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.
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 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?
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
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
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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...
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...
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...
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...
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...
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
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...
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...
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...
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...