Thermal expansion Definition and 276 Threads

It is generally said that thermal expansion is a process determinated by the anharmonic terms in the potential of a crystalline solid. However, in the Course of Theoretical Physics by Landau Lifshitz, Statistical Physics part 1, paragraph 67, a form for the coefficient of thermal expansion is...

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...

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...

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...

Homework Statement There is liquid in a cylindrical container at some level. Now when the container is heated, the level of the liquid remains the same in the container. What is the relationship between the coefficient of linear thermal expansion of liquid and the container ? Homework...

I have two questions on fine points of thermal physics. 1. Is an isotropic solid's volume-expansion coefficient beta exactly equal to 3 times its linear-expansion coefficient alpha, or is it only approximately equal? Some textbooks (Fischbane, Walker, Young) say the relation is exact, while...

So I've been working at a steel mill where we deal with billets cooling from temperatures around 1200 C to between 10-25 C. I have access to average thermal expansion coefficients over this temperature range. First question: Over a large temperature range as aforementioned am I correct in...

Homework Statement The coefficient of linear expansion of a rod of length 1 meter (at 300K) varies with temperature as ##\alpha=\frac{1}{T}##, where T is the temperature. Find the increment in length when the rod is heated from 300K to 600K Homework Equations $$\Delta L=L\alpha \Delta T$$ The...

Homework Statement Since the 1980's a total of 20 x 10^22 J of additional energy has been absorbed by the worlds oceans. This is 90% of the additional heat our planet is storing as a consequence of global warming. The surface area of the worlds oceans is 361,900,000 km^2 and we will assume this...

Homework Statement I want to find the mathematical proof to show that the density of an object changes with thermal expansion. My professor showed this in class and it was horribly wrong because he let a few things out. The book I'm reading showed it in 4 steps and left out a lot of the crucial...

this is a picture of my notes for thermal expansion for linear vs area. my question is why does the area coefficient of expansion for the area = 2(liner coefficient of expansion). any insight would be appreciated.

Homework Statement A spherical brass shell has an interior volume of 1.60 x 10-3m^3. Within this interior volume is a solid steel ball that has a volume of 0.70 x 10-3m^3. The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole...

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...

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...

At one point I had been trying to construct an equation which would calculate the tension on a tuned string with a change in temperature (and therefore the fundamental frequency), but found my calculations were wrong. By extension, the purpose of the project was to be able to calculate what...

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...

Good day, I am currently developing a thermal expansion analysis of a pipe line, I need to validate if the current installed Gimbal joints will withstand those conditions. These gimbal joints just allow angular movement. Is there any software or method that can help me as reference for this...

I'd like to setup an Excel spreadsheet to demonstrate the expected change in string frequency due to small changes in temperature. How should I go about doing this? This is the data from the piano that I can gather: -string length -string diameter -string area -string/partial frequency How do...

Homework Statement I'm looking for a good explanation, not interested in the answer. A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C. How much more interior space does the dome have in...

We say the expansion coefficient of steel is 12 × 10 -6 m/m°C, Young's modulus 210 × 109 N/m2 and yield stress 250 mega Pascal. With 100 meters length and 0.1 m2 section area , If we increase its temperature 10 °C, how much energy will be produced by expansion force in Joules? with young's...

Hi, I am trying to design a tubular probe that's made of stainless steel (304), from what I've read it has a Thermal expansion coefficient of around 9.6 x10^-6 in/in/F give or take on the quality. I want to fill this tube halfway with an Epoxy, however from what I've read this epoxy has a...

Hello everyone! First time asking a question here, go easy on me! I am a first year Mech-Eng student in Ireland, and I need some guidance from one of the amazing brains here at physicsforums. I am told by my thermofluids lecturer that in thermal expansion, the amount of material expanding is...

Hi, The coefficient of thermal expansion for aluminium is 23ppm/C at 20C = 0.000023m per degree in temperature (C). Is this temperature: (1) the temperature of the air circulating around the material in the sun, (2) the temperature in the shade at that time of the day, or (3) the tactile...

The "coefficient of linear expansion" (≡k) was defined in my book by the following relationship: ##\Delta L=Lk\Delta T## Where L is length and T is temperature I'm wondering, is this just an approximation? Because, if you were to increase the temperature by \Delta T and then calculate the new...

Looking for some information on how a shrink fit collar actually works. I get the basic principle that you heat it, it expands, fit the collar, let it cool and it contracts and grips as a collar. However, if you heat a material am I right in saying that it expands in all direction. If this is...

Homework Statement "see attachment" "q1" Homework Equations V=\frac{-A}{r}+\frac{B}{r^{10}} A=5*10^-30 B=8*10^-121 V=potential energy r=interatomic separation distance Coefficient of thermal expansion = \frac{change in L}{L*change in T} The Attempt at a Solution I have...

Homework Statement Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 63.1 m of copper pipe whose inside radius is 7.69 x 10^-3 m. When the water and pipe are heated...

Hi All, I would like to ask if what supplier's fabricate Low Coefficient of Thermal Expansion (CTE) glass tubing for Fiber Optics application. or What type of glass do we need in Low CTE? It will serve as the packaging for DWDM components. Hoping for your response. Thank you.

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...

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...

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...

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...

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...

Are there any theories or thoughts that view spacetime as 'having' a coefficient of thermal expansion... analogous to the CTE of water? An inflection with density in regards to temperature?

Hey fellas please consider helping me with this.. There is a bar of some material that is heated from state 1 to 2 to 3. If l1 is the length at 1 then we have, l2 - l1 = l1(1 + a(t2-t1)) l3 - l1 = l1(1 + a(t3-t1)) If, t3-t2 = t2-t1, Then l3-l2 = l2-l1 But if it is written l3 - l2 =...

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...

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...

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...

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?

Homework Statement A brass bar and an aluminium bar are each attached opposite each other to immovable walls. (There is a diagram, but I think the idea is clear enough). There is a gap between the two bars of 1.3x10-3m at 28°C. At what temperature will the gap be closed? coefficient of...

I have an aluminum disc that is 15in in diameter and about 1in thick. I am going to put it in a 400°F oven and I need to know how much the diameter will expand. One of the engineers I work with(i'm an intern) is using what I found to be the linear expansion equation (ΔL/Li=αΔT)...so Length...

1. a steel plug has a diameter of 10.0 cm at 30 degrees celsius. at what temperature will the diameter be 9.986 cm? 2. a steel measuring tape is exactly 50,000 m long at 20 degrees celsius . (a) what is the length on hot summer when the temperature is 35 degrees celsius? (b) if such steel tape...

Homework Statement At a temperature of 18°C a beam of diffracted monochromatic x-rays is observed at an angle of 150.8° to the incident beam after being diffracted by a crystal with cubic structure. At a temperature of 318°C the corresponding beam makes an angle of 141.6° with the incident...

Homework Statement 1. a 100m long copper wire of diameter 4mm is heater from 20C to 80C. What is the change in the length of the wire? 2. a 0.2m diameter aluminium sphere is cooled from 250C to 0C. What is the change in the volume of the sphere? The coefficients of linear and cubic expansion...

Homework Statement Three identical wires Lo, diameter d, are arranged like a Y letter (please see attachment) Each end of the wires is secured to a wall. Initial tension is approximately zero. If the wires are cooled ΔT, find the distance the knot moves to the right and the final tension in...

I was just wondering what would be sources of error in calculating thermal expansion

Homework Statement A ring of aluminum has a hole in the middle. When the ring is heated: a) the hole decreases in diameter b) the aluminum expands outward and the hole remains the same size. c) the area of the hole expands by the same percent as the area of the aluminum. d) the area of...

Homework Statement As shown in attachment a steel cable is stretched between two poles. In 20°C temperature the cable remains horizontal (the length of the cable 10m). At a higher temperature θ°C the cable bends like in attachment. The lamp hanging from the mid-point could be...

Consider a rod of length 'l'. When heated, its temperature got increased by 't'. Increase in its length = l\alphat. total length be (l1) = l + l\alphat. Again the rod is heated and the temperature further got increased by 't'. Total length be l2. l2 can be calculated in two ways, l2 = l1 +...