What is Expansion: Definition and 1000 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.

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  1. J

    Isobaric vs. isothermal expansion

    We have a piston with ideal gas in it and a weight. The weight is placed on the piston. The gas is heated externally and the gas expands. Will the expansion be isobaric or isothermal? One argument would be: the expansion will be isobaric because the weight is providing constant pressure. The...
  2. sitkican

    Multipole Expansion of a Thin rod

    Homework Statement Consider a very thin rod lying on the z axis from z = −L/2 to z = L/2. It carries a uniform charge density λ. Show that away from the rod, at the point r (r >>L), the potential can be written as V (r, θ) = (2Lλ/4πε0)(1/L)[ 1 + 1/3(L/2r)2P2(cos θ) + 1/3(L/2r)4 P4(cos θ) + · ·...
  3. N

    B If energy is created with expansion and it has no limit....?

    Then is potential energy infinite (potential energy=energy that can be created)
  4. JulienB

    Multipole expansion of a line charge distribution

    Homework Statement Hi everybody! I'm very stuck trying to solve this problem, hopefully some of you can give me a clue about in which direction I should go: Determine the multipole expansion in two dimensions of the potential of a localized charge distribution ##\lambda(\vec{x})## until the...
  5. Ryaners

    Thermo: isothermal, reversible expansion of ideal gas

    Homework Statement Two moles of a monatomic ideal gas are at a temperature of 300K. The gas expands reversibly and isothermally to twice its original volume. Calculate the work done by the gas, the heat supplied and the change in internal energy. So: T = 300K; ΔT = 0 n = 2; R = 8.314 J K-1...
  6. G

    Isothermal Expansion of Supersonic Flow

    Hi, In a standard converging-diverging rocket nozzle, we have (ex.) the relation:(1-M^2)\frac{dV}{V}=-\frac{dA}{A}By substituting in definitions, we can obtain\left(1-\frac{V^2}{\gamma R T}\right)\frac{dV}{V} = -\frac{dA}{A}This shows the dependence on temperature. The relation assumes that...
  7. e2m2a

    A Inertia & Accelerated Expansion: How Does Machian Explanations Fit In?

    I understand that some old Machian interpretations of inertia require a closed universe. Now that it has been confirmed that the universe is expanding forever and is not closed, how does Machian explanations of inertia fit in with this?
  8. F

    I Length contraction vs expansion

    I'm coming across a contradiction that I can't resolve. Two points on the ground are separated by 30km. If you're in a moving frame at velocity +v relative to the ground and you view those two points on the ground, would those two points be greater or less than 30km apart? At first, I thought it...
  9. G

    B Why Contraction in Relativity Theory?

    I have a very hard question: why in the Relativity theory the contraction is present always - along the x-axis or a speed v, instead of an expansion along the other dimensions, transversal to the v? Is there any mathematical proof, the contraction is the one correct, and any other possibility...
  10. Mayan Fung

    Why does the entropy increase in free expansion of an ideal gas?

    I learned that $$ dS = \frac Q T$$ In free expansion of Ideal gas, it is obvious that Q = 0. However, the entropy increases. I guess the reason is that it is because the process is not quasistatic. If I am right, why is this process not quasistatic. If I am not, what's wrong with the formula...
  11. D

    A Proof of expansion of a certain value

    How do I begin proving: sum(k>=1)8/(k^4+4)=pi*coth(pi)-1? I got this from Mathematica. Thanks in advance for any help.
  12. D

    Testing multipole expansion Application ID: 31901

    like in the manual i have done the following steps 1.built 100nm radius sphere 2.pressed build all 3. added air material 4.added silicon materal withrefractive index 1.5 5. selected all the domains and pressed Build All but when i press both "test application" or "compute" i get an empty...
  13. G

    I Accelerated expansion and Hubble plot

    Hello! I have a question regarding the effect of the accelerated expansion of the universe on the Hubble plot (redshift over luminosity (or distance). I understand that for relatively nearby galaxies, this appears to be a linear relationship but that because of the accelerated expansion of the...
  14. SpinzTronics

    Thermodynamics - expansion, compression, work

    Hi everyone! I am confusing myself with this topic and I would appreciate some insight into this. You see, one takes the area of a PV graph to obtain the work done on the system (for compression) or by the system (for expansion). However, I am learning that in the irreversible path, compression...
  15. M

    MHB Difference in expansion of brackets

    Let's say that there is an expression $x^2+y^2=14$ Cannot this expression be written as $(x+y)^2 = 14$ taking out the square which is common to both the terms $x$ and $y$ but after writing like that doesn't this become $x^2+2xy+y^2$=14 So writing the expression like that would it remain...
  16. C

    Crower steam expansion stroke for two stroke/rotary engines

    I was interested in whether it might be possible to incorporate a steam expansion power stroke into a two stroke or a rotary engine. The difference would be that unlike the convention Crower six stroke cycle there would be compressed air in the combustion chamber, without some sort of valve...
  17. K

    I Dark energy and expansion of space

    universe is expanding since the bigbang so therefore space is expanding, but apparently dark energy remains constant, it apparently isn't getting diluted as the universe expands is energy being created, specifically the energy in vacuum?
  18. G

    I Is time rate getting faster with cosmic expansion?

    Hi, layman here, but hopefully reasonably educated. I did not know whether this question might fit better under relativity or under cosmology so I'm posting it here. General Relativity tells us that time slows down in gravity wells. The cosmic expansion tells us that the energy density in space...
  19. Oannes

    Finding Increse in Volume Given Temp, Vol Expansion....

    Homework Statement I am supposed to find the increase in volume, or more specifically how much mercury will rise inside of a thermometer, given the following values. The volume expansion is 1.8 * 10-4/C(degree Celcius). The temperature increase from 30 to 70 degrees F (already converted the...
  20. newjerseyrunner

    B Combine a horizon line with expansion

    In this thread let's forget math, we don't have math to describe these energies anyway. Observation tells us that at extremely high energy densities there is some expansive force that vastly overwhelms everything else. Expansion has become the only viable explanation to what we observe. So I...
  21. T

    I Series Expansion to Function

    I ran across an infinite sum when looking over a proof, and the sum gets replaced by a function, however I'm not quite sure how. $$\sum_{n=1}^\infty \frac{MK^{n-1}|t-t_0|^n}{n!} = \frac{M}{K}(e^{K(t-t_0)}-1)$$ I get most of the function, I just can't see where the ##-1## comes from. Could...
  22. Pao44445

    Volume Expansion: Find Petrol Overflow After Temp Change

    Homework Statement a steel tank is 70 litres,full of petrol. If a temperature is change from 20o C to 35o, find the increased volume of petrol that overflows (βsteel = 950 x 10-6 ) βpetrol = 36 x 10-6 ) Homework Equations Δv=βv0ΔT The Attempt at a Solution I know that both the steel...
  23. D

    I Eigenvalues, eigenvectors and the expansion theorem

    If i have an arbitrary ket then i know it can always be expressed as a linear combination of the basis kets.I now have an operator A which has 2 eigenvalues +1 and -1. The corresponding eigenvectors are | v >+ = k | b > + m | a > and | v >- = n | c > where | a > , | b > and | c > are...
  24. K

    Performing a Taylor Series Expansion for Lorentz Factor

    Homework Statement Perform a Taylor Series expansion for γ in powers of β^2, keeping only the third terms (ie. powers up to β^4). We are assuming at β < 1. Homework Equations γ = (1-β^2)^(-1/2) The Attempt at a Solution I have no background in math so I do not know how to do Taylor expansion...
  25. R

    Solve Isothermal Expansion: Find v2 Given P1, P2 & v1

    Homework Statement Let P2 = 10^6 N/m^2, P1 = 4X10^5 N/m^2 and v = 2.5m^3/kmole Find the specific volume v2. Homework Equations Isothermal process, ideal gas. There is also a picture but it's just a generic P = constant/V plot. The Attempt at a Solution The volume given is the specific...
  26. D

    I Thermal expansion in harmonic potential

    It is generally said that thermal expansion is a process determinated by the anharmonic terms in the potential of a crystalline solid. However, in the Course of Theoretical Physics by Landau Lifshitz, Statistical Physics part 1, paragraph 67, a form for the coefficient of thermal expansion is...
  27. Elvis 123456789

    Adiabatic expansion of an ideal gas

    Homework Statement An ideal monatomic gas has initial pressure Po and occupies initial volume Vo. The gas undergoes an adiabatic expansion in which the volume is doubled. Calculate in terms of Po and Vo a) the final pressure of the gas b) the change in its enthalpy during the...
  28. M

    MHB Binomial Expansion - Fractional Powers

    Hello! We know from 'Binomial Expansion' that (1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+... for \left| x \right|<1 . Why doesn't it work for other values of x? I can't understand this condition. I would be really grateful for clear explanation!
  29. P

    Isothermal compression and adiabatic expansion

    I want to know if a specific amount of gas has been compressed isothermaly an then released to expand freely, how much of the energy that has been spent on compressing the gas can be recovered. As for example, 1 gm-mole of Nitrogen has been compressed to 1/4th of its initial volume from at 1...
  30. Alettix

    B Binomial Expansion with Negative/Rational Powers

    Hello! When studying binominal expansion: ## (a+b)^n = \sum_{k=0}^{n}{{n \choose k}a^{n-k}b^k} ## in high school, we proved this formula with combinatorics considering that "you can choose either a or b each time you multiply with a binom". Probably, this is not a real mathematical proof at...
  31. M

    MHB Considering the expansion , Find the value

    Considering the expansion of $(x-y)^3$ , Find the value of $2\left(24^3-3*24^2*4+3*24*4^2-4^3\right)$ Any Ideas on how to begin ? (Mmm)
  32. Mr Davis 97

    First order term in the taylor expansion of ln(x) abut 1

    Homework Statement What's the first order term in the expansion ln(x) about x = 1? Homework Equations Taylor series formula The Attempt at a Solution The question is multiple choice, and the choices are x, 2x, or (1/2)x. However, when I calculate the first order term in the expansion of ln(x)...
  33. C

    Sum of sinosoids that can be a Fourier Series expansion

    Homework Statement I was given a problem with a list of sums of sinusoidal signals, such as Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion. Homework Equations [/B]The Attempt at a Solution My guess is that it has something to...
  34. Amara

    Taylor expansion of the relativistic Doppler effect?

    [Note from mentor: this thread was originally posted in a non-homework forum, therefore it does not use the homework template.] I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help...
  35. T

    I Infinity vs Expansion: Is an Infinite Universe Compatible with Expansion?

    I had a question after watching a Discovery Channel show on the universe. They talked about how some speculate the infinitude of the universe as opposed to a finite sized universe and I have also heard the same on this forum...and it got me to thinking... Isn't an infinite universe...
  36. S

    Expansion and elasticity of brines

    Hello, I am currently looking at a way to calculate brine density using temperature, pressure and salinity. I found the following page which describes the change in fluid density with pressure and temperature : http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html...
  37. D

    A A question about the mode expansion of a free scalar field

    In the canonical quantisation of a free scalar field ##\phi## one typical constructs a mode expansion of the corresponding field operator ##\hat{\phi}## as a solution to the Klein-Gordon equation...
  38. karush

    MHB What is the Integral Expansion for UHWO 242?

    $$\displaystyle I=\int \frac{3{x}^{2}-{x}^{2}+6x-4}{({x}^{2}+1)({x}^{2}+2)} \\ =\frac{2}{3}\ln\left({x}^{2}+1\right)-3\arctan\left({x}\right) +\sqrt{2}\arctan\left({x/\sqrt{2}}\right)+C$$ Was going to take this a step at a time so by observation this looks like an expasion The way the answer...
  39. A

    Automotive New In tube end forming practices -- Can I downsize and then upsize a pipe end?

    In tube end forming practices, is it possible to first reduce the diameter of the pipe (tube 0.9mm thick) and then expand it, at the same end, by about 1mm in total, with a transistion radius of 8mm ? Please see attached image. Though it might be exaggerated, but the image should suffice. I want...
  40. P

    I How is motion in space different than motion in spacetime?

    If two particles are moving apart, how is it determined if they are moving through space or if the motion is due to the expansion of space-time? Especially if there was no other frame of reference.
  41. D

    What is the significance of thermal expansion coefficients in material research?

    Hi all, I am very new to physics and have little to no background in engineering, however I am a biochemistry major whoe somehow wound up in material research lab. One thing I am having trouble understanding the thermal expansion coefficients, how they relate to each other and which one I...
  42. P

    B How does the Universe's expansion relate to Newton's 1st law

    How does the universe's expansion relate to Newton's 1st law. In other words, is all the expansion due to an unknown cause at the big bang and the 4 forces now act on it? Or maybe is the expansion not really due to a force (as is gravity) so the 1st law doesn't apply?
  43. P

    I Scale factor/redshift formula wrong at the end?

    In this video: The professor at the end (at about 7:28), used the formula for scale factor and redshift as a(t) = 1/z, instead of the actual one a(t) = 1/1+z. And when we apply both of them, they give very different results. So, how could the professor use the first formula, which we were...
  44. K

    I Redshifts of galaxies and the expansion of the universe

    (Sorry for my poor English.) I was watching a PBS video on expansion of the universe and the guy says the wavelength of a photon emitted in a supernova becomes larger as it travels to the Earth. Is it because the photon lose energy (to space)? If so, is that energy contributing to the expansion...
  45. Zachary96

    Work done by a van der waal gas/real gas in a expansion

    Edited: To summarize the below attached jpg file is the formula for work done by a van der waals gas in a isothermal reversible expansion. Is there a way to find the work done by a van der waal gas in a isothermal irreversible expansion? i.e the real gas expands against a constant pressure (in...
  46. martinbandung

    How does temperature affect the expansion of steel railway track?

    https://drive.google.com/file/d/0Byoif068nH-zbk8tVmhCQVlYMlk/view?usp=drivesdk 1. Homework Statement The steel railway will be constructed in a place that temperature can change 8°C. Length of each rail is 10 m. With α=11*10^-6 . Minimum space required between the rail is... Homework...
  47. S

    Thermal expansion of liquid in a tube

    Homework Statement A cylindrical glass tube (linear thermal expansion coefficient ##\alpha##) contains liquid (volume thermal expansion coefficient ##\beta##). The height of the tube is ##h_{t,0}## and the height of the liquid inside of it is ##h_{l,0}##. If the temperature changes of an amount...
  48. mertcan

    A Taylor expansion metric tensor

    hi, when I dug up something about metric tensors, I found a equation in my attached file. Could you provide me with how the derivation of this ensured? What is the logic of that expansion in terms of metric tensor? I really need your valuable responses. I really wonder it. Thanks in advance...
  49. R

    Taylor Expansion: Computing x^2 + x^4/12

    Hello friends, I need to compute the taylor expansion of $$\frac{x^4 e^x}{(e^x-1)^2}, $$ for ##x<<1##, to find $$ x^2 + \frac{x^4}{12}.$$ Can someone explain this to me? Thanks!
  50. U

    I Exploring the Expansion of Universe & Motion of Galaxies

    i have a question about the motion of galaxies and the speed limit of light. using Hubble's law, it is theoretically found that after a certain distance(about 4200 mega parsec or something) from a observer, the galaxies are moving faster than the speed of light. consider the following...
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