What is Thermal expansion: Definition and 276 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.

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  1. F

    Why Is Volume Excluded in My Thermal Expansion Calculation?

    Homework Statement Hell people I am stuck on this problem I solved and got the correct ans but. I somehow stumbled on the right answer by accident. My work is correct buy I have one question. 1.) on a hot day , a cubical swimming pool is filled to within 1.9 cm of the top with water at...
  2. F

    Thermal Expansion of Cube and Sphere

    Homework Statement A solid sphere and a solid cube are made from the same material. The sphere would just fit within the cube, if it could. Both begin at the same temperature, and both are heated to the same temperature. Which object, if either, has the greatest change in volume? The...
  3. D

    Thermal expansion of a copper cylinder

    Homework Statement A copper cylinder is initially at 20.0 degrees c At what temperature will its volume be 0.150 % larger than it is at 20.0 degrees c Homework Equations delta v = Beta vo (delta T) dv= beta vo dtThe Attempt at a Solution ive found an answer of 49.41 degrees c I believe its...
  4. fluidistic

    Linear thermal expansion, theoretical instead of experimental

    Is there a known formula or method to find the linear coefficient of thermal expansion for all materials? I'm curious about what are the variables.
  5. A

    Thermal expansion of a glass bottle

    A typical mercury thermometer is made up of a thin, cylindrical capillary tube with a diameter of 0.0040 cm, and the spherical bulb with a diameter of 0.25 cm. If we DON'T Neglect the expansion of the glasas, find the change in height of the mercury column for a temperature change of 30 degree...
  6. N

    How Hot Must the Steel Rim Be to Fit Over the Cast Iron Wheel?

    Homework Statement The question is : Wheels for railway cars are made of a disk shaped cast iron body of outer diameter 930.0 mm and a steel rim of inner diameter 927.0 mm at 20 degrees Celsius. To what temperature must the steel rim be heated so that it will just slip over the cast iron body...
  7. T

    Thermal expansion of a metal round disk with hole in the middle

    This is my first post on this forum because I have a question that I cannot seem to answer myself. At my working place we have a machine where a metal conveyor belt is running through a section of the machine where the temperature is constant at 320 degrees Celcius. On this conveyor belt are...
  8. P

    Thermal Expansion: Find % Change in Density & Metal ID

    Homework Statement When the temperature of a metal cylinder is raised from 0 degrees C to 100 C,its length increases by 0.23%. (a) Find the percent change in density. (b) What is the metal? Homework Equations ∇L = Lα∇T The Attempt at a Solution
  9. A

    Strange behavior of thermal expansion and resistivity equations

    The equation of linear thermal expansion is l=l_0\left[1 + \alpha(t - t_0)\right] (it is similar also to the equation of resistivity, \rho=\rho_0\left[1 + \alpha(t - t_0)\right]) \alpha is a constant dependent only on the material we are speaking about. Now, let's say I have a bar 100 m long...
  10. M

    How Does Initial Water Height Impact Thermal Expansion Calculations?

    Homework Statement Hello, I'm doing a lab on the Thermal Expansion of Water. I went through the whole lab and got good data based on the the proposed theory however I didn't record the initial height of the water in the pipette. The set up looked like this...
  11. R

    Derive the density relation to thermal expansion

    Homework Statement Show that it follows from \frac{dV}{V} = \beta dT that, for small changes, density has a similar linear relationship to thermal expansion, namely \frac{d\rho }{\rho } = - \beta dTHomework Equations The Attempt at a Solution Well, at first glance this one seems ridiculously...
  12. S

    Thermodynamics - Thermal expansion (linear)

    Homework Statement Two cubic samples of the same dimensions (length L) have thermal conductivities \kappa_1 and \kappa_2. The slabs are placed adjacently horizontally | 1 | 2 | Obtain expressions for the heat flow rate through the composite slab if the temperature difference is applied a)...
  13. J

    [Thermo.] thermal expansion and isothermal compressibility coefficients.

    Homework Statement A certain metal whose thermal expansion coefficient \beta is 5,0 × 10^-5 °C^-1 and whose isothermal compressibility \kappa_T is 1,2 × 10^-6 atm^-1 is at an initial pressure of 1 atm and an initial temperature of 20°C. A thick layer of Invar is thermally insulating the...
  14. R

    Piping Anchor Force due to Thermal Expansion

    Hey guys, I've got an L-bend of pipe carrying hot water that I'm trying to analyze. I've been using the ASHRAE and MechE Handbook of Calculation methods to determine the forces on the anchors due to thermal expansion, but I'm arriving at very different numbers. Here are my specs: An 8"...
  15. D

    How to find the thermal expansion coefficient?

    following is an example question i found on a lecture slide. I need some explanation to understand it. http://img266.imageshack.us/img266/7062/thermal.png Uploaded with ImageShack.us In this example, Is it possible to get the thermal expansion coefficient from the data given in the...
  16. P

    Thermal Expansion of ethanol problem

    Homework Statement 1. You pour 108 cm3 of ethanol, at a temperature of - 10.0 C, into a graduated cylinder initially at 20.0 C, filling it to the very top. The cylinder is made of glass with a specific heat of 840 J/kgK and a coefficient of volume expansion of 1.2 × 10-5 K-1; its mass is 0.110...
  17. E

    Thermal Expansion of a copper sphere

    Please help with the below question: I have given my attempt below! "A copper sphere of radius 2.000 cm is placed over a hole of radius 1.990 cm in an aluminum plate at 20 deg. C. At what common temperature will the sphere pass through the hole?" My answer: ((∆T(23* 10-6)(0.01990)-...
  18. S

    Mechanics of Materials: stress due to thermal expansion

    Homework Statement The magnesium allow tube (AM1004-T61) AB is capped with a rigid plate. The gap between E and end C of 6061-T6 alluminum alloy solid circular rod CD is d[m] when the temperature is T_1 degrees celcius. [PLAIN]http://img27.imageshack.us/img27/8867/problemwn.jpg The...
  19. P

    Thermal Expansion, Young's Modulus

    Homework Statement 6. A steel beam is used in the road bed of a bridge. The beam is mounted between two concrete supports when the temperature is 23⁰C, with no room for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the...
  20. P

    What is the final temperature of ethanol after thermal equilibrium is reached?

    Homework Statement 1. You pour 108 cm^3 of ethanol, at a temperature of - 10.0 C, into a graduated cylinder initially at 20.0 C, filling it to the very top. The cylinder is made of glass with a specific heat of 840 J/kgK and a coefficient of volume expansion of 1.2 × 10^-5 K^-1; its mass is...
  21. T

    Calculating Thermal Expansion and Bending in a Pipe

    I was wondering if anyone could provide me with some info on a problem I am facing. I have a pipe of 10m and 16" diameter. It has steam flowing through it, and due to inaccurate desuperheating we have a difference of temperatures at the bottom at top of the pipe. Assuming we have a...
  22. L

    Help: The thermal expansion coefficient of spring.

    Hi, everyone. I am just curious about the following question: Does the thermal expansion coefficient of a spring be the same as a slab with the same material? Thanks very much.
  23. R

    Free Thermal Expansion and Stress

    This is a question put to me by a colleague of mine which I don't quite know how to answer and has lead to a confusion ( or may be a misconception of physics) The question is as follows: When a solid rod is heated it undergoes a Free Thermal Expansion > means that the energy of the atoms...
  24. M

    Change in Resistance due to Thermal Expansion

    Homework Statement The filament of a lightbulb has a resistance of R0=12 Omegas at 20 degrees Celsius and 140 Omegas when hot. a) Calculate the temperature of the filament when it is hot, and take into account the change in length and area of the filament due to thermal expansion...
  25. S

    Stuck with a problem on linear thermal expansion of solids

    stuck with a problem...on linear thermal expansion of solids Homework Statement I just read a problem 2day...it's on linear thermal expansion of soild...can anyone guide me through...it says..." A sqaure ABCD is made with two different metals...the coefficient of thermal expansion of the...
  26. L

    Solving Thermal Expansion for Separation of Metals

    Homework Statement A brass ring of diameter 10.00cm at 20.0*C is heated and slipped over an aluminum rod of diameter 10.01cm at 20.0*C. Assuming the average coefficients of linerar expansion are constant, to what temperature must the combination be cooled to separate the two metals...
  27. T

    Calculating Expansion Cracks Width for Concrete Highway -30°C to +32°C

    Homework Statement A concrete highway is built of slabs 12 m long (20°C). How wide should the expansion cracks be (at 20°C) between the slabs to prevent buckling if the range of temperature is -30°C to +32°C? ________ cm Homework Equations change in L = L original * alpha * change...
  28. T

    Emergency Thermal Expansion question(Mech. Materials)

    If the change in temperature is negative: 1st of all, is it possible? and second, if it's a bar between two rigid supports, does the reaction would have to be in tension instead of compression to compensate for the bars trying to contract due to temperature? Also what if it has an axial force...
  29. G

    Thermal Expansion: Square & Hole Expansion

    Homework Statement You have a square which has a hole inside. When the temperature increases how does it expand? Homework Equations The Attempt at a Solution I know that the hole will expand along with the square, but I don't see why. Can't it expand in both directions: the...
  30. T

    How Wide Should Expansion Cracks in Concrete Slabs Be to Prevent Buckling?

    Homework Statement A concrete highway is built of slabs 14 m long (20 degrees Celsius) How wide should the expansion cracks between the slabs be (at 15 deg Celsius) to prevent buckling if the range of temperature is - 30 deg Celsius to 48 deg C? Homework Equations...
  31. S

    Thermal Expansion Stress

    I'm designing a system that will thermally cycle a stainless steel substrate up to 1200C from room temperature; right now my design consists of clamping the substrate onto a plate using a bolt head/washer with a nut on the other end of the screw, as shown on the attached figure. I want to...
  32. S

    Thermal Expansion of a hemisphere

    Homework Statement 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 the summer, when the temperature is 30? Homework...
  33. P

    How does temperature affect the height of a liquid column in a glass tube?

    A 1.55 m long vertical glass tube is half-filled with a liquid at 23.0°C. How much will the height of the liquid column change when the tube is heated to 40.0°C? Take αglass = 1.0 × 10-5 °C-1 and βliquid = 4.0 × 10-5 °C-1. First I found how much the height of the glass changed by using...
  34. C

    Thermal expansion (anharmonic effect)

    i have a question regarding calculating the thermal expansion parameter \alpha it is given by: \alpha = \frac{1}{L} \frac{\partial L}{\partial T} = \frac{1}{3B} \sum \frac{\partial(hw)}{\partial V} \frac{\partial n}{\partial T} now, I am not quite sure how i calculate d(hw)/dV. how is w...
  35. M

    Thermal Expansion of Water in glass

    Homework Statement An ordinary drinking glass is filled to the brim with water (266.3 mL) at 3°C and placed on the sunny pool deck for a swimmer to enjoy. If the temperature of the water rises to 32°C before the swimmer reaches for the glass, how much water will have spilled over the top of...
  36. M

    Thermal Expansion Concrete Problem

    Homework Statement A highway is made of concrete slabs that are 15 m long at 20.0 degrees Celsius. (a) If the temperature range at the location of the highway is from -20.0degrees Celsius to +40.0degrees Celsius, what size expansion gap should be left (at 20.0degrees Celsius) to prevent...
  37. N

    Calculating Thermal Expansion of a Cookware Pot

    Homework Statement Some cookware has a stainless steel interior (alpha = 17.3 *10^- 6) and a copper bottom (alpha = 17.0 * 10^-6) for better heat distribution. Suppose an 8.0 in. pot of this construction is heated to 620 C on the stove. Homework Equations Delta L = alpha* Lo * delta T...
  38. Q

    Thermal Expansion of Gas - am I on the right track?

    Question: One mole of an ideal gas with cv=2.5R, initially at 0.0degC, is heated at constant pressure. How much heat is needed to double its volume? Solution: Know: n=1 T0=273.15K cv=2.5R \DeltaP=0 Vf=2V0 H=U +PV and thus, Q= \DeltaH Q=ncv\DeltaT We can rearrange to find...
  39. X

    Thermal Expansion of two Metals

    Homework Statement The inner diameter of a steel ring is 2.0000 cm, and the diameter of an aluminum disk is 2.0100 cm. Both are at 430 degrees C. At what common temperature will the disk t precisely into the hole in the steel ring? alpha(Steel) = 1.3e-5 alpha(Al) = 1.9e-5 Homework...
  40. R

    Effect of thermal expansion on restraints

    When a beam undergoes thermal expansion and the restrains that support the beam are fixed so that no movement is allowed, how do you calculate the force reactions within the restraints? The restraints are two walls, and before expansion occurs no horizontal reaction forces are present. Since...
  41. X

    Thermal Expansion of wires within a structure - see picture

    Homework Statement dB = 12mm (0.012m), dC = 20mm (0.02m), E = 140GPa and the coefficient of thermal expansion, α = 12e-6/°C. Homework Equations δ = (R*L)/(E*A) The Attempt at a Solution Please see picture for my attempt. I don't know how the thermal expansion, which...
  42. A

    Thermal Expansion of a copper cylinder

    Homework Statement A copper cylinder is initially at 20.0 C Homework Equations At what temperature will its volume be 0.150 % larger than it is at 20.0 C The Attempt at a Solution \DeltaV =betaV\DeltaT .15=5.1x10^-5(Tf-20)
  43. D

    Thermal Expansion - Pendulum of a Grandfather Clock

    Thermal Expansion -- Pendulum of a Grandfather Clock Homework Statement The pendulum in a grandfather clock is made of brass (coefficient of linear expansion = 19 x 10^-6) and keeps perfect time at 17 degrees Celsius. How much time is gained or lost in a year if the clock is kept at 28...
  44. H

    Thermal Expansion of Aluminium Sleeve over Steel shaft

    Homework Statement An aluminium sleeve of internal diameter 4.000cm at 10 degrees Celsius is heated and slipped over a steel rod of diameter 4.040cm (at 10 degrees Celsius. When the aluminium sleeve and steel rod return to room temp they are impossible to separate. Assume that the...
  45. T

    Copper Pipe Expansion: 2.5m Length Rise to 86.5°C

    Homework Statement A 2.5 m length of copper pipe extends directly from a hot-water heater in a basement to a faucet on the first floor of a house. If the faucet isn't fixed in place, how much will it rise when the pipe is heated from 20.0°C to 86.5°C. The coefficient of linear expansion for...
  46. S

    Thermal expansion of solid cylinder with blind hole

    Friends, I have a 20mm dia.,30mm height, solid rod of stainless steel with a hole of dia.5mm, depth of 15mm at the center of the rod.(solid rod with a blind hole). Means wall thickness is 7.5mm radially and 15mm thick at the bottom. When I heat the solid rod to a temperature, we are sure the...
  47. W

    Linear Thermal Expansion: Bridge Joints

    SOLVED Homework Statement A bridge is made with segments of concrete 80 m long (at the original temperature). If the linear expansion coefficient is 1.2 x 10^-5 (1/degrees C), how much spacing is needed to allow for expansion for an increase in temperature of 50 degrees F? Answer in units of...
  48. Y

    What is the change in length of an aluminum rod after adding 12500 J of energy?

    Homework Statement An aluminum rod is 23.0 cm long at 20°C and has a mass of 350 g. If 12500 J of energy is added to the rod by heat, what is the change in length of the rod? Answer is in mm Homework Equations Q=m*c*delta T deltaL=alpha*L0*deltaT alpha=24x10^-6 c=900j/kg The...
  49. S

    How Can I Calculate the Coefficient of Thermal Expansion for a Material?

    Homework Statement At 20°C, a rod is exactly 21.03 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270°C, where the rod now measures 21.26 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? The linear...
  50. T

    Linear thermal expansion, a space between two metal rods

    Problem: The brass bar and the aluminum bar are each attached to an immovable wall. At 21.8 °C the air gap between the rods is 1.33 x 10-3 m. At what temperature will the gap be closed? length of brass is 2.0 meters, aluminum is 1.o meters Why my solution isn't working I'm not entirely...
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