Thermal expansion Definition and 263 Threads

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...

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...

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...

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)...

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...

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"...

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...

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...

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)-...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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)

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...

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...

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...

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...

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...

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...

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...

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...

Hi, I've done the problem but I'm unsure of my answer. I would be glad if you could check it out. Homework Statement A steal pendulum is considered a clock at a certain temperature. What is the maximum variation of temperature we can submit to the pendulum if it cannot delay more than one...

Homework Statement Prove that the volume thermal expansion coefficent of a solid is equal to the sum of its linear expansion coefficients in the three directions: B = Ax + Ay + Az Homework Equations B = (dV/V)/dT A = (dL/L)/dT The Attempt at a Solution My thought was using dV/V...

Homework Statement The temperature of a block of lead is raised from 0°C to 100°C. What is the percentage change in its density? (The density of lead at 0°C is 11,300 kg/m3.) Homework Equations ΔV = Vi βΔT The Attempt at a Solution it gave the wrong answer when i tried to use the...

Homework Statement In a bimetallic strip of brass and copper which curls when heated, the brass is on the inside of the curve. True or false? Homework Equations deltaL=alpha*Lo*deltaT The Attempt at a Solution It is false but I do not get why. Brass has a higher coefficient...

Homework Statement A hole in an aluminum plate has a diameter of 1.179 cm at 22.00 degrees Celsius. Part A asks for the diameter of the hole at 199 degrees Celsius.? Part B asks for the temperature of the hole when its diameter is 1.177 cm? Homework Equations ∆L = alpha L(0) ∆T...

Homework Statement A steel plate has a circular hole with a diameter of 1.000 cm. In order to drop a Pyrex glass marble 1.003 cm in diameter through the hole in the plate, how much must the temperature of the system be raised? (Assume the plate and the marble always have the same temperature)...

I've been scouring the web in search of a Joule Thomson coefficient value for methane, but so far no luck. I have the volume, temperature, and specific heat as well... so I could also use the coefficient of thermal expansion for methane.. but I can't find that anywhere either! Does anyone...

Homework Statement When the temperature of liquid mecury increases by one degree celsuis , its volume increases by one part in 5500. The fractional increase in colume per unit change in temperature(when the pressure is held fixed ) is called the thermal expanision coefficient , \beta...

A rod is measured to be exactly 21.81 cm long using a steel ruler at a temperature of 21.5°C. Both the rod and the ruler are placed in an oven with a temperature of 345.0 °C where the rod now measures 21.93 cm using the same ruler. What is the coefficient of thermal expansion for the material of...

A brass piston of diameter 25 cm at 20 degrees C must be able to function at 150 degrees C. In order to do so it must fit inside a steel cylidrical chamber. What must the minimum initial diameter of the cylinder be so that the piston never rubs against it. alpha=2x10^-5 for brass...

Homework Statement When the temperature of a metal cylinder is raised from 0.0°C to 100°C, its length increases by 0.23%. Find the percent change in density. Homework Equations ∆L = L∆T p=m/v The Attempt at a Solution I don't have any real idea how to start the problem. How...