Abeka Physics Section 14.2 pg. 211 - 213 Flashcards
How are roads and bridges designed to prevent buckling?
> Although the atoms in a solid do not move readily away from fixed positions, they are in a continual state of vibration
when temperature rises, the atoms vibrate more energetically and push farther apart from each other, and as a result, the whole solid expands
when the temperature decreases, the atoms vibrate more compactfully, and as a result, the whole solid contracts and develop cracks
to prevent the expansion, buckling, and cracking of roads due to temperature changes, bridges, roads, and sidewalks are made in sections separated by rubber strips, expansion plates, or gaps to allow for expansion in the summer and contraction in the winter
Define linear expansion
> linear expansion - expansion along any line through the solid
Give the formula for find linear expansion
change in length = alpha x length(sub 1) x delta T
where alpha represents the coefficient of linear expansion
length(sub 1) represents the original length
delta T represents the final temperature minus the original temperature
Describe the alpha in the linear expansion formula
> alpha in the linear expansion formula is the coefficient of the linear expansion
the coefficient of the linear expansion represents the increase in the length of a dimension per unit original length when the temperature rises one degree
for a given solid, alpha has nearly constant value
alpha does differ greatly from solid to solid
What advantages does Pyrex glass have?
> Pyrex glass expands very little when heated, it is useful in scientific laboratories
also, Pyrex glass can be heated without breakage because it does not develop internal stresses due to one part expanding much faster than another
Solve this: A single steel span in a bridge is 100.00 m long at 0degrees Celsius. (a) How long is the span at 45 degrees Celsius? (b) If there are three such spans in one bridge, how much will the length of the bridge increase from 0 degrees Celsius to 45 degrees Celsius?
(a) To find the linear expansion, use equation 7. Given that length(sub 1) is 100.00 m, delta T is 45 degrees Celsius, alpha for steel is 11 x 10^-6/degrees Celsius (from Table 14.1), substitute to obtain
linear expansion = alpha x length(sub 1) x delta T
linear expansion = (11x10^-6/degrees Celsius)(100.00m)(45 degrees Celsius)
linear expansion = 0.0495m = 0.050m
the overall length then is
length(sub 1) + linear expansion = 100.00m + 0.0495 m = 100.05 m
(b) the total expansion is
3 delta length = 3(0.0495m) = 0.15 m
Give the area expansion formula
delta A = gamma x A(sub 1) x delta T
where delta A stands for area expansion
gamma is the coefficient of area expansion
A(sub 1) is the original cross-sectional area
delta T is the temperature final minus temperature initial
Why is it easier to unscrew a metal jar lid from its glass jar when the metal lid is warm than when it is cold?
Because upon being heated, a solid expands not only in every linear dimension but also in cross-sectional area
>the cross-sectional area expansion allows for more wiggly room between the metal lid and the jar
Describe what happens when a material with a hole is heated
When a solid is heated, it expands
>when the cross-sectional area of a material expands, so does the cross-sectional area of any holes within that area
>this occurs because the material expands away from the hole, not into it
Give the volume expansion formula
delta V = Beta x V(sub 1) x delta T
where delta V represents the volume expansion
beta is the coefficient of volume
V(sub 1) is the original volume
delta T is the temperature final minus temperature initial
Describe volume expansion
When a solid is heated, any empty space fully or partly enclosed by the solid enlarges as if it were made of solid material
>the effect of rising temperature on a glass beaker, for example, is to cause not only volume expansion of the glass but also of the interior space; as a result, the beaker attains a slightly greater capacity
Describe the relationship between the coefficient of linear expansion to the coefficient of area expansion and the coefficient of volume expansion
> gamma–the coefficient of area expansion–can be regarded as 2 alpha (the coefficient of linear expansion)
beta–the coefficient of volume expansion–can be regarded as 3 alpha (the coefficient of volume expansion)
Describe liquid expansion
> heat causes greater expansion of liquids than of solids
>the volume expansion of a typical liquid exceeds that of a typical solid by a factor of ten
What is the exception to the rule that a liquid expands when temperature rises?
> water shrinks in volume between 0 degrees Celsius and 4 degrees Celsius because the melting process at 0 degrees Celsius is incomplete
therefore, since the arrangement of molecules in liquid water is more compact than in ice, water has a maximum density four degrees above its melting point
example: when temperatures plunge in late autumn, the coldest water in a lake or pond approaching 0 degrees Celsius is found not at the bottom but at the top
so it is the top that freezes first, thus insulating the warmer water at the bottom from further loss of heat
Solve this: A hard rubber cube has a volume of 1000.cm^3 at 0 degrees Celsius. If the cube is submerged in boiling water (100. degrees Celsius), what is its volume after reaching thermal equilibrium?
At thermal equilibrium the cube will be at a temperature of 100. degrees Celsius. To find the volume expansion of the cube, use equation
delta V = 3alpha x V(sub 1) x delta T
In Table 14.1 the value of alpha for hard rubber is listed as 80. x 10^-6/degree Celsius
V(sub 1) is stated to be 1000.cm^3, and delta T is 100. degrees Celsius. Next substitute,
delta V = 3(80.x10^-6/degree Celsius)(1000.cm^3)(100degrees Celsius)
delta V = 24 cm^3
final volume is as follows:
V + delta V = 1000. cm^3 + 24 cm^3 =
1024 cm^3
