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.
If I understood well, cosmology makes a difference between matter moving in spacetime and the expansion of spacetime itself. Are these concepts experimentally distinguishable, or this distinction is only in our theories?
ΔL= αLoΔT
ΔL = (23*10^-6)(0.2480 m)(28.30°C)
ΔL = 1.61 * 10^-4
Period is 1s, so each second the pendulum moves 1.61 * 10^-4 m
1.61 * 10^-4 m/s *(60s/1min)*(60min/1hr)*(24hr/1day) = 13.95 m/day
T = s (1:1 ratio)
13.95 seconds. But the answer is actually 69.3 s. Is the equation T = 2π√L/g...
Space evidently is expanding, so we say that the very fabric of space time is expanding uniformly in all directions, so two questions
1)originally this expansion was driven by the energy content within the universe aka the dense hot matter , versus nowdays the acceleration is picking up speed...
I hope that I am conveying what I see in my head clearly. I guess that I am visually imagining the 3 spatial dimensions projected on the 2d surface of a sphere and as that sphere expands that the increased distance between 2 points would happen what seems like at an accelerating rate because of...
Let's say I have a liter of gas at pressure of 4 atm and T=900K. I use it to move perfect massless frictionless and insulative piston to compress a liter of 1 atm, T=300K gas. When the pressure on both sides is equal and the piston stops moving, will the temperature on both sides of the piston...
I am trying to find out where to get the Thermal coefficient of expansion for glycerin. The only thing I keep getting when using Google is mathematical examples that use glycerin as an example and its coefficient but I need to know where this number is coming from.
Ex:
4.85 × 10^-4 (°C)-1
I get
$$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$
as the coefficient. I was just unsure how to evaluate it numerically from here. Any suggestions would be appreciated. Thank you.
Homework Statement: Use Taylor expansion to show that for ##u \in C^4([0,1]) ## $$ max |\partial^+\partial^-u(x) - u''(x)| = \mathcal{O}(h^2)$$ For ##x \in [0,1]## and where the second order derivative ##u''## can be approximated by the central difference operator defined by...
I do not understand how this formula is derived:
Can somebody help me?
Source:
https://www.corzan.com/en-us/piping-systems/specification/thermal-expansion
Summary: Is it possible to tell the current average universe expansion rate i.e. acceleration of expansion in m/s^2 ?
Is it possible to tell the current average universe expansion rate i.e. acceleration of expansion in m/s^2 ?
If i say in relation to earth, does this make it easier to answer...
I am searching for the appropriate methodology/equation(s) to step beyond Boyle's Law to account for the phase change and solve this problem.
All suggestions/guidance is greatly appreciated!
Bruce
Part (a)
ΔS = ∫ (dq/T)
because: dq = PdV = (nRT/V)dV
Then:
ΔS = ∫ (1/T)*(nRT/V)dV
ΔS = nR ∫(1/V) dV
ΔS =nR[ln(V2/V1)]
Part (b)
This is where I'm stuck. I know [P + a/(v/n)2][v/n - b] = RT can be solved for P and simplified to
P = [RT/(v-b)]-[a/v2] since n=1mol
But I don't know how to proceed...
Summary: Can someone give me a basic high level overview on how to do a binomial expansion?
I'm studying for my E&M test and going over multipole expansion. I'm particularly confused about these lines (Griffiths E&M 4th Edition)
𝓇^2_{\pm} = r^2 \left(1\mp \frac{d}{r} \cos\theta +...
for the case, r>>r' the higher-order term like 1/r^2 and above that is negligible.
so V(r)=cons.*1/r*P0(cos a)
but for the case r'>>r will it be V(r)=cons.*1/r'[ summation Pn(cos a')t'^n] where t'=r/r'
now if we neglect higher-order term of r/r' then V(r)=cons.*1/r'*P0(cos a') which is...
Hi everyone,
I'm interested in relativistic anisotropic hydrodynamics and often a "gradient Expansion" is mentioned in articles, but not how this works exactly. I gathered that this is some kind of expansion of the energy-momentum tensor. Can someone explain to me how this expansion is set up...
Summary: The universe is expanding, so at one point in the past it must have been all concentrated into a single point. But is this really an accurate observation?
Hi,
This is my second probably naive question that's been on my mind as a lay-scientist for a long time (the other will hopefully...
This is a repost as I didn't read the community guidelines the first time. Hopefully this is better!
First thing I did was write down both the linear and volume expansion formulas.
I then multiplied my alpha by 3 and used the volume expansion equation for both materials.
∆V oil > ∆V pot, at the...
Summary: Help with volume and length expansion question
Hi, I am struggling with this question. I understand that beta = 3 alpha so you use this to sub into the volume expansion equation. Is this correct? Can someone please provide a step by step instruction on how to do this question? Thank you !
The rates I've come across are 67, 71 and 74. Obviously it's not 74 as it was just announced. Is it one of these other numbers, something else? I'm only asking out of curiosity.
Suppose light travels during a time interval of t2 - t1, where the scale factors at t1 and t2 are a(t1) and a(t2) respectively.
If we consider an infinitesimally small interval of time dt during this interval, without accounting for expansion we would expect light to travel a distance cdt. How...
A basic question... The further a galaxy is from ours, the more redshift, the faster it is moving away from us. This is taken as a sign the universe is expanding at ever increasing rate.
Yet... As we look farther out into space, we are also looking back in time. If the farther we look back in...
Disclaimer:
I am parroting the information in this from articles that I've read. This post is to try to get a better understanding of what they are talking about and if any of it is relevant.
I came across an article regarding the Big Bang while looking into the current rate of universe...
In the process of developing a tank venting program and starting to investigate how to incorporate tank gas expansion cooling I realized that since: T=P/nR with R constant and the reduction of P and n directly proportional then this equation implies all tank ventings are isothermal. What am I...
Given that the expansion takes place "in nothing".
Given that all space-time exists all of the time. (past/present/future)
If the ultimate fate of the Universe is that it collapses back in upon itself.
Shouldn't a singularity of space-time occur instantaneously?
After all, all time existed...
Recently I was thinking about the Hubble's constant (which, actually, is not Hubble's and not constant...) and wondering: if the universe is expanding at 70 km/s each Mpc, then there's possible to calculate some expansion of space, say from me to a person 1 meter away from me (theoretically)...
So I'm on page 67 of Marion/Thornton's "Classical Dynamics of Particles and Systems" and I'm in need of some help. I understand that so far there's is an equation that cannot be solved analytically (regarding motion due to the air resistance and finding the range of the an object shot from a...
I have been playing around with Taylor expansion to see if I can get anything out but nothing is jumping out at me. So any hints, suggestions and preferably explanations would be greatly appreciated as I’ve spent so so long messing around with it and I need to move on...
But as always, thank you
Hello everyone. I am currently using the pca function from MATLAB on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...
Summary: Expansion of matter in the visible universe, total volume of space outside the visible universe, black hole mechanics, and general questions from an uneducated but extremely interested evolved monkey.
Hello everyone! I do not know the rules of this forum, or any forum for that matter...
I expanded the exponential with the derivative to get:
## Z = \Bigg(1 + \frac{1}{2} \frac{\partial}{\partial x_{i}} A^{-1}_{ij} \frac{\partial}{\partial x_{j}} + \frac{1}{4} \frac{\partial}{\partial x_{i}} A^{-1}_{ij} \frac{\partial}{\partial x_{j}} \frac{\partial}{\partial x_{k}} A^{-1}_{kl}...
As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The...
I tried diffrentiating upto certain higher orders but didn’t find any way.. is there a trick or a transformation involved to make this task less hectic? Pls help
So the universe is expanding, and galaxies are getting farther apart from one another on average. Does this motion count the same as ordinary motion, in that if a galaxy is being expanded away from us at 0.5c, that clocks in that galaxy would appear to tick slower at 0.866 the rate of clocks here?
I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2.
There's a great example in wikipedia which is almost...
Space/time is relative. What is the expansion relative to? Is there a reference point of no expansion to make a comparison? Accelerated contraction would appear to be expansion by an observer looking back in time so how can we be certain that the universe is expanding instead of collapsing at...
In an isothermal process, for an expanding gas ##\Delta U_{sys}=0## and ##Q=-W## but then,
How can we evaluate ##Q_{surr} ##?
It should be ##Q_{surr}=-Q_{sys}##, but I don't know how to show it in equations.
If I try to get the result through the principles:
##\Delta U_{sys}=-\Delta U...
What happens to the fabric of spacetime during the expansion of the universe? Does it stretch or expand? If it does not stretch or expand, does new spacetime form to "fill the gap" as such?
Hypethotically speaking, I have two celestial objects separated by a gap 1 mile wide. Due to the...
I realize that my understanding of this matter and it's vast number of related concepts is rudimentary and incomplete.
Kindly forgive my ignorance and try to explain your thoughts in layman's terms.
Thank you for your time.
I'm not an expert in this matter, and at best only aware of some superficial facts and a layman's understanding of them. So please forgive me for any ignorant mistakes in my thoughts, and kindly point them out to me.
Going by the Lambda-CDM model, the expansion of the Universe will eventually...
Is the likelihood (or unlikelihood) of a Big Rip changed by the new findings of faster universe expansion (https://www.sciencedaily.com/releases/2019/04/190425104128.htm).
In
https://www.physicsforums.com/threads/will-the-big-rip-basically-be-the-big-bang-for-the-next-universe.971039/, phinds...
For the reversible expansion of an ideal gas the heat flowing out of the surroundings and into the system is equal to the work done by the system. Since both system and surroundings have the same constant temperature the entropy increase of the system is equal to the entropy decrease of the...
While doing some calculations I came across some terms which are ##\frac{(v•\vec \nabla)v}{a(t)}## and ##\vec \nabla•[\rho(1+\delta)v]## where all quantities have spatial dependence other than "a" which has only time dependence ,
the first term here is canceled and the the second term is...
Hi! Obviously my understanding is at a pretty elementary level, but nevertheless I'm puzzled by the reaction of astronomers and astrophysicists to the discrepancy in the measurements of the expansion of the early universe based on the Cosmic Microwave Background, and the measurements of its...