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.

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

    Lagrangian for a free particle expansion problem

    Hello, this is probably one of those shoot yourself in the foot type questions. I am going through Landau & Lifshits CM for fun. On page 7 I do not understand this step: L' = L(v'^2) = L(v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2) where v' = v + \epsilon . He then expands the...
  2. M

    Adiabatic expansion with temperature dependent heat capacity.

    Homework Statement 1 mole of an ideal gas initially at 100° C and 10 atm is expanded adiabatically against a constant pressure of 5 atm until equilibrium is re-established. Given that the temperature dependence of the heat capacity is CV = 18.83 + 0.0209T calculate deltaU, deltaH and deltaS...
  3. C

    What is the maximum volume expansion coefficient of ?

    Homework Statement You are building a device for monitoring ultracold environments. Because the device will be used in environments where its temperature will change by 211°C in 2.99s, it must have the ability to withstand thermal shock (rapid temperature changes). The volume of the device is...
  4. C

    Linear expansion of a pendulum

    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...
  5. S

    What is the Relationship Between Maclaurin Series and Infinite Series?

    Homework Statement Use Maclaurin’s theorem to derive the first five terms of the series expansion for ##(1+x)^{r}##, where -1<x<1. Assuming the series, obtained above, continues with the same pattern, sum the following infinite series ##1 + \frac{1}{6} - \frac{(1)(2)}{(6)(12)} +...
  6. B

    Thermal Physics Expansion Coefficient Problem

    Homework Statement When the temperature of liquid mercury increases by one degree Celsius (or one kelvin), its volume increases by one part in 550,000. The fractional increase in volume per unit change in temperature (when the pressure is held fixed) is called the thermal expansion coefficient...
  7. S

    Finding the Maclaurin Series Expansion of (1+x)ln(1+x)

    Homework Statement Given that ##f(x)=(1+x) ln (1+x)##. (a) Find the fifth derivative of f(x), (b) Hence, show that the series expansion of f(x) is given by ##x+\frac{x^{2}}{2} -\frac{x^{3}}{6} + \frac{x^{4}}{12} - \frac{x^{5}}{20}## (c) Find, in terms of r, an expression for the rth term...
  8. N

    Higher order derivatives with help of Taylor expansion?

    Homework Statement Function f(x) = x^2/(x-1) should be expanded by Taylor method around point x=2 and 17th order derivative at that point should be calculated. Homework Equations Taylor formula: f(x)=f(x0)+f'(x0)*(x-x0)+f''(x0)*(x-x0)^2+... The Attempt at a Solution I...
  9. S

    What are the constants in the binomial series expansion for (1+mx)^-n?

    Homework Statement For ##n>0##, the expansion of ##(1+mx)^{-n}## in ascending powers of ##x## is ##1+8x+48x^{2}+...## (a) Find the constants ##m## and ##n## (b) Show that the coefficient of ##x^{400}## is in the form of ##a(4)^{k}##, where ##a## and ##k## are real constants. Homework...
  10. X

    Partial fraction expansion

    Homework Statement I'm taking the Laplace transform of F(s), and the first thing is to expand it by partial fraction or something so that I can match F(s) with a table of laplace transforms. Homework Equations The Attempt at a Solution Does partial fraction even work? I've got two...
  11. N

    What are past values of the Hubble constant and is there an archive for them?

    Hello, I've been looking round trying to find a history of records, showing the speed of which the universe is expanding? Would this just be the hubbles constant? If so I'm looking for past Hubble constant values. Is there an archive for this? or is there a way to work past Hubble constant's to...
  12. H

    Early cosmic inflation and the expansion of the universe.

    My question is regarding the early inflationary phase of the Big Bang. As I understand it, inflation is what gave rise to the expansion energy of the universe. Meaning, inflation gave the 'push' so to speak that set the everything moving apart. This makes sense because obviously the universe...
  13. J

    The Unruh Effect and Expansion of the Universe

    The Unruh Effect predicts that a uniformly accelerating observer in a vacuum field (full of perturbations) will observe an effective temperature. We know that space is expanding at an accelerating rate. My question is then, in all inertial reference frames would all 'observers' in the universe...
  14. dexterdev

    Which of the signals is not the result of fourier series expansion?

    Homework Statement Which of the signals is not the result of Fourier series expansion? options : (a) 2cos(t) + 3 cos(3t) (b) 2cos(\pit) + 7cos(t) (c) cos(t) + 0.5 Homework Equations Dirichlet conditionsThe Attempt at a Solution From observation, I thought all are periodic and so must be...
  15. R

    Doppler effect vs expansion effect on wavelength

    Could you please clarify for me how much each of these contribute to the red shifting of light from distant objects? It seems to me that red shifting of light from near by objects i.e. within our galaxy would be affected more by the Doppler effect whereas for intergalactic objects the red...
  16. F

    MHB Taylor Series Expansion of $e^{-(q+s)^2}$

    Use taylor series to show that the infinite series from n=0 of $$\frac{s^n}{n!}\frac{d^n}{dq^n}(e^{-q^2})=e^{-(q+s)^2}$$
  17. MarkFL

    MHB Jeffrrey's question at Yahoo Answers regarding binomial expansion

    Here is the question: I have posted a link there to this topic so the OP can view my work.
  18. srfriggen

    Expand (1-2i)^10 without the Binomial Expansion Theorem

    Homework Statement Expand (1-2i)^10 without the Binomial Expansion Theorem I know I need to put this in polar form and then it's simple from there, however, I am simply having a difficult time finding the angle. Drawing the complex number as a vector in the complex plane I get a...
  19. G

    Can (x+y)^(1/2) be expanded using the binomial series?

    Is it possible to do a binomial expansion of (x+y)^{1/2}? I tried to compute it with the factorial expression for the binomial coefficients, but the second term already has n=1/2 and k=1, which makes the calculation for the binomial coefficient (n 1) weird, I think. Any advice?
  20. P

    Amount of work done in an isothermal expansion

    Homework Statement 500 Cal are added to a gas inside a cylinder with a piston (containing one mole) by an external heating device. The volume of the gas doubles without any change in it's temperature of 300K. How much work is done on the piston? Homework Equations The Attempt at a...
  21. anubodh

    Liquid oxygen expansion in vaccum

    Homework Statement There are 2 containers.Outside temperatue is -190 degree celcius.(boiling point of liquid oxygen is -180 degree celcius).One is filled with vacuum and can have a minimum height of 6000m and other is filled with liquid oxygen (1140 kg/m3 density) at -190 degree celcius...
  22. K

    Coefficient of linear expansion / Bragg peaks

    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...
  23. D

    Laurent expansion for a complex function with 3 singularites

    Homework Statement Hey guys, So I need a bit of help with this question: Find three Laurent expansions around the origin, valid in three regions you should specify, for the function f(z)=\frac{30}{(1+z)(z-2)(3+z)} Homework Equations None that I know of...just binomial expansion...
  24. G

    MHB Stochastic Taylor's Expansion (Ito Rule)

    Good day. For $k\geq0$ a continuous function on $\mathbb{R}_+$ and $\{W_t\}$ a standard Brownian motion, could you help me find the Taylor's expansion of the following exponential: $e^{-\int_0^t k(s) dW_s}.$ For the case where $e^{-k W_t}$ where $k>0$ is a constant, I was able to recompute...
  25. D

    Laurent expansion for a complex function

    Homework Statement Expand f(z)=\frac{1}{z-4} in a laurent series valid for (a) |z|<4 and (b) |z|>4 Homework Equations The formula for laurent expansion... \sum_{n=-∞}^{+∞}a_{n}(z-z_{0})^{n} where a_{n}=\frac{1}{2\pi i}\oint_c \frac{f(z)}{(z-z_{0})^{n+1}}dz The Attempt at a...
  26. C

    Expansion of gas into cylinder

    Homework Statement Consider two rigid cylinders, P and Q, with respective volumes VP and VQ with VP << VQ. They are connected by a capillary. Initially cylinder Q is empty and cylinder P contains an ideal monatomic gas at 300K and pressure 1 bar. A moveable piston in P is used to maintain the...
  27. K

    Circle Expansion on Expanding Sphere

    Homework Statement How would a circle on a sphere expand as a function of the sphere's radius as the sphere expands? Homework Equations none were provided The Attempt at a Solution \S=4\,\pi \,{R}^{2} A=\pi \,{r}^{2} {\it dA}=2\,\pi \,r{\it dr} {\it dS}=8\,\pi \,R{\it dR}...
  28. N

    Thermal expansion of water and a bubble

    Homework Statement A scuba diver is 17.4m below the surface of the lake, where the water temperature is 8.25∘C. The density of fresh water is 1000 kg/m3. The diver exhales a 23.6cm3 bubble.What's the bubble's volume as it reaches the surface, where the water temperature is 15.1∘C? Homework...
  29. Y

    Help in deriving series expansion of Helmholtz Equation.

    Orthogonality of spherical bessel functions Homework Statement Proof of orthogonality of spherical bessel functions The book gave \int_{0}^{a}\int_{0}^{2\pi}\int_{0}^{\pi} j_{n} (\lambda_{n,j}r) j_{n'} (\lambda_{n',j'}r) Y_{n,m}(\theta,\phi)\overline{Y}_{n',m'}(\theta,\phi) \sin\theta...
  30. N

    How much does a steel measuring tape expand on a hot day?

    Homework Statement A 61.00m long steel measuring tape is calibrated for use at 20.0∘C. How long is this tape under the following conditions: a hot day with 38∘C? Express your answer using four decimal places and include the appropriate units. i've been losing my mind over this, i swear...
  31. Gamma

    Why Does a Sealed Water Bottle Crack in the Freezer?

    This is not a homework question, but a conceptual question that I am trying to understand. We all have experienced/heard that if you put a completely full water bottle with the cap on in the freezer, the bottle cracks as the water freezers. The explanation is that the water expand as it...
  32. C

    Is the Universe Expanding Through Space or is Space Itself Expanding?

    As I understand it distant objects are so far away from us, not because they are moving away from us through space but because the very space between them and us is expanding. Am I right in thinking that one bit of evidence for this is that some galaxies are 30 billion light years away? So...
  33. Russ Edmonds

    My expansion cloud chamber movie

    Hi all, below is a video showing a compilation of many expansions of my Wilson cloud chamber. The tracks shown are mostly alpha and cosmic rays. The chamber uses a rubber bulb from a turkey baster as the expansion piston. The object in the chamber is a cork with a radium paint coated pin. I'm...
  34. S

    MHB Coefficient in a Laurent Expansion in terms of an Integral

    Hi guys, i need your help to go about his question, Question: $$\text{Show that the coefficient }C_n \text{in the Laurent expansion of }$$ $$f(z)=(z+\frac{1}{z}) \text{ about z=0 is given by}$$ $$C_n=\frac{1}{2\pi}\int^{2\pi}_0 \cos(2cos(\theta))cos(n\theta)\, d\theta ,n\in\mathbb{z}$$
  35. A

    Why Doesn't Volume of Crystal Depend on Temperature?

    In the harmonic approximation, why is the volume of a crystal not temperature dependent? Does it have something to do with the fact that the amplitude of a harmonic oscillator is independent of the frequency?
  36. U

    Taylor Expansion on Determinant

    Homework Statement Show by direct expansion that: det (I + εA) = 1 + εTr(A) + O(ε2) Homework Equations f(x) = f(a) + (x-a)f'(a) + (1/2)(x-a)2f''(a) + ... The Attempt at a Solution Does the question mean Taylor expansion when they say 'direct expansion'? I'm kind of stuck on...
  37. P

    Archived Isothermal expansion of gas question

    Hello, I am just wondering if it is possible to actually do the following question based on the information given Homework Statement An isothermal reversible expansion, for which pV=constant as shown by the curve joining State A and State B, takes a system from State A to State B along...
  38. Z

    Taylor expansion of e^(2-x)

    Homework Statement Find e^{2-x} using taylor/mclaurin expansionHomework Equations e^1 = \sum_{n=0}^\inf \frac{1}{n!} e^x = \sum_{n=0}^\inf \frac{x^n}{n!} The Attempt at a Solution Can I just do: e^{1+1-x} [\sum_{n=0}^\inf \frac{1}{n!}*\sum_{n=0}^\inf \frac{1}{n!} *...
  39. anemone

    MHB How can we approach a seemingly senseless binomial expansion problem?

    Hi MHB, I've come across this problem and I think I've observed a pattern when I tried to solve it by using the method of comparison with some lower values of the exponents, but then I just couldn't deduce the answer to the problem because the pattern suggests that I can't. Here is the...
  40. A

    Why space expansion is limited to scales larger than galaxy clusters?

    Hello everyone, I have a question about metric expansion of space. According to Wikipedia (ok probably is not the best source, but I have only a qualitative understanding of physics) the expansion occurs only at scales larger than galaxy clusters...
  41. M

    Decrease in pressure due to adiabatic expansion derivation?

    Homework Statement Show that \frac{dp}{p} =\frac{\gamma}{\gamma-1}\frac{dT}{T} if the decrease in pressure is due to an adiabatic expansion.Homework Equations Poisson equations: Pv^{\gamma} Tv^{\gamma - 1} Ideal Gas Law: Pv=R_{d}T, where R_{d} is the dry air gas constant. Hydrostatic...
  42. M

    Calculating compressed air expansion when heated

    Can anyone help me with this calculation? I'm trying to figure out how much compressed air (generated from screw compressor) will expand by a ratio of what when fed into a wood furnace. 1) Wood Furnace Fuel Input: 30kg dry wood fuel/hr 2) Compressed Air Pressure: 8 bar 3) Compressed Air Flow...
  43. D

    MHB Inhomogeneous DE via expansion

    Solve inhomogeneous differential equation \[ y'' + k^2y = \phi(x) \] with homogeneous boundary conditions \(y(\ell) = 0\) and \(y(0) = 0\) by expanding \(y(x)\) and \(\phi(x)\) \begin{align*} y(x) &= \sum_na_nu_n(x)\\ \phi(x) &= \sum_nb_nu_n(x) \end{align*}...
  44. C

    Expansion of Van der waals for small pressure

    Homework Statement In the VDW eqn of state, ##(P + a/v^2)(v-b)=RT## write Pv as a function of {P,T} and by expanding the result in powers of P or otherwise show that the first terms of a Virial expansion in powers of P for a VDW gas are given by $$Pv = RT + \left(b - \frac{a}{RT}\right)P +...
  45. D

    Joule Expansion: Cooling Effects & Kinetic Energy

    I read on 27 chapter from Blundell's Thermal Physics 2nd edition. For ideal gases, Joule expansion doesn't cool gases. But for real gases, Joule expansion makes cooling effects. And this book(page 314) says that when gases expand, their potential energy of molecular interactions...
  46. K

    Determinant's solving without expansion

    Solve without expanding the determinant having elements which are listed as follows row-wise = {1^2,2^2,3^2,2^2,3^2,4^2,3^2,4^2,5^2} where , the determinant is of the order 3 I have tried some combinations of operations performed row or column wise that could produce 2 zeros either in one of...
  47. M

    Expanding Inhomogeneous Poisson Processes Using Taylor Series

    I'm at the end of a very long Poisson Processes question, involving inhomogeneous Poisson Processes. I just need to be able to expand the following expression to be able to complete the question. exp[{(sin ∏h)/∏} -h] Would anyone please be able to provide some help, with steps please!
  48. Y

    Complex analysis - partial fraction expansion

    Homework Statement Show that: Ʃ(-1)n/(n^2+a^2) (from n=0 to ∞) = pi/[asinh(pi*a)], a\neq in, n\in Z. Homework Equations f(z) = f(0) + Ʃbn(1/(z-an)+1/an) (from n=1 to ∞) , where bn is the residue of f(z) at an. The Attempt at a Solution The main problem is I don't how to pick the...
  49. J

    Please identify a series expansion

    Hi, Could someone please identify the following series expansion for me, if possible: $$f(x) = 1/h\int_x^{x+h}f(t)dt + A_{1}Δf(x) + A_{2}hΔf'(x) +...+ A_{m-1}h^{m-2}Δf^{(m-2)}(x) +r$$ where $$A_{m}$$ are, as far as I know, plain constants and $$Δ = [x, x+h]$$. I think this result was...
  50. R

    Taylor Expansion of f+df About x?

    How would one expand f+df about x? I'm messing something up in the process and can't seem to resolve it lol
Back
Top