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.

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  1. 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...
  2. 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?
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. mertcan

    A How Is the Taylor Expansion Applied to Metric Tensors?

    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...
  9. 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!
  10. 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...
  11. I

    Why Don't First-Order Terms Disappear in the Taylor Expansion for Scalar Fields?

    Homework Statement Page 35 of Jackson's Electrodynamics (3rd ed), it gives the following equation (basically trying to prove your standard 1/r potential is a solution to Poisson equation): \nabla^2 \Phi_a = \frac{ -1 }{ \epsilon_0 } \int \frac{ a^2 }{( r^2 + a^2)^{5/2} } \rho( \boldsymbol{x'}...
  12. binbagsss

    Chain rule / Taylor expansion / functional derivative

    Homework Statement To show that ##\rho(p',s)>\rho(p',s') => (\frac{\partial\rho}{\partial s})_p\frac{ds}{dz}<0## where ##p=p(z)##, ##p'=p(z+dz)##, ##s'=s(z+dz)##, ##s=s(z)## Homework Equations I have no idea how to approach this. I'm thinking functional derivatives, taylor expansions...
  13. mertcan

    I Taylor expansion and parallel transport

    hi, first of all in this image there is a fact that we have parallel transported vector, and covariant derivative is zero along the "pr"path as you can see at the top of the image. I consider that p, and r is a point and in the GREEN box we try to make a taylor expansion of the contravariant...
  14. mertcan

    A Expansion of covariant derivative

    (V(s)_{||})^\mu = V(s)^\mu + s \Gamma^\mu_{\nu \lambda} \frac{dx^\nu}{ds} V(s)^\lambda + higher-order terms (Here we have parallel transported vector from point "s" to a very close point)Hi, I tried to make some calculations to reach the high-order terms for parallel transporting of vector...
  15. Italian_Mike

    I Vacuum energy versus expansion of the Universe

    If vacuum energy has a non-zero value, is the vacuum energy density (vacuum energy over a given volume of void space) being reduced over time due to the expansion of the Universe? If so, is there any consequence on the particle-antiparticle creation/annihiliation process? Will there ever be a...
  16. Thales Costa

    Change in Enthelpy for Nitrogen at constant temp

    Homework Statement Calculate ΔH for 2 mols of Nitrogen for the following transformation: 1 bar, 21°C → 200 bar, 21°C Given that molar Cp = 4R 2. The attempt at a solution How am I supposed to find the ΔH? From what I learned, there can only be a change in enthalpy when there's a change in...
  17. stevendaryl

    B Why Is the Sun Expanding & Getting Hotter?

    I have read popular accounts about the future predictions (the far future--a billion or so years from now) for our sun, and they say that as the sun ages, it will begin to expand and get hotter, eventually making Earth too hot for life. Is there a simple explanation for why the sun, after being...
  18. marcelhattingh

    B How do we know we are not inside a blackhole?

    If you fall into a black hole, that what is closer to the singularity, will fall faster that than what is further. However, space before and after you, is falling in with you. So from each General Relativistic perspective of "you", because there would be no inertial frame to orient yourself (you...
  19. Buckethead

    B Expansion of space and momentums of galaxies

    It is my understanding from reading a few threads that remote clusters don't have any "speed" relative to us, they are simply moving away. Does this mean they have no momentum? And if that is true, does that imply that they have no mass (in this context, not in a local context). And if that is...
  20. Tardis Traveller

    Ideal Gas Expansion: Finding Depth of Tank

    Homework Statement A bubble comes from the bottom of the tank of water to the surface and triples in its volume. If the temperature of the tank of water doesn't deppend on the depth what is the depth of the tank that the bubble was at? Homework Equations ##PV=nRT## The Attempt at a Solution...
  21. karush

    MHB Focusing on the I in I don't want to do this anymore

    w8.5.2 $$ \int \frac{x^4}{(4-x^2)} dx \implies -\int\frac{x^4}{(x^2-4)} dx $$ by division $$\displaystyle\int\dfrac{16}{x^2-4}+x^2+4 \ dx \implies 16\int \frac{1}{(x+2)(x-2)}+ x^2+4 \ dx $$ $$\frac{1}{(x+2)(x-2)}=\frac{A}{x+2}+\frac{B}{x-2} \displaystyle =...
  22. E

    Theories and questions on the expansion of the universe

    The universe is expanding at an accelerated rate. Space has no edge. If space is geometrically "round," meaning that a long enough journey could bring you back to where you started, then it could be said that the universe has no outer edge. At the moment of the big bang, the universe created...
  23. C

    Adiabatic expansion of infinite square well

    Homework Statement Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur at...
  24. bananabandana

    I What Is the Correct Expansion of \( e^{\frac{1}{z-1}} \)?

    So, I was doing a question on Laurent series. Part of it asked me to work out the pole of the function: $$ exp \bigg[\frac{1}{z-1}\bigg]$$ The answer is ##1## - since, we can write out a Maclaurin expansion: (1) $$ exp\bigg[\frac{1}{z-1}\bigg] = 1+\frac{1}{z-1}+\frac{1}{2!}\frac{1}{(z-1)^{2}}...
  25. S

    Decoupling Compression and Expansion of a turbine

    Hi, I just want to double check something: My understanding is that the higher the compression pressure the higher the amount of energy per unit mass it will take to compress a given mass of gas. So my question is, would a decoupled system where the compression can take place over a longer...
  26. S

    Expanding Fraction with Infinite Value: Simple Expansion Homework Solution

    Homework Statement I am trying to expand \frac{1}{(1+\frac{a^2}{z^2})^{1/2}} for z>>a. Homework EquationsThe Attempt at a Solution First, I rearranged the equation to (1+\frac{a^2}{z^2})^{-1/2}. After this, since z>>a, can I assume z takes a value of infinity and say the first term is 1+0=1...
  27. Erenjaeger

    Calculating Thermal Expansion: Glass Rod Length, Diameter, and Volume Increase

    A) The active element of a laser is made of a glass rod 25.0 cm long and 1.40 cm in diameter. Assume the average coefficient of linear expansion of the glass is equal to9.00 10-6 (°C)−1. The temperature of the rod increases by 64.0°C. i) What is the increase in length? I worked this out to be...
  28. P

    Multipole expansion of Vector Potential (A)

    Homework Statement So my teacher, as we made the multipole expansion of Vector Potential (\vec A) decided to proof that the monopole term is zero doing something like this: ∫∇'⋅ (J.r'i)dV' = ∮r'iJ ndS' = 0 The first integral, "opening" the nabla: J⋅(∇r'i) + r'i(∇⋅J) this must be equals 0 J =...
  29. E

    I Spacetime expansion and conservation of energy

    I came across this issue a while ago, when spacetime expands, then energy doesn' seem to be conserved? But does not that violate the law of conservation of energy? I don't get it, how can spacetime expansion happen without energy issues? Thanks in advance
  30. Einstein's Cat

    B What is the reason for galaxies fading in the distant future?

    Galaxies that are greater than a distance of c/H metres from Earth have recessional velocities exceeding the speed of light and begin to fade. Thus, theoretical astronomers 3 trillion years in the future will see only the Milky Way in the night sky. What is the reason for this fading of galaxies?
  31. F

    What is the Formula for Minor Loss Due to Expansion?

    Homework Statement from the previous thread , https://www.physicsforums.com/threads/minor-loss-in-pipe.869148/ , i know that formula of loss due to contraction can also be expressed as k[( mean velocity )^ 2 ] / 2g how about the formula of minor loss due to expansion , can we expressed as...
  32. T

    B Is expansion caused by unknown tension in space/time?

    I was playing around in the kitchen today. You know how when you drop some pepper in a calm glass of water the flakes instantly seem to repulse from each other and expand over the entire surface? I believe this is due to surface tension in the skin of the water. Could expansion be possibly...
  33. T

    B How to apply Einstein's STOR to expansion

    Einstein's STOR states that if I was in an upward accelerating elevator I would not be able to tell if the weight I would be experiencing was due to acceleration or gravity from my frame of reference. This identical appearance idea work for expansion also? It has been stated many times that...
  34. Ranku

    I Exponential expansion of inflation

    The expansion of the inflationary universe is said to be roughly exponential. Why is it called "roughly" exponential?
  35. Willfrid Somogyi

    I Flat vs Open Universe: CMBR & Type Ia Supernovae

    So CMBR points to a flat universe, and this seems to be the generally accepted model. But in a flat universe is expansion not supposed to slow exponentially, stopping after an infinite time? How does this fit with the observation that distant type Ia supernovae show the universe's expansion to...
  36. F

    Minor loss due to sudden expansion

    Homework Statement why the minor loss due to sudden expansion is given by formula of [( v_c - v_2) ^2 ]/ 2g ? Homework EquationsThe Attempt at a Solution can it be [( v_2 - v_1) ^2 ]/ 2g ?
  37. W

    I Expansion of the universe, a poor choice of words?

    I think cosmologists use a poor choice of words when they say the universe is expanding. I don't dispute any of the science behind the "expanding" universe but I do want to dispute the appropriateness of the phrase to the science. I think people typically understand expanding to mean: getting...
  38. C

    What is the Final Temperature of Methane Gas After Adiabatic Expansion?

    Methane gas at 550K, 5 bar is expanded adiabatically and reversibly to 1 bar. Find the final temperature of the gas. I have made little progress with this... I've calculated the initial volume, and that is all so far. Obviously to find the work usually I'd integrate pressure with respect to...
  39. Allen_Wolf

    B Is Dark Energy Really Driving the Expansion of the Universe?

    I have a doubt on the expansion of the universe. In the recent years, it has been observed that the universe is expanding in an increasing speed. So the existence of dark energy was suggested. Actually is the speculation that the universe is expanding in an increasing speed because of dark...
  40. P

    Estimate time scale of expansion of a star

    Homework Statement A star experiences a sudden increase in pressure to a new value P'. Taking the average density as ρ and the radius R, estimate the time scale of expansion of the star. (Ignore gravity altogether). Homework Equations The only thing I can see in my notes that may (or may not)...
  41. F

    A Alpha Variation vs Cosmological Expansion: Basics Explained

    hello, My question will be quite naive for experts and reflects the fact that I'm new to the subject of varying the fine structure constant alpha and mainly need an introductory reference ... so if someone has a good one to advice ...thanks a lot i just don't understand the basics: how people...
  42. A

    I Dark Energy vs Gravity: Expansion vs Contraction

    Hi all, A naive question: My understanding is that dark energy drives the expansion of space - that is, the distance between two points in space increases over time - with the important note that it is space itself that is expanding. However, when talking about gravity (where one says that...
  43. M

    Head Loss and Pressure Rise During Gradual Expansion

    Homework Statement , There is an Head Loss question, two pipes join and expanding parts 30 degrees from the horizantal. Homework Equations The Attempt at a Solution Before attemting a solution I try to understand what a1=a2=1.06 is? Would you like to give some information about it...
  44. F

    Formula of friction loss due to expansion

    Homework Statement in the first picture , K_L = [ [(1/C) -1] ^2 ] taking the diagram in the first picture as an example , the K_l = [(1- (Asmall/ Abig)) ^2 ] , the A small represent the area at A2 , Abig = A1 ? Am i right ? Homework EquationsThe Attempt at a Solution
  45. F

    Friction losses due to expansion vs losses due to contract

    Homework Statement i was told that the losses during expansion are usually much higher than losses during contraction in pipe . is it true?why? Homework EquationsThe Attempt at a Solution
  46. Kuzon

    What's wrong with my math?[Thermal volume expansion]

    Homework Statement Homework Equations Coefficient of water expansion for volume given by the textbook is 207 x 10^-6 The Attempt at a Solution [/B] I did 80.4*0.000207*0.000369 = 0.00000614119 m^3
  47. F

    Loss due to contraction vs loss due to expansion

    Homework Statement why the formula of fricitional pipe loss due to contraction is given by formula : kc(V^2)/2g ? why the formula of fricitional pipe loss due to contraction can't be formula : (Va^2)-(Vb^2)/2g ? ,where Va= velocity at inlet , Vb = velocity at outlet ? Homework EquationsThe...
  48. sara lopez

    Thermodynamics: air expansion in a cylinder

    Homework Statement Consider air expansion inside a cylinder. Assume that the volume and initial pressure is 1 ft^3 and 1500 PSI ABS respectively. If the expansion process is reversible and the path is given by P.V^1.4=constant. Calculate the total work done by the gas to reach the final volume...
  49. N

    Insights A Brief on the Expansion of the Universe - Comments

    nikkkom submitted a new PF Insights post A Brief on the Expansion of the Universe Continue reading the Original PF Insights Post.
  50. P

    Binomial expansion for fractional power

    Homework Statement So, I'm solving a dipole thing and I have these vectors: |r + d - r'| = (r² + d² - r'²)(1/2) Homework Equations I want to expand this but I have no idea how! I know I may have an infinite power series, but I may expand at the square terms tops... Before I needed to do the...
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