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. C

    Expansion of Space vs Velocity in Space

    As far as I know, the main argument for the statement that the universe is expanding is that the velocities of galaxies increase proportional to the distance. This together with the cosmological principle indicates that every point in the universe observes the same thing, something that is...
  2. A

    Coefficient of x^r in Expansion of (1+x)(1-x)^n

    I am puzzled by the following example of the application of binomial expansion from Bostock and Chandler's book Pure Mathematics: If n is a positive integer find the coefficient of xr in the expansion of (1+x)(1-x)n as a series of ascending powers of x. (1+x)(1-x)^{n} \equiv (1-x)^{n} +...
  3. N

    Does the bond between atoms affect Thermal Expansion?

    Homework Statement From a journal I read that the cobalt-based perovskite cathode usually has better ionic and electrical conduction but higher TEC compare to Maganite-based perovskite cathode. Because of the Co-O bond is weaker than Mn-O bond. e.g. Cobalt-based perovskite cathode...
  4. J

    On general expansion of cos nΘ

    So I know \cos n \theta + i \sin n \theta = (\cos \theta + i \sin \theta)^n and by applying binomial to the RHS and taking the real part gives you: \cos n \theta = \sum_{k=0}^{\lfloor {n \over 2} \rfloor} C^n_{2k} (\cos^2 \theta - 1)^k \cos^{n - 2k} \theta . I have come across another...
  5. B

    Taylor Series Expansion About a Local Minimum

    Hello everyone, I am currently reading chapter two, section 3 of Griffiths Quantum Mechanics textbook. Here is an excerpt that is giving me some difficulty: "Formally, if we expand V(x) in a Taylor series about the minimum: V(x) = V(x_0) + V'(x_0) (x-x_0) + \frac{1}{2} V''(x_0)(x-x_0)^2...
  6. T

    Power Expansion (Complex variables)

    Homework Statement Use the power series for e^z and the def. of sin(z) to check that sum ((-1)^k z^(2 k+1))/((2 k+1)!) Homework Equations The Attempt at a Solution I apologize, but I am not particularly good with latex. Therefore, I attached a picture of my solution thus far...
  7. @

    Was the expansion of the universe always greater than c?

    After some thinking, I have concluded that the expansion of the universe must have started at the speed of light or greater than the speed of light but not less than speed of light. I say this because if the expansion of the universe at the instant of the big bang was less than the speed of...
  8. T

    Expansion of a local dissipation function

    Hello everyone, I'm studying the finite strain theory and have come across the maximum dissipation principle. It implies a dissipation function defined as D=\tau:d-\dfrac{d\Psi}{dt} \tau denotes the Kirchhoff stress tensor, d the eulerian deformation rate and \Psi=\Psi(b_e,\xi) the free...
  9. D

    Expansion Info-Representation With Arbitrarily Adjustable Decimals

    The following is what I call an expansion info-representation: ... _ _ _ _ _4.3 _ _ _ _ _ ... A) Each of the underscores represent placeholders for digit selection. (Psst: a whim) B) The decimal can be arbitrarily adjustable or fixed for the purpose of experiment. I'm going to try...
  10. B

    Must (Ve) expansion of the universe be C?

    Is there any experimental, practical reason or aspect of the theory/model that requires that the speed of expansion of the universe be ≥ C? The Hubble constant, the only experimental datum, comes from a formula Ve/T0*Ve that allows any possibility. If we considered Ve = C/2 , R would be 7.2...
  11. D

    Expansion of Cos(x) in Hermite polynomials

    [/itex]Homework Statement Find the first three coeficents c_n of the expansion of Cos(x) in Hermite Polynomials. The first three Hermite Polinomials are: H_0(x) = 1 H_1(x) = 2x H_0(x) = 4x^2-2The Attempt at a Solution I know how to solve a similar problem where the function is a polynomial of...
  12. T

    Rate of expansion of the universe

    So I know that the rate of expansion of the universe is increasing, i.e. the 2nd time derivative of the size of the universe is positive. But, is the next time derivative (i.e. 3nd time derivative of the size of the universe) positive of negative? Do we have enough information to determine this...
  13. Y

    Is the expansion accelerating or decelerating?

    According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past? For example, there are two galaxies A and B at distance of 5 and 10 billion years respectively. Now, when we observe A we are...
  14. V

    Proving c_{n} = 0 Using Taylor Expansion: Homework Help

    Homework Statement Suppose that f(x)=\sum_{n=0}^{\infty}c_{n}x^{n}for all x. If \sum_{n=0}^{\infty}c_{n}x^{n} = 0, show that c_{n} = 0 for all n. Homework Equations The Attempt at a Solution I know, by using taylor expansion, c_{n}=\frac{f^{n}(0)}{n!}, and because...
  15. kelvin490

    Why Is Work Calculated Using External Pressure P2 in Gas Expansion?

    In the case of gaseous expansion, if the pressure of gas is P1 and the external pressure is P2, suppose P2<P1, we know from textbook that the work W is the negative of P2 times the increase in volume, but why P2 instead of P1? We would get different result if we use P1, should the work done on...
  16. QuarkCharmer

    Boolean logic expansion issue (POS -> CPOS)

    Homework Statement Convert f=(x'+y)(x+z)(y+z) from product of sums form, into the canonical product of sums. Homework Equations boolean logic, et al. The Attempt at a Solution This is boolean logic (so + is "or" and * is "and" etc..) There has to be some stupidly simple thing...
  17. Dale

    Expansion tensor on rotating disk

    Hi Everyone, Suppose that we have cylindrical coordinates on flat spacetime (in units where c=1): ##ds^2 = -dt^2 + dr^2 + r^2 d\theta^2 + dz^2## I would like to explicitly calculate the expansion tensor for a disk of constant radius R<1 and non-constant angular velocity ##\omega(t)<1##. I...
  18. K

    What is the 1st Order Expansion Problem for a Function with a Logarithm?

    I'm a bit frustrated at the moment, as this minor problem should be fairly easy. But I seem to go wrong at some point... So I've got to do a 1st order expansion of the function \begin{equation} f=\frac{\cos(\theta)}{\sin(\theta)}\ln(\frac{L\sin(\theta)}{d\cos( \theta)}+1) \end{equation}...
  19. M

    Does Material Expansion Impact Accuracy in Thermal Expansion Experiments?

    A glass bottle is filled with salted water, and a pipette is inserted in the top through the cork. ( Leaving the bottle sealed). A thermometer is also inserted to keep record of the temperature. The glass bottle is then inserted in ice until the water reaches Zero Celsius. Finaly, the...
  20. N

    Volume Expansion: Answers to Homework Questions

    Homework Statement A standard mercury thermometer consists of a hollow glass cylinder, the stem, attached to a bulb filled with mercury. As the temperature of the thermometer changes, the mercury expands (or contracts) and the height of the mercury column in the stem changes. Marks are made on...
  21. I

    Question: Expansion of the universe

    Hello, I started this account to ask you about that, if the place of big bang was in the middle and we are on its right side, we can't observe that what was on the left side? My train of thought: << (Left side, object) <<<(Big Bang)>>> (Right side, we) >>
  22. M

    Conserved charge in FRW expansion

    Hi all, I'm reading Kinney's lectures on inflation: http://arxiv.org/abs/0902.1529 and got stuck trying to show that for some comoving length scale \lambda, the quantity \left(\frac{\lambda}{d_h}\right)^2 |\Omega -1| is conserved, if w is constant in the equation of state. Here d_h is...
  23. Soumalya

    Law of expansion for super heated steam

    Ideal gas behavior of super heated steam Why is super heated steam said to exhibit ideal gas behavior?
  24. aleemudasir

    Can we ask such a question about expansion of universe?

    How far is it correct to ask, "What is universe expanding into?". How to solve this paradox?
  25. P

    Inflation and superluminal expansion

    Inflation is often referred to as a period of 'superluminal' or 'faster-than-light' expansion (e.g. see article on Wikipedia and hundreds of research papers on the subject). This has always bugged me. What exactly is superluminal about an inflating universe that does not apply to a non-inflating...
  26. R

    Which expansion is used for this result?

    exp (hv/kT) - 1 For hv<<kT exp (hv/kT) - 1 is approximately equal to hv/kT thanks for any ideas.
  27. W

    How Does Integration by Expansion Work for Sine Integrals?

    Consider the integral \begin{equation} I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt \end{equation} show that \begin{equation} I(x)= 4+ \frac{2x}{\pi}x +O(x^{3}) \end{equation} as x\rightarrow0. => I Have used the expansion of McLaurin series of I(x) but did not work. please help...
  28. R

    MHB Is McLaurin Expansion the Key to Solving Integration by Expansion?

    Consider the integral \begin{equation} I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt \end{equation} show that \begin{equation} I(x)= \frac{2x}{\pi} +O(x^{3}) \end{equation} as $x\rightarrow0$. => I Have used the expansion of McLaurin series of $I(x)$ but did not work. please help me.
  29. A

    Thermal Expansion of a circular steel plate

    Homework Statement A circular steel plate of radius 15 cm is cooled from 350 C to 20 C. By what percentage does the plates area decorate ? Homework Equations A=∏r^2 Af = Ai (1+2∂ΔT) specific heat of steel = 12 x 10^-6 The Attempt at a Solution r = 15 cm = .15 m Ai = .070685 m^2...
  30. jegues

    How to Solve Partial Fractions Expansion?

    Homework Statement Find the partial fractions expansion in the following form, G(s) = \frac{1}{(s+1)(s^{2}+4)} = \frac{A}{s+1} + \frac{B}{s+j2} + \frac{B^{*}}{s-j2} Homework Equations The Attempt at a Solution I expanded things out and found the following, 1 = A(s^{2} + 4)...
  31. U

    Liquid-Vapour Interface: Adiabatic Expansion

    Homework Statement Part(a): Show dL/dT can be expressed as: Part(b): Show L = L0 + ΔCT for an indeal gas Part(c): Show the following condition holds for an adiabatic expansion, when some liquid condenses out. Homework Equations The Attempt at a Solution Finished parts (a)...
  32. S

    Find the first eight coefficients of the power series expansion.

    Homework Statement Problem: Find the first eight coefficients (i.e. a_0, a_1, a_2, ..., a_7) of the power series expansion y = ##Σ_{n = 0}^{∞}## [##a_n## ##x^n##] of the solution to the differential equation y'' + xy' + y = 0 subject to the initial-value conditions y(0) = 0, y'(0)...
  33. C

    Thermodynamics - Ideal gas expansion

    Homework Statement 2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there? T=350K, Q=2.1E5 J, Vi=x, Vf=4x Homework Equations ΔU=Q-W W=\intpdV U=nCvT The Attempt at a Solution I'm not sure if I'm even on the...
  34. U

    Virial Expansion, Van Der Waals Gas

    Homework Statement Taken from 'Concepts in Thermal Physics': Homework Equations The Attempt at a Solution For the step highlighted in red, why does the '-1' go into the integrand?
  35. U

    Van der Waals Equation, Virial Expansion

    Homework Statement Taken from Concepts in thermal Physics: Homework Equations The Attempt at a Solution Shouldn't the van der waal's equation be: p = \frac{RT}{V_m -b} - \frac{a}{V_m^2} pV_m = \frac{VRT}{V_m -b} - \frac{a}{V_m}
  36. T

    Partial Fractions in Laurent Series Expansion

    Homework Statement f = \frac{1}{z(z-1)(z-2)} Homework Equations Partial fraction The Attempt at a Solution R1 = 0 < z < 1 R2 = 1 < z < 2 R3 = z > 2 f = \frac{1}{z(z-1)(z-2)} = \frac{1}{z} * (\frac{A}{z-1} + \frac{B}{z-2}) Where A = -1 , B = 1. f = \frac{1}{z} *...
  37. I

    What Is the Coefficient of Linear Expansion of Copper Based on Bragg Angles?

    Problem statement: The Bragg angles of a certain reflection from copper is 47.75◦ at 20◦C but is 46.60◦ at 1000◦C. What is the coefficient of linear expansion of copper? (Note: the Bragg angle θ is half of the measured diffraction (deflection) angle 2θ). Attempt at solution: Using...
  38. T

    You can edit the title of the first post and add [solved] at the beginning.

    I'm confused by problem 2.31 in mathematical tools for physics. Problem: 2.31 The Doppler effect for sound with a moving source and for a moving observer have different formulas. The Doppler effect for light, including relativistic effects is different still. Show that for low speeds they are...
  39. C

    Integrating a Taylor Expansion with Limits: Finding the Exact Value

    Homework Statement expand f(x) = x^4 - 3x^3 + 9x^2 +22x +6 in powers of (x-2) Hence evaluate integral, (limits 2.2 - 2) f(x) dx Homework Equations Taylor expansion for the first part integral f(x) dx with limits 2.2-2 The Attempt at a Solution Expansion of the function...
  40. KiNGGeexD

    Using Taylor expansion to find the limits of a function

    https://www.physicsforums.com/attachments/68247 I had been assigned this problem, I worked out the expansions (for practice) so they could have errors in them! I got to a point (in the photograph) where I could take out a common factor of 1/x but I'm pretty stumped although via other methods...
  41. Soumalya

    Constant pressure or isobaric expansion of gas

    It is said that in an isobaric expansion of a gas pressure remains constant throughout the expansion process. Suppose we have a quantity of gas at initial pressure P1 and volume V2 in a piston cylinder arrangement.We heat it slowly such that it expands to obtain a state with pressure P2 and...
  42. T

    One Dimensional Slab Heat Transfer Taylor Expansion in Glasstone

    Hi There, I came across the following passage in Sam Glasstone's 'Nuclear Reactor Engineering' See where I underlined in red that taylor series expansion? I don't understand how (dt/dx)_(x+dx) is equal to that. I know it's a Taylor series expansion, but where did the x+dx go?
  43. I

    Expansion of space vs stuff just moving away

    NOTE: I am not a cosmologist, so if any of my statements are not correct please tell me. When we observe distance galaxies we can measure how fast they move away using the red-shifting of their light. So how do we know space itself is expanding vs the galaxies are just moving away relative to...
  44. K

    Derive the analytic expression of a function by its Taylor expansion

    Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...
  45. S

    MHB Applying Shannons Expansion Theorem

    Wasn't exactly sure where to post this. Wanted to see if I did this correctly.Can someone check my work please? Problem: Consider f defined below. Apply Shannon's expansion theorem (also given below) with respect to input y as if you were implementing this function using a 2:1 MUX. Find the...
  46. M

    Large N Expansion: Getting Started

    Hello. Apparently for SU(N) gauge theories there is a perturvative approach call "large N expansion". I need a working knowledge of this method but I can not find it in any textbook only in research papers that are rather for the expert. Someone has any suggestion where should I get started...
  47. A

    Manufacturing question for thermal expansion disagreement

    Hello, my colleague and I are having a disagreement about the amount of thermal expansion in a particular part we are working on (manufacturing environment). It is a piece of structural steel, which has a thermal expansion value of 12 (10^-6/K according to the chart at...
  48. U

    Why does the series Taylor expand as e^-nx?

    In this section, they derive the Sommerfeld formula. In the first step it seems like they have expanded ##\frac{1}{(1+e^x))^2}##. I'm not sure why does the series taylor expand as ##e^{-nx}##? Also how did they get from the 2nd to the 3rd step? Simply by comparing terms we see they are...
  49. D

    Fourier expansion of boolean functions

    Any boolean function on n variables can be thought of as a function f : \mathbb{Z}_2^n \rightarrow \mathbb{Z}_2 which can be written as f(x) = \sum_{s \in \mathbb{Z}_2^n} \hat{f}(s) \prod_{i : x_i = 1} (-1)^{x_i} where \hat{f}(s) = \mathbb{E}_t \left[ f(t) \prod_{i : s_i = 1}...
  50. A

    How do I find the n+1 and n-1 order expansion of a Legendre series?

    Homework Statement Find the n+1 and n-1 order expansion of \stackrel{df}{dy}Homework Equations (n+1)Pn+1 + nPn-1 = (2n+1)xPn ƒn = \sum CnPn(x) Cn = \int f(x)*Pn(u)The Attempt at a Solution I know you can use the recursion relation for Legendre Polynomials once you combine Cn with the...
Back
Top