07-1
07-1
Temperature
Deﬁnition: The translational (
e.g.
, wiggling around) energy
...
of particles in a system.
No practical way to measure
velocity of
every
particle
in most systems of interest.
Instead,
temperature scales
are deﬁned.
There are two types:
•
The
thermodynamic temperature scale.
“Really” measures temperature.
•
Practical temperature scales.
Approximations of thermodynamic scale.
Much easier to measure temperature on a practical scale.
For temperatures of interest, diﬀerences are very small.
07-1
EE 4770 Lecture Transparency. Formatted 13:25, 23 December 1997 from lsli07.
07-1
07-2
07-2
Kelvin’s Thermodynamic
Temperature Scale
Due to William Thomson, a.k.a., Lord Kelvin (1824-1907).
Start with a precise temperature that can easily be reproduced.
The
triple point
of water,
T
tr
,isused
.
T
tr
is temperature at which
water can simultaneously be in
the solid, liquid, and gas states: 0
.
01
◦
C.
•
Conﬁne an ideal gas in a container of ﬁxed volume,
S
.
•
Bring the gas to temperature
T
tr
.
Call the pressure of this gas
P
tr
.
By deﬁnition
(of the Kelvin scale) this temperature is
T
tr
,
273
.
16 K.
The ideal gas law:
PS
=
n
<
T
.
Substituting,
P
tr
S
=
n
<
273
.
16 K. Then
n
<
=
P
tr
S
273
.
16 K
.
•
Bring the same system to another temperature,
T
.
Call the pressure at this temperature,
P
.
Solving for
T
in the gas law:
T
=
n
<
.
Substituting for
n
<
using the quantity obtained above yields
T
=
273
.
16 K
P
tr
S
= 273
.
16 K
P
P
tr
.
07-2
EE 4770 Lecture Transparency. Formatted 13:25, 23 December 1997 from lsli07.
07-2
07-3
07-3
Practical Temperature Scales
Designed to be easy (relatively) to measure.
Scales are revised every few decades.
Latest revision in 1990, called ITS-90.
(International Temperature Scale.)
Older scale (1968), IPTS-68.
(International Practical Temperature Scale)
Diﬀerence between ITS-90 and IPTS-68
is as large as 0
.
4
◦
Cat800
◦
C.
At human-tolerable temperatures,
diﬀerence is in hundreths of a degree.
All practical scales are identical at the triple point of water.
How a practical temperature scale is deﬁned:
A set of ﬁxed points is established,
for example the triple point of water.
A temperature is assigned to each ﬁxed point,
based on the thermodynamic scale.
Accurate thermometers (transducers) are chosen.
Functions are deﬁned mapping
the thermometers’ output to temperature
so that they pass through the ﬁxed points.
⇒
Temperatures deﬁned in terms of ﬁxed points and special transducers.
07-3
EE 4770 Lecture Transparency. Formatted 13:25, 23 December 1997 from lsli07.
07-3
07-4
07-4
For ITS-90:
•
(
.
65 K
,
5
.
0K)
Vapor-pressure relation between two isotopes of helium.
•
(3
.
0K
,
24
.
5561 K)
Helium ﬁxed-volume thermometer.
(Like thermometer used in thermodynamic scale,
except helium replaces the ideal gas.)
•
(13
.
8033 K
,
1234
.
93 K)
Resistance of platinum.
•
>
1234
.
93 K:
Based on radiated light.
07-4
EE 4770 Lecture Transparency. Formatted 13:25, 23 December 1997 from lsli07.