulant Expansion: How Does It Work?

    Can anyone tell me how a cumulant expansion, like the one on the picture, works? If I take the logarithm of the expansion in eq. (29-26) I don't get what is stated below. What should I do to get that?
  31. S

    Does universe expansion create new points in space?

    apologies if this has been asked before: I'm trying to understand the expansion of the universe and i was wondering. . . . as the universe expands, are new points of space (or is it spacetime) being created? if the answer is 'yes', what are the ramifications of this? my understanding...
  32. kelvin490

    Why dU may not equals dW in free expansion?

    From a video lecture, it is mentioned that "dU≠dW in Joule's free expansion if the process is irreversible and adiabatic" Mentioned in around 36:00-38:00 in the video: What I would like to ask is why in this irreversible adiabatic process, dU≠dW? Is it because the W here doesn't include other...
  33. B

    Thermal expansion (Simple) (attempt posted)

    Homework Statement I'm looking for a good explanation, not interested in the answer. A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C. How much more interior space does the dome have in...
  34. nuuskur

    Taylor Series for Square Root Function

    Homework Statement Expand ##f(x) = \sqrt{2x+1}## into a Taylor series around point ##c=1##. Find the interval of convergence. Homework EquationsThe Attempt at a Solution I do know that ##f(x) = \sum\frac{1}{n!}f^{(n)}(c)(x-c)^n## assuming the function is representable as a Taylor series. How...
  35. Stephanus

    What is the cause of space expansion in the universe?

    Dear PF Forum, Thanks readers for giving me so many explanations about space expansion in my previous thread. However, I've forgot to ask 2 things that I'd like to know the answer. Space is expanding. According to Hubble Law? What cause space expands? 1. Dark Energy? 2. Does space its own have...
  36. goonking

    Why does the coefficient for steel in expansion change with temperature?

    Homework Statement Homework Equations ΔL = α L0 ΔT The Attempt at a Solution I converted the 0.62 mm to meters, giving 0.00062 m am I suppose to convert the degrees from Celsius to K? why is the coefficient for steel in K-1? What does that even mean? anyway, I converted C to K and answer I...
  37. R.Mesri

    How much energy is produced during thermal expansion?

    We say the expansion coefficient of steel is 12 × 10 -6 m/m°C, Young's modulus 210 × 109 N/m2 and yield stress 250 mega Pascal. With 100 meters length and 0.1 m2 section area , If we increase its temperature 10 °C, how much energy will be produced by expansion force in Joules? with young's...
  38. CassiopeiaA

    Does Inflation Refer to the Expansion of Space or the Entire Universe?

    A very fundamental doubt. Was inflation expansion of just space or the universe with whatever the state of matter it had?
  39. B

    Lorentz Factor Expansion: Analytic Continuation Value

    simply put, objects with mass cannot be accelerated to exactly the speed of light as the Lorentz factor will diverge to infinity. If you take the Maclaurin expansion of the Lorentz factor And then allow the velocity of the object to hypothetically be equal to the speed of light or let B=1 then...
  40. T

    Dimension change of opening through concrete slab expansion

    Hi, apologies for the length of this, I'm hoping as a group you knowledgeable established or future Engineers and Physicists can help me out with a problem. I have been having a discussion with a colleague about expansion of a 6m x 7m integrally waterproofed (Kryton KIM) concrete slab roof that...
  41. S

    Adiabatic Free Expansion and Reversible Isothermal Path

    Homework Statement Consider an ideal monatomic gas that undergoes an adiabatic free expansion starting from equilibrium state A with volume 500 cm3, pressure 40 kPa and temperature 300K to state B, which has a final equilibrium volume of 1000 cm3. Construct an reversible isothermal path that...
  42. C

    Triple Expansion Gas Turbines Project - Help Needed

    hi all am looking to do a project using triple expansion of gas like the old steam engines had. I've got 3 points of gas/compressed air at different pressures to run 3 turbines. am thinking of using a central shaft and sizing the turbines to produce the same rpm and torque down the drive...
  43. D

    Radiation Far Zone Expansion - 65 Characters

    So using the lorenz gauge and maxwells equations we find that both the scalar and vector potentials obey the wave equation with a charge/current density source. ##\Box \phi= \frac{\rho}{\epsilon} ## ##\Box\vec{A} = \mu \vec{J}## So using the greens function for the wave equation we can...
  44. hyperickz

    Joule's Expansion & Entropy Production

    We all know that in free expansion of gases under adiabatic condition and keeping the temperture constant ,we get that no work is done by the gas.Moreover since del(Q)=0, del(U)=0 according to first law of thermodynamics.But we get a increase of entropy by an amount Rln2.Now the question is that...
  45. A

    Universe expansion is accelerating?

    Hi i have a question, i m a engineer but i have probably a dumb question ¿if the Expansion of the Universe is accelerating, but exist a speed limit "c" this tell me that at one point the universe will expand at a constant rate?
  46. S

    Explaining Universe Expansion Through Gravity & 3D Geometry

    Hi, This is my first post and I've joined simply to see what anyone may make of the following idea. Given the relatively recent depictions of the universes 3d structure as something akin to nodes with filaments connecting them. It seemed that the expansion of the universe could be explained by...
  47. S

    What does the maximum work of a reversible expansion mean?

    What does it mean by maximum work of an isothermal, reversible expansion of a perfect gas from initial volume Vi to final volume Vf at temperature T? I understand that heat enters the system during this expansion to ensure that no internal energy is lost but it doesn't really help in anyway...
  48. B

    What if expansion rate of a universe is the speed of light?

    What If we accept starting point of the big bang as the central point and what If the equatorial expansion rate of a spinning universe was the speed of light, how would it impact universe? ( In this question, you may think yourself as an observer from out of universe. I try to mean with "the...
  49. M

    MHB Taylor expansion of second order

    Hey! :o I have to find the Taylor expansion of second order of the following functions with center the given point $(x_0, y_0)$. $f(x, y)=(x+y)^2, x_0=0, y_0=0$ $f(x, y)=e^{-x^2-y^2}\cos (xy), x_0=0, y_0=0$ I have done the following: The Taylor expansion of second order of $f...
  50. C

    Taylor series expansion of an exponential generates Hermite

    Homework Statement "Show that the Hermite polynomials generated in the Taylor series expansion e(2ξt - t2) = ∑(Hn(ξ)/n!)tn (starting from n=0 to ∞) are the same as generated in 7.58*." 2. Homework Equations *7.58 is an equation in the book "Introductory Quantum Mechanics" by...
Back
Top