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Unformatted text preview: TEMPERATURE (6) Now we have four fundamental dimensions:
“L" a a _,,7L, Length, Time, Mass, Temperature
L T M 6
6 is a dimension— you cannot derive it from L, T and M.
Temperature Scales: The units of 6 were historically determined by reference to the
properties of water at normal atmospheric pressure (~ 105 N/mz) C_els_iﬁ Fahrenheit
Melting pt. of ice 0 °C 32 °F
100 180
Boling pt. of water 100 °C 212 °F
Hence a temperature difference of 5 °C is ual to 9 °F and therefore the readings on the
two scales are related by the equation 5—9—32 =%— For example, the normal body temperature of 98.6 °F (only in the USA) is W =, 37°C (in France) V EFFECTS OF CHANGING 6 SOLIDS
A solid has both shape and size so the effects of changing 6 appear on length (wire),
Area (plate) and volume (parallelepiped). Length: for most solids increasing the temperature causes an increase in length
£=£0[1+a(6—60)]' Where a is called the coefﬁcient of linear expansion [measured in [°C]“1 or °F"1J and is typically about 10'5 [°C]_] . Area: will involve changing two dimensions, say Z and b
Z=£0[1+a(6—60)] b=b0[1+cx(6—60)]
so A=£b=£ob0[1+a(6—6o)]2
=A0[1+2a(6—60)]
since a <<1. * Volume: Now 3 dimensions are involved V=V0[1+3a(6—00)] =ai+ﬂW—aﬂ
With a = 3a LI UILDS
Liquids only have size and no shape, so only volume changes occur V=nh+ﬂw~aﬂ and typically 13 is about 10'4 [°C]‘1 or about 10 times the volume expansion coefﬁcient of
a solid. It is important to note a very important and highly unusual property of water. If you cool
water it will indeed contract until the temperature reaches 4 °C. ON FURTHER
COOLING WATER EXPANDS by about 1 part in 104 when it starts becoming ice at 0°C. During this solidiﬁcation there is a further expansion of about 10 per cent. GASES ‘
Gases have neither shape nor size and therefore have to be treated separately since
Volume (V), Pressure (P), and temperature (6) are all interrelated. Temperature Const. P For a given amount of gas, pressure and (N/mz)
volume are inversely related (Boyle’s Law).
—If you double the pressure, volume becomes '
one half as large and vice verse. In other words, P V = Constant : Constant
,V P Volume (Const. ) Study P as a function of temperature. P H?)
For a low pressure gas you ﬁnd  LN! '
P = P0 (1+ 0 0 )
1 1
c = — °C
273 ( ) Redeﬁne Temperature T = (6 + 273 ) °C P a T New Scale (Vol. Const)
Kelvin scale or Ideal gas scale
Pressure Constant /
/
/
Now V varies as W
V V[l 0] ‘2” 1 (0y1 (9 ‘
= + c c = — °
0 273 ( “44> ' so One can write
V a T [P Constant] If we combine all three we can write PV:NkBT where N = No. of gas particles in container
k3 is Boltzmann’s Constant
1 .38 x 1023' J oules/Kelvin T is in Kelvin scale T = [273 + 0°C] Chemists write this equation as
P V = nRT
R = NAkB
NA = Avogadro’s N0. = 6.02 x 1023
Number of particles in one mole. ...
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 Spring '10
 Shawhan
 Physics

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