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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A gas cutting-torch was used to split an I-beam lengthwise. When the last inch was cut, the two halves flew apart, with a great energy release. The halves are then seen to be curved where they were straight. The workman was unsurprised but the cameraman was thankful for a warning...
I have a problem with the method that they solved. This is what I mean ##\delta t= \frac{\pi L\alpha \delta T}{\sqrt{gL}}##. You can derive this equation by using errors and approximations here delta t is a tiny(not infinitesimal) change in time period, delta T is a tiny change in temperature...
Hello, assuming to keep an aluminum alloy motorcycle frame not in use, still, will the daily temperature variations cause thermal fatigue due to the continuous expansions and retractions or is the force developed by a few degrees of variations not sufficient to create microstructural dislocations?
For this problem,
The solution is,
I understand their logic for their equation, but when I was trying to solve this problem, I came up with a different expression:
##\Delta A = \Delta L_x\Delta L_y##
##\Delta L_x =\Delta L_y = \Delta L## since this is a square.
##\Delta A = \Delta L^2##...
Greetings everyone.
I learned that the distance between molecules in liquid increases while the temperature increases. Hence, its density is decreased. The process is thermal expansion. At the same time, the collision between molecules would be more frequent when the temperature increases...
I am interested in the potential for air bubbles in a plastic structure to expand with heat, and put pressure on the plastic surrounding the air bubble.
In this case the plastic structure is formed by melting a thermoplastic powder. In between the grains of powder are voids with air in them. As...
I was reading about thermodynamics in my textbook wheni came across the following thermodynamics constants:
However, i don't understand why did we define 1/V inthe constants. What is the point in doing this?
so I have never seen this unit before. 10^-6m/mK for the thermal expansion (linear expansion). I believe this unit is micrometers divided by mili kelvins?
Suppose a square shaped object has an initial length of L1 and final length (after thermal expansion) of L2. Initial temperature is T1 and final temperature is T2. Suppose it has an area of A. So initial area is A1 and final area is A2 (after thermal expansion). Here A1 = (L1)^2 and A2 = (L2)^2...
Suppose each side has initial length ##l##. The solution taught to me is as follows.
Considering the lengths of the rods after expansion, we write $$\dfrac{3l^2}{4}\left(1+\mu\theta\right)^2+\dfrac{l^2}{4}\left(1+\alpha\theta\right)^2=l^2\left(1+\lambda\theta\right)^2$$ according to the...
I'm trying to figure out how to relate expected thermal expansion of a uv cured polymer within a rigid cylinder to a modulus specification. The issue is the expected change in refractive index due to thermal expansion. The expansion coefficients are not available. Anybody have an idea. Do...
Hi all,
I am having trouble getting repeatable results from a linear regression formula that simply uses temperature vs load cell output especially with rapidly increasing/decreasing temperatures.
This appears to be a result of the thermal co-efficient of our temperature sensor being almost...
Hello everyone,
Once I got through the VDW state equation I came to the expression of the thermal expansion coefficient. When I place the values I get an illogical answer. Is there a problem with the units? (Please ignore the values)
Thanks.
This is the unit equation I get to and get stuck:
My idea is this: tensor stress is directly related to the internal pressure of a solid. That is to the force that the neighboring atoms exert each other in relation to a unit of surface.
When I heat a solid we can have the phenomenon of thermal expansion: this is connected to the fact that a...
So guys I had physics lab where we used Steam Generator, Pasco interface and Capstone. In a nutshell there is graph attached below and formula, please write the solution with this formula.
Hi all,
For area expansion, I know the equation goes like:
Hence, my answer to part i is
##\begin{aligned}A=A_{0}\left( 1+2\alpha \Delta T\right) \\ = 52\left( 1+2*24\times 10^{-6}\right) \left( 100\right) \\ =52.2496cm^{2}\end{aligned} ##
Now I am unsure how to proceed with part 2 in this...
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...
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
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 !
I tried following:
$$ \Delta l = \alpha l_0 \Delta T $$
$$ (\Delta l)^2 l_0 = \alpha l_0^2 \Delta T \Delta l $$
$$ \Delta A l_0 = \alpha A_0 \Delta T $$
$$ \Delta A = \frac{ \alpha A_0 \Delta T }{ l_0 } $$
If we remember that:
$$ \Delta l = \alpha l_0 \Delta T $$
So we have
$$ \Delta A = \frac{...
Homework Statement
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Oceans cover 2/3 of the earth’s surface, with an average depth of 3.7 km. The average surface temperture is 17◦ C. Taking this temperature as representative of the entire ocean, and knowing that the coefficient of volume expansion for water at this temperature is β = 1.7...
Homework Statement
Im hoping that this experimental setup is common enough in 1st year physics that someone could at least point me in right direction because I may be misunderstanding how the arm and pointer connect together.
I need to come up with an equation that relates how far the metal...
Homework Statement
A steel ring with a hole having area of 3.990 cm2 is to be placed on an aluminum rod with crosssectional area of 4.000 cm2. Both rod and ring are initially at a temperature of 35.0°C. At what common temperature can the steel ring be slipped onto one end of the aluminum rod...
Homework Statement
Homework Equations
ΔL=LαΔT
σ=EΔL/L
The Attempt at a Solution
For part a, I used the coefficient of linear expansion for copper and the change in temperature to find the change in length (0.068%). I thought part b had the same answer. The two are attached, and I would...
Homework Statement
A glass bottle of nominal capacity 250 cm3 is filled brim full of water at 20oC. If the bottle and content are heated to 50oC, how much water spills over? (For water, β=0.21X10-3 K-1. Assume that the expansion of the glass is negligible.)
Homework Equations
(dv/dT)/v =...
Homework Statement
An iron ring of radius 2.1 m is to be fitted on the rim of a wheel of radius 2.121 m. The coefficient of volume expansion for iron is 3.6 x 10-5 K-1. By how much should the temperature of the ring be increased?
(a) 532 °C
(b) 833 °C
(c) 278 °C
(d) 378 °C
Homework Equations...
Using a pump we are cycling water through a capsule with filter media inside; while measuring the flow rate (l/min) and the pressure (psi) going in and the pressure going out. The water is cycled back into the same storage tank. As the flow rate increases the differential pressure should change...
Homework Statement
A part of a circular ring is missing .What happens to the angle when temperature is increased ?
1) θ increases
2) θ decreases
3) θ remains same
4) θ increases initially but becomes constant after a particular temperature .
Homework EquationsThe Attempt at a Solution
As...
For thermal expansion in a bottle - is there a theoretical model on the pressure exerted on the inside of the bottle due to the air inside expanding when the bottle heats up.
The air will be expanding randomly in all directions so the pressure exerted at any point on the inside of the bottle...
We did an activity today in class where we placed an empty 2L bottle in the Freezer, let it contract, then calculated the coeffcient of volumetric expansion using ΔV = VoβΔT. We got pretty close to the accepted value. The question is...
Does the coefficient of thermal expansion only work for...
I have 1" aluminum rod and I want to dril a hole in a steel structure for the bolt.
If I have a 1" drill and take .001" inches off of it at the machine shop, so that it is now 0.998 inches, there will have to be about a 200°C difference in temperature between the two articles (aluminum...
Homework Statement
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A bimetallic strip is made of metal which has coefficient of thermal expansion is equal to α1 and the other's is equal to α2 at the temperature of T0. The temperature is increased to T0 + ΔT (ΔT > 0). The strip curves as shown in the figure. If both strip have the same...
Homework Statement
By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny.
Homework Equations
$$G=U-TS+PV$$
$$dG=\mu...
By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0.
I tried but I got something funny.
My working:
Okay, I will give a quick run down of what I am trying to do here. What I want to do is build a tesla turbine from old hard drive disks. Being that they're already rated for high RPM, it seems like a viable option. Now these disks are probably going to be aluminum and I am probably going to buy...
Homework Statement
A one-liter pot is completely filled with oil. Heat is applied to the pot&oil and the temperature rises from 15°C to 190°C. How much oil is spilled over?
The linear coefficient of thermal expansion for oil is 0.68*10-3; the one for the pot is 2.4*10-5
Homework Equations...
Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...
Homework Statement
The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional...
Homework Statement
A bridge with a steel framework is 500.000m long on a winter day at 5.0 C. For steel use 11.0x10^-6/ dC a) Find the length of the bridge on a summer day when the bridge temperature is 55.0 C. Keep 6 significant figures in this part and in part b). The bridge is built in the...
Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement.
Many Thanks
I have a question about thermal expansion of liquid into a gas void.
Imagine a closed upright cylinder filled mostly with water – say 99%, and the remaining 1% is gas.
Now imagine that you heat the cylinder and its contents.
The water will expand by ΔV owing to thermal expansion. The gas...
Homework Statement
Find the common temperature at which the inner diameter of the ring is 0.05% larger than the diameter of the sphere.
Given:
Lead sphere
d = 5cm
To = 70°C
∝ = 29x10-6/C°
Steel ring
d = 4.9975cm (the sphere is 0.05% larger than the inner diameter of the ring, hence this value)...
Homework Statement
A rectangular windshield is to be assembled by installing a glass plate on a 3 ft by 1 ft frame at 60°C. The glass plate is cut at 68°F in such a way that its length is three times its width. The linear expansivity of glass is 5 x 10-6 /C°. (a) What area of the glass plate at...
I am trying to find examples problems on thermal expasions related to the subject of measurement technique Google but I can't find them.. I don't know exactly what could be asked but the problem will be related to: "expansion of measurement device" is given, and "expansion of measured...
Homework Statement
Homework Equations
ΔL = LαΔT
The Attempt at a Solution
What I did was to set the diameter of the inside of the brass ring + the change in diameter of the brass ring equal to the diameter of the steel rod + change in the diameter of the steel rod. So,
Lbrass + ΔLbrass =...
I have a pipe holding liquid at 80°C. The outside atmosphere is -2°C.
The pipe gets a temperature gradient over the wall thickness. The outside fibers will thus restrain the inner fibers from expanding. I would like to know the increase in the inner dia of the pipe.
I have found temperature...