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郭日僑萋
三期星日五廿月二年〇七九一曆公年九十五國民華中
育教僑華 M
(square ofq* can be negligible)
da again measured.
Suppose
Cubioal Expansion
Expansion in three dimensions is characterised
by the relations
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PHYSICS (17)
Thermal expansion of solid
(++)
Most solids expand when heated in
•N• 7. (1+/2+)
where V is the original volume
Vis the final volume
in the coef. of oubical expansion
t is the temperature change
For practical purposes:
03/31 12:3
Change in Density of a substance when hasted
Before heating
- X1 (nasa)
(volume)
(density)
length
linear expansion
Nase is constant.
(a) volume
superficial expansion cubical expansion.
Therefore
After heating
(mass) (volume) (density)
An object is first weighed in sir, and thea
weighed when it is totally inserted in the liquid et
zoom temperature. The liquid is then heated to a
higher temperature and the apparont weight of the body
and, are the respective weight
of the body in air, in the liquid at room telpĄ, GAL in the liquid at a higher temperature.
upthrust of liquid at room temp. volume of liquid displaced x density
upthrust of liquid at higher temp. volume of liquid diepd. x density then
Dand
where o is cubical doef. of the polid t is the temperature rize
concern with the coef, of expansion // of
· Exceptions &
(1) Water contracts whan heated from
0 deg 0 to 4 deg C
(11) type-metal alleya expand on cool-
ing to fill the mould and give a sharp-edged shape
(iii) stretched india-rubber contracta
when heating
Kost substances in the form of long thin roda are heated, they expand in length in such a manner that, over a more or less lintted range of temper- atures, the fractional increase in length per degree. of temperature is fairly constant. This constant is known as the thermal coefficient of linear expansion. The coefficient of linear expansion (x) of a solid- is defined as the increase in length of unit ler th when the temperature increases by one degree, Math ematically this is stated i
e loft +act)
DI
where is the length at the original temp
is the change in temperature
Lis the final length
a is the coefficient of linear
The value & can be found in tables of physical constant for all common substances. It is to be noted that since. o is a fractional change in length per « unit of temperature, ite numerical value depends upon
(a) the temperature scale used, example
in the case of steel
-0.000012/dsg C
- 5/9 x (0.000012).
** 0.0000067/deg F
the longer its original
(b) the original Leit expands.
length, the more
(0) the temperature rise.
Problem Procaduras
Problems dealing with linear expansion must invo- lve the concepts of thermometry. Care should be taken not to memorixe symbols. Symbols alone are meaningless. In the solutions of problems, and when ever symbols are introduced, detail statements should be given on the symbols used. An equation with symbols alone is also meaningless, Formulae are shorthand expressions. They urs simply memory-joggers that help you to remember.
Example 17
In the design of a modern steel bridge, provisions must be made for expansion. How much does this amount to in the case of a bridge two miles long which is sub... jected to temperatures ranging from -40°F to 110°F, assuming an average expansion coefficient of 0.00001) per degree C
Starting from the definition, it is clear that either the temperature range must be expressed ir Centigrade degrees, or the coefficient must be conver ed to Fahrenheit degrees.
The temperature range 18 Irom -40 to 110 deg or 5/9 of 150 - 83.3 deg C
The expansion - coef. of z original I temp. rise
linear expn. length 0.000012 x (2 x 5280) x 83.3 1.2 x 10-5
x 2 x 5:28 x 10 x 0,833 x 10.56 ft.
Superfidial expansion
Expansion in two dimensions is characterized by: the relations
£ - 4 (1 +6+)
where 4 is the volume at temperature befora
heating.
A is the final temperatura
8 is the superficial coef. or
t is the rise in temperature
For practical purposes:
The relation can be verified by assuring the sides of a square be unity and the temperature rise. also be one degree. Thuả
original length = 1 unit temperature zine » 1 degras Tinasr coef.
final length l·
final area. A − (1 +α
1+24
(1+0);
therefore,
vhan ne
D2 (1 +/+)
D2 = D1/(1 +/+)
If the substance contracts on heating or at normal substance is cooled through t degrees the formula becomes
Example 17-2
D2 = D1/ (1 +/+)
A piece of metal weighs 160 gu., and when weighed under water at 4°C ite apparent weight le 140 gm. A150 100 om of the same matal at ♬ degrzes C becomes 100,18 on when heated to 94 deg G. What would be the 5.0. of the metal at 94 degrees 07
0.18
Voer, of linear expansion of metaz
100 x 90 1
0.00002/c
weight in air.
G. at
8
apparent loss of weight in water 160 20:
Density at
Density at 94
Answer:
8/1.0054
3 x 9,00002" x 90
» 7.96 gm/0.0.
of the getal at 94 °C is 7.96,
A short cut in problem solving.
Changes of area and volume can cal- culated from the change in the linear dimensions of a body. If the fractional change in linsar dimensions is x percent then the fractional change in area will be 2x % and in volume 316.
A body made of the same material throughout will not be distorted by
expansion. For example.
(a) an annular ring becomes a larger rings both inner and outer radii increase....!
(b) a hole in a metal plats becomes
a larger hole when hosted
an empty relative density bottle increases ite internal as well as its external volume," and so its fluid capacity is increased..
angion of Liquids
Liquid has no fixed shape, linear and srez ezpan- sions have no meaning.
Cubical expansion of liquid in considered only.
This observed volume change for a liquid is in- fluenced by the expansion of the container which must be used to hold it.
Care must be taken that
Real expansion - apparens expansion + expansion
of container Coef. of real
coef. of
+boar, or the Szpansion
apparent expn. container
tions of Apparent Coef, of
By S.G. hottie method or weight thermenster
The mass of liquid filling the veggel is first measured, The vassel is then placed in water bath and is heated to a known temperatura, Since the liquid expands: some of it is expelled from the vessel through the spaning at the top, and when the vessel is revoighed, the masa of liquid left in the vessel is determined"
Suppose-m, and n„ are the masses of the lliquid Tilling the bottle at fon mperaturas t, and
'Apparent couf.
mass expelled"
masa" left x temp. riES
The hydrostatão (Archimedes' Principle) methed for the apparent coefficient of expansion,
oan be calculated as all known.
Example :17-3
and't si
1 barometer having a brass scala tarda 77.24 on
a temperature of 20 dag. C. What would be the reading at 0° dag. 67. T
Ma Coef. of ozbioal sxpn. of mercury m 18
Ceof, of linear expa, of brang – 19 ≈ 10
Consider two factors affecting the reading: (1) Cooling the scale causes it to contract and
se increases the reading.
|(2) Coeling the mercury increases its density and
-se deoraagse the reading
The increase in reading due to scale contraction
77.24 x 19 x 10 x 20 cm
The height of mercury column H im
E = 77.24(1 + 20 x 19 x 10°) Consider the atmospheric pressure remains the anne in both 20 and 0 daɛrea C
Example 17-2
20206
+ 20 ± 0.00018:
+ 20 x 0.00018)
Sincs 1/(1+a)2 = (1+a)
28
(if a là very small)
1:20
20 0.00018
Bzol 1
20 = 0.00018).
77.24(1+20 x 0.000019)(1-0.00018)
77.24(1 +0.00038
77.24 0.25
76.99 on
0.0036)
Apiece of metal weighs 40 g in air, 35.2 gm when immersed in aliquid at 5 deg C and 35.25 at 35 dag G. Hnd the coafficient of expansion of the liquid if the ceefficient of linear expansion of the astal is 0.0002 per deg C,
Less in weight at
40-35.2
4.8
Leas in weight at
40-35.25 4.75 gm.wt.
I density:35
28
olusio
density,
x. consi
dansity
density
307-
30/1
Volume
35
(1 + 0.00006 x 30)===!
418 0.0018 x
30/7
1,0018 x.4.8 4.75
1.0018 4.8 £4.75
4.75
1.0018 x 4.5 4.75 4+75 x 30
0.00041 par deg C
Answer: The coer. of expn. of the liquid is
0.00041 par deg: C.