Expansion Definition and 1000 Threads

Homework Statement I don't need help solving I just need some clarification. Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy). On my test I was asked to calculate the work of the isentropic expansion of a carnot engine with air...

Hello Everyone, Back when Einstein was formulating General Relativity his equations just could not predict a static universe. I have read that they actually predicted an expanding Universe. Later Friedmann derived an equation from GR that would explain how an Expanding Universe would evolve...

We have 2 (insulated) partitions, one with the gas, another vacuum, separated by a stop cock. We remove the cock, letting the gas expand into vacuum . I understand that since there is no opposing force on the expanding gas ,the work done by the gas is zero . But work done by gas is given by...

Firstly, I assume that I'm correct in assuming that since expansion is accelerating it will increase to any arbitrarily large value at some point in the future. If this is true, there must be some point at which particle/antiparticle pairs (due to uncertainty) are carried away from one another...

Since the universe is expanding at an accelerated rate and accelerating frames can perceive that motion as being the result of a gravitational field, have we ever been able to sense a gravitation field fluctuation in the Earth that occurs every 24 hrs? Would someone not be facing the direction...

Homework Statement A saturated water vapor mix in a 0.05m3 piston-cylinder at 200C with a quality of 0.5 expands adiabatically, producing 500kJ work with a final temperature of 50C. Find: a) final quality b) change in entropy[/B] Homework Equations Q-W=ΔU x=(vavg-vf)/(vg-vf) uavg=uf+xufg...

Hello, If a thermal linear expansion happens to a meter stick, for instance a 50 m steel meter stick, the new length would be 50(1+(coefficient of expansion )(ΔT)). My question is would this also work if we choose different segment of the meter stick?For example, Can the new length for the part...

Homework Statement I need to calculate the electric field on the midplane of a uniformly polarized cylinder at a large distance from the center of the cylinder. The question also says that because the distance is large compared to the radius the dipole dominates the multipole expansion...

New member here, thanks for your patience. The farthest galaxies are the most redshifted, but doesn't that old light tell us more about the rate of expansion closer to the beginning of the Universe?

In a quantitative science verbal phrases like "rate of expansion" have to correspond to mathematically well-defined quantities. As far as I know, in Cosmology the only quantitative handle in common use that corresponds to "rate of cosmic expansion" is the Hubble constant, and as best we can...

Homework Statement A brass rod (linear expansion coef 19*10-6/°C) has a radius of 8139 cm and a copper (linear expansion coef 17*10-6/°C) sheet has a hole or radius 8139+8.86cm. What temperature change (K) is required to close the gap? Homework Equations ΔL/Lo = αΔT? The Attempt at a Solution...

Here is the second paragraph from the article on metric expansion of space from Wikipedia Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the Universe we inhabit. However, the model is valid only on large...

If I induce vacuum in a glass tube and then I open the lid of the glass tube, air rushes into fill in the vacuum. Can vacuum be regarded as a sort of potential energy, able to exert a force? Can a vacuum tube be considered as a potential storage device for energy, just like a container filled...

Wouldn't the explanation that fits fundamental laws (e.g. Conservation of E) while making the least asumptions be an ongoing bang-crunch-bang...scenario? Why couldn't expansion be eventually reigned in by forces, dark matter and the like - ultimately leading to contraction? Why shouldn't...

Hello guys, I have some troubles to understand a reversible adiabatic expansion. we have dq=0 and dw=-pdV and for a perfect gas dU= Cv*dT. I don't really understand why dU= Cv*dT since we have a variation of volume and it is established that dU= Cv*dT when we haven't any modification of the...

Can anyone help me understand how to arrive at the expression (16) in the following link? http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-50532009000700002&lng=en&nrm=iso&tlng=en I don't see how it follows from insertion into (14), but I have seen exactly this transition happen...

Consider two self-adjoint operators A and B with commutator [A,B]=C such that [A,C]=0. Now I consider an operator which is a function of A and is defined by the series ## F(A)=\sum_n a_n A^n ## and try to calculate its commutator with B: ## [F(A),B]=[\sum_n a_n A^n,B]= \\ \sum_n a_n...

Homework Statement Find the expansion coefficients of a generic vector (λ, μ) ∈ ℂ^2 in the orthonormal basis: { i/sqrt(2) (1, 1), 1/sqrt(2) (1, -1) } Homework Equations λ_i = |v_i> |v> The Attempt at a Solution I don't think this should be difficult. But, clearly, as I am posting here, I do...

A number of contemporary models propose that the universe was contracting prior to expansion. However I have found this critique of such a proposal from Geroge Elliss: “initial conditions have to be set in an extremely special way at the start of the collapse phase … in an acausal way (in the...

Per my layman's understanding, the apparent force of gravity, as explained by the general theory of relativity, is actually the result of rectilinear motion at uniform speed through warped spacetime. 1. If that's the case, what actually causes gravity for objects at rest with respect to the...

Hello, I'm trying to determine a way of calculating the thermal expansion of a volume of water. The formula I have come across is: ΔV = βV0ΛT The general consensus seems to be that water expands roughly 4% from 20°C to 100°C, or 4.2% from 4°C to 100°C...

The exponentials ##\phi_p(x)=e^{ipx} ##(where ## px=p_\mu x^\mu##), are solutions of the free KG equation ## (\partial_\mu \partial^\mu+m^2) \phi =0##. I can expand the solutions of the interacting KG equation ## (\partial_\mu \partial^\mu+m^2)\psi=V\psi ## in terms of solutions of the free KG...

In his book, Theoretical Concepts in Physics, Malcolm Longair describes two experiments that Joule performed involving gas expansion (the discussion starts on pg. 217). In both experiments, there is a chamber containing gas, labeled A, and a chamber that is evacuated, labeled B. There is also a...

Does it make a sense to define the Taylor expansion of the square of the distance function? If so, how can one compute its coefficients? I simply thought that the square of the distance function is a scalar function, so I think that one can write $$ d^2(x,x_0)=d^2(x'+(x-x'),x_0)=d^2(x',x_0) +...

Hi! From this text: http://arxiv.org/pdf/nucl-th/0004061v1.pdf I need to resolve these integrals. 1) Equation (5), \int e^{-\omega_1/T}d{\vec k}_1 =? where \omega_1=\sqrt{m^2+{\vec k}^2_1} What function is K_2(m/T)? 2) Equation (26), \rho_s(T) Thanks!

Homework Statement The energy and pressure of black body radiation depend on T and V as Eq(1) & Eq(2). Suppose that the temperature and volume of a box of radiation change adiabatically. Find the relation between dE and dT in this process. Next, using Eq(1), show that T ∝V^-1/3 Homework...

I have some homework that I am just not able to figure out. There is a 2kg parcel of air at T1=32°C and p1= 0.8 atm This parcel of air expands until it is at T2=12°C Also, during the expansion 3.2 g of water will condense due to the dT (ΔvapH (water) = 40.65kJ mol-1 Also: Cv=0.718 kJ...

Hi, We all know the universe is expanding and it's doing so at a rate greater than the speed of light. But what does expansion mean? Popular Science videos usually give the loaf of bread example expanding in the oven. But even the loaf of bread has limits, it can only expand so far. Do we know...

I read in "The Theory of Everything" of Stephen Hawking that all of the galaxies are running away from ours. That made me think that the Milky Way is the center of universe, since each galaxy is running away from us(like waves on the surface of water centered at one point which is the Milky...

Homework Statement [/B] Consider a hydrogen atom which, in t = 0, is in the state given by \psi(\mathbf{r},t>0)=\frac{A}{4\pi}R_{10}(r)+\frac{cos\alpha}{4\pi}\left(\frac{z-\sqrt{2}x}{r}\right)R_{21}(r) Expand ψ in terms of the {Φnlm} basis of normalized eigenfunctions...

Homework Statement divide in partial fractions: x^3 -3x^2+x-12 / x^4+5x^2+4 Homework EquationsThe Attempt at a Solution I factored x^4+5x^2+4 to (x^2 +1) (x^2+4) x^3 -3x^2+x-12/(x^2 +1) (x^2+4) = A (x^2+1)/(x^2 +1) (x^2+4) + B (x^2+4) /(x^2 +1) (x^2+4) they all have the same...

Is it possible to measure the universe' expansion in m/s^2 instead of metres per second per parsec?

I thought about the Taylor expansion on a Riemannian manifold and guess the Taylor expansion of ##f## around point ##x=x_0## on the Riemannian manifold ##(M,g)## should be something similar to: f(x) = f(x_0) +(x^\mu - x_0^\mu) \partial_\mu f(x)|_{x=x_0} + \frac{1}{2} (x^\mu - x_0^\mu) (x^\nu -...

I get that Planck length is derived from h, G and c. But as a theoretical measure of length how is it affected or not affected by cosmological expansion?

Greetings, I am new to this forum and would like to present a discussion. If a miniscule black hole is created in the LHC. Is it probable the LHC is capable of creating more than one black hole during a single event collision? Considering fact and theory provided by credible research. Could...

[Moderator's note: Spun off from another thread, where it was off topic. Please start a new thread when you have questions on a new topic.] Photons lose energy when they travel long distances. Where does that energy go? What happens to that energy? Is there any theory regarding this?

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >[/color] hi I've got a problem that I've partially worked but don't understand the next part/have made a mistake? f(x)=0 for -π<x<0 and f(x)=x for 0≤x≤π i got a0=π/4 and an=0 and bn=0 if n is even and...

Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 4) Continue reading the Original PF Insights Post.

Hi, newbie reading the forum with interest, and trying to understand how expansion manifests itself physically. Four possibilities; 1. New space is created between existing space, pushing galaxies apart 2. Existing space is stretched, pushing galaxies apart 3. Empty space is nothing, and...

From what I have read, it sounds like GR predicts that under certain conditions, space itself will expand. If this is incorrect, please just let me know and ignore the below. While I don’t know the math involved in GR, I can understand explanations of how gravity distorts space-time, to alter...

I have a problem understanding the concept of thermal expansions of solids with a hole in it. I do not want to accept face value the traditional explanation i am given that hole will increase in size because i am told to imagine if the hole was never cut. I fail to see the congruency in these...

Hello all, Is there any direct relation ship exists between the thermal expansion and density of polymer material (eg. PMMA, Teflon) ? Like, Lorentz- lorentz law relates directly the refractive index and density of the polymer. similarly any laws relating (thermal expansion and density of...

I accept that what I write below will be unpopular and argued with vehemently, however I think it should be considered with an open mind and recognised for the sense that it has. Originally the concept of an expanding universe (and therefore by extrapolation the concept of the Big Bang that...

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 2) Continue reading the Original PF Insights Post.

If space will be expansion then it effect on Earth diameter. If Earth become narrow then how gravity force work ?

I have a paradox that I don't know the answer to. Special relativity has no preferred frame, but it seems like adding an exponential expansion to space introduces such a frame. The Setup Suppose we're in a universe with a much faster expansion rate, where the space between any two objects...

Homework Statement Let ##x_n## be the solution to the equation ##\left( 1+\frac{1}{n} \right)^{n+x} = e## Calculate ##\lim_{n\to \infty} x_n## Homework Equations N/A The Attempt at a Solution Since ##\lim_{n \to \infty} \left(1+ \frac{1}{n} \right) = e## that tells me that ##\lim_{n\to...

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math Continue reading the Original PF Insights Post.

If I understand what the BB Theory proposes, all the universe was originally confined to the size of something very small, like a dot or an atom. This small dot or atom or whatever was said to explode, although some say there was no explosion in the sense of a bomb going off, but would be more...