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.
Homework Statement
A solid's thermal expansion coefficient is defined as
δ= \left(\frac{1}{V}\frac{∂V}{∂T}\right)
In the Debye model and at the low-temperature limit, show that δ is a positive quantity and is proportional to T^{3}. At the high-temperature limit, show that δ is still...
Hi everyone.
I was wondering if there is a convention for solving heat conduction problems. Specifically should one account for thermal expansion? The SI units for thermal conductivity are W/m/K. Does m include thermal strains already?
It seems for basic problems it would be easier to...
Homework Statement
A non-isotropic material is heated, fractional increase in length is different along different directions. With length l1=6.1 cm and l2=6.0 cm. In direction of l1, the coefficient expansion is \alpha1= 10×10-5 K-1 and direction l2 is \alpha2= 40×10-5K-1. The plate is heated...
Homework Statement
(B) http://imgur.com/VL4aG
although I showed the rest of the problem for context if needed
Homework Equations
ΔL=αLΔT
The Attempt at a Solution
I'm a little confused by the wording of the problem. When we find the shift in ΔN, are we actually finding Δ(ΔN)...
Homework Statement
In an experiment, a small radioactive source must be moved at extremely slow speeds. A positioning device based on thermal expansion was devised where the radioactive source is attached to one end of an aluminum rod and a heating coil is wrapped around a selection of the rod...
Homework Statement
Two metal bars are made of invar and a third is made of aluminum. At 0°C, each of the 3 bars is drilled with two holes 40cm apart. The bars are assembled into an equilateral triangle.
Homework Equations
a)ignoring expansion of the invar, find the angles between the...
Homework Statement
Coefficient for thermal expansion for glass is β1 = 25x10^-6 K^-1
Coefficient for thermal expansion for this particular liquid is β2 = 300x10^-6 K^-1
The glass cup is completely filled with the liquid at 4.0 L. The temperature of the glass and liquid both increased by...
Homework Statement
I am working on this ahead of my fall class and don't actually want the answer...
just pointers to help me understand something.. Thanks guys! :)
I am really rusty with my general physics and calculus knowledge =(
The original question asks me to prove that, for a...
Homework Statement
A hole in an aluminum plate has a diameter of 1.178 cm at 23 degrees Celsius. (a) What is the diameter of the hole at 199 degrees Celsius? (b) At what temperature is the diameter of the hole equal to 1.176 cm?
Homework Equations
The coefficient of linear expansion (α)...
1.Homework Statement .
Can someone give me more accurate mathematical models on thermal expansion? for example, linear expansion.
2.Relevant equations
L=L0(1+α∆T)
this equation is not accurate. for example.
When an object 100m long at 0oC (example: aluminum, α=2.4x10-5) is heated to...
Homework Statement
I only know volumetric expansion and linear expansion which require the coefficient constants that are not given in the problem. I also read somewhere that the mass remains constant during thermal expansion or is this false?
The problem is attached pls take a look at it...
Need help on Thermodynamics problem: thermal expansion to be more specific!
A steel ring with a 2.5000in- inside diameter at 20.0°C is to be warmed and slipped over a brass shaft with a 2.5015in outside diameter at 20.0°C.
Part A:
To what temperature should the ring be warmed?
Part B...
Homework Statement
A brass rod's length is measured at 20.0 degrees C with a metre steel rule. The length of the rod is determined to be 0.5260 m. The measurement is repeated at 61.6 degrees C. Taking into account the expansion of the rule and rod, what is the new measured length in metres...
A brass plug is to be placed in a ring made of iron. At 10°C, the diameter of the plug is 8.731 cm and that of the inside of the ring is 8.719 cm.
a) They must both be brought to what common temperature in order to fit?
b) What if the plug were iron and the ring brass?
formula for...
Homework Statement
ABS plastic melts (and solidifies) at 105 °C. You want to inject it into a steel mold. When the part comes out at 20°C you want it to be 7.250cm long. Edit: If this isn't clear, it wants to know how big the steel mold should be.
α for ABS plastic α= 53.0x106/C°, for steel α=...
Hi, I have been asked to determine the stress in a bar which has a diameter of 50mm when the temperature changes from 20 C to 50C. That's the first part.
Secondly, I need to then answer whether or not the stress will be sufficient enough to raise a constraining load of 40 tonnes.
Young's...
Homework Statement
You have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0 degrees Celsius and 150.0 degrees Celsius. Assume that the coefficients of expansion are constant over this temperature...
I have a bearing that is fixed into its housing by means of an interference fit (to test the effects of having a bearing that has become stuck due to build up of contaminants). I am using a bearing of ID 15.92mm ± 0.005 made of High lead Tin Bronze Alloy with a thermal coefficient of expansion...
A brass ring of diameter 10.00 cm at 19.9°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 19.9°C. Assume the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to separate the two metals?
Brass=19 x 10^-6...
Homework Statement
At 5°c, a steel tank is 6m high, 9m in diameter, and contains oil to the 5.9m level. A heating coil is put into service, causing 3.4m^3 of oil to spill over the top of the tank by the time the final temperature is reached. Calculate the final temperature, if the coefficient...
Hi Physicsforums,
I was trying to derive the formula that the coefficient for volume expansion, β, is 3 times the coefficient for length expansion, \alpha.
As a reminder, the formulas are:
\DeltaL = \alphaLo\DeltaT
and \DeltaV = \betaVo\DeltaT
where, supposedly, \beta = 3\alpha...
Homework Statement
A 1-liter aluminum container at 20oC is filled with 0.975 liters of mercury at
20oC. If both the container and the mercury are heated, at what final temperature
will the mercury completely fill the container?
αAl = 24 × 10-6 (Cº)-1; βHg = 1.82×10-4 (°C)-1
Any help on...
Homework Statement
Consider a bar of aluminum which is 10 cm X ½ m X 20 m. If the bar undergoes a change in its temperature from 10° C to 20° C, determine the new dimensions of the bar.
Homework Equations
ΔL=αL0ΔT
α=24x10-6
The Attempt at a Solution
I understand how the formula...
Homework Statement
A vertical glass tube of length L = 1.2800000 is half-filled with a liquid at 20.0000* C. How much will the height of the liquid column change when the tube is heated to 30.0000*C?
Glass linear expansion co = 1e-5/K
Liquid volume expansion co = 4e-5/K
Homework...
Homework Statement
At 19°C, a rod is exactly 20.01 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 219°C, where the rod now measures 20.18 cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?
Homework...
Homework Statement
""If the coefficient of thermal expansion of steel is 1.1 x 10^ -5 ℃^ -1 and a railway rail is 4. 5 m long, how much would the length Δ L of the rail increase by if the temperature changes from -10 ℃ to 30 ℃? ""
Could anyone direct me to a youtube video, or something...
Explain why the thermal expansion of a spherical shell made of a homogeneous solid is equivalent to that of solid sphere of the same material.
I guess these equations would be of some help.
(ΔA)=A*2α*(ΔT)
α→ Coefficient of linear expansion.
A→ Area
T→ Temperature
(ΔV)=V*3α*(ΔT)...
Homework Statement
A crystal is heated from 0 to 100 degrees celcius, its lattice parameter 'a' increases by 0.17% due to thermal expansion. if we observe an x-ray reflection at a bragg angle theta= 19.3 degrees at 0 degrees celcius, by how much will theta change when the sample is heated to...
Homework Statement
Prove that the volume thermal expansion coefficient of a solid is equal to the sum of its linear expansion coefficients in the three directions. \beta=\alphax +\alphay+\alphaz
For isotopic solid when \beta = 3\alpha
Homework Equations
\beta=[1/v][dv/dt]p= \alphax...
thermal expansion of wire??
hi I've got this 3mm iron-chromium-aluminium wire fixed at both ends, heated to approx 1000k (max 1200K) and suspended horizontally approx 1metre long.
the wire it would appear has been extended by about 8mm, similar to what would be expected when its hot, only it...
Homework Statement
To a very good approximation, ammonia obeys the Bertholet equation of state,
which readsPV=nRT+\frac{9}{128}(\frac{nRTc}{Pc})(1-6\frac{Tc^2}{T^2})Pa)Suppose we have 500 grams of ammonia under a pressure of P=3.04 atm
and at T=323K. Calculate the volume of ammonia according...
Homework Statement
You use a steel measuring tape and measure the length of an aluminum bar. You measure a length of 20.700 m when the temperature is 21.2 degrees C. What is the measured length when the temperature is 29.4 degrees C?
Homework Equations
L = L0(1+\alpha\DeltaT...
Homework Statement
Determine the actual shape of a copper bar in contact with a furnace at a constant 200 C at one end and a constant ice bank at 0 C at the other end.
Diameter of the rod is 2.54 cm. Length is .5 meters. Thermal conductivity of copper is 380 J /
(smC)
Homework...
Homework Statement
A student measures the length of a brass rod with a steel tape at 20.0°C. The reading is 80.00 cm. What will the tape indicate for the length of the rod when the rod and the tape are at each of the following temperatures?
a) -18.0°C
Homework Equations...
We know that youngs modulus(E) is stress/strain. In case of free body thermal expansion, if the material is allowed to expand and contract freely, than there are no stresses in the body. The body has only strains.
That means the stresses are zero in case of free expansion. So in this case...
Homework Statement
Homework Equations
\alpha(T)dT = \frac{\partial L}{L} <--- Differential Equation given on formula sheet
The Attempt at a Solution
\alpha(T)dT = \frac{\partial L}{L}
\int_{l_0}^{l_1} \frac{\partial L}{L} = \int_{T_0}^{T_1} \alpha(T)dT...
Homework Statement
Homework Equations
\alpha(T)dT = \frac{\partial L}{L} <--- Differential Equation given on formula sheet
The Attempt at a Solution
\alpha(T)dT = \frac{\partial L}{L}
\int_{l_0}^{l_1} \frac{\partial L}{L} = \int_{T_0}^{T_1} \alpha(T)dT...
Homework Statement
A copper plate of length 1 m is riveted to two steel plates of same length and same cross-section area at 0°C. The tension (in kilo Newton) generated in copper plate when heated to 20°C is 56n. Find the value of n. (Given Ys,Yc,αs,αc,A)
The Attempt at a Solution
I...
Homework Statement
A cylinder is made up of three layers. The outermost (3) is concrete, the middle (2) is air, and the innermost (1) is aluminum. Three diameters are given, which measure from the outer ends of the given layer.
d1 = 11.845cm
d2 = 11.900cm
d3 = 12.000cm
\alphaAl = 2.3*10^-5...
Homework Statement
This is more of a concept that I am confused on.
IF there are 2 metals, one on top of the other, and they are attached to each other and attached to a wall, and the only thing different between the two metals is the thermal expansion. When heated will the metal curve...
A lead rod and a common glass rod both have the same length when at 21.0° C. The lead rod is heated to 50.0° C. To what temperature must the glass rod be heated so that they are again at the same length?
I did this:
L = a*L0*T
a (thermal expansion) of lead = (29e-6)
a (thermal expansion) of...
1. A mercury thermometer has a bulb of volume .100 cm^3 at 10degreesC. The capillary tube (initially empty) above the bulb has a cross-sectional area of .00012 cm^2. How much will the mercury rise when the temperature rises by 30degreesC? Ignore the thermal expansion of the glass bulb and tube...
I have been trying to find an answer for this for quite some time and found this forum which could help me.
Does an initial stress (elastic strain induced in a metallic component) change its thermal expansion coefficient? if yes then what is the relationship?
In simpler terms, does 2...
Homework Statement
A glass tube of radius 0.80cm contains liquid mercury to a depth of 64.0cm at 12deg. Find the depth of the mercury column at 100 deg.
Assume that the linear expansion coefficient of the glass is 10 X 10^-6 K-1 and the linear expansion coefficient of mercury is 0.61 X 10^-4...
Homework Statement
Hello all,
I need to find the change in internal energy (delta U) and work done (W) by an aluminum rod (from the expansion) as it is heated from 20C to 100C.
Initial Length = 2m
I found delta length = .00384m
diameter = .01m
radius = .005m...
Homework Statement An ordinary drinking glass is filled to the brim with water(268.4mL) at 2.0C and placed on the sunny pool deck to enjoy. If the temp of the H2o rises 32.0C, how much water will spill out of the glass?Assuming no expansion for glass...
Homework EquationsB=207*10^-6 for...
Homework Statement
A steel rule is calibrated for meauring lengths at 20.00 C. The rule is used to mesure the length of a Vycor glass brick; when both are at 20.00 C the length is 25.00cm. What is the length of both the rule and the brick when at 80.00 C
Homework Equations
coef of glass...
Homework Statement
Find the change in diameter of the metal rod.
So I did a lab in class. We heated up a metal rod by putting it in a "jacket" and heating it with steam and it expanded. We were asked to calculate the liner coefficient. Well I did that just fine. I determine that the rod...