Chapter 6
Temperature Scales and
Thermometers
6.1
Purpose
Temperature is an important property of physical systems. It was not well understood until
the latter 1800’s. Today there are many different types of temperature measuring devices.
In this lab we will experiment with one of the oldest but most straightforward thermometers,
a copper bulb containing a gas. The bulb’s temperature is determined from the pressure of
the enclosed gas. We will then construct a temperature scale and determine absolute zero
temperature at which molecular motion ceases.
6.2
Introduction
Throughout history, a variety of mechanical devices for measuring temperature have been
used. You are probably most familiar with the ordinary red-liquid thermometers and simple
dial thermometers, which are most often seen. You may also have seen older, glass medical
thermometers, which have a mercury column in a glass tube. Each of these types of thermometers makes use of the expansion or contraction of certain substances when changes in
temperature occur. The substance, which expands in the usual red-liquid thermometer and
thus indicates higher temperatures, is most often alcohol with red dye. The ordinary dial
thermostat, which we see in daily use, have within them a ’bi-metal’ element. This is two
pieces of different metals joined together. They have differing rates of thermal expansion
and contraction and thus a metallic coil formed of such metal pairs will tend to wind or
unwind with temperature changes. Electronic thermometers make use of the fact that some
materials have very well-defined electrical resistance which varies predictably as temperature
varies.
In addition to a device to measure and display temperature, one needs certain standards
with which to compare temperatures and to calibrate various temperature-measuring devices.
You are probably most familiar with the Fahrenheit scale which defines an ice + water
mixture as 32 and defines boiling water (at an atmospheric pressure equal to sea level) as
212. You are undoubtedly aware of the Celsius scale, which defines those two temperature
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The Pascal:
The Torr:
The lb/in2 (psi)
1 Pa = 1 N/m2
1 Torr = 1 mm Hg
1 lb/in2 = 6870.8 Pa
1atm = 1.01 x 105 Pa
1 atm = 760 Torr
1 atm = 14.7lb/in2
Table 6.1: Units for Pressure
standards as 0 and 100 respectively.
A constant-volume gas thermometer consists of a fixed volume of gas connected a pressure
gauge. Pressure is the force per unit area that the gas molecules exert on the container as
they collide with the walls of the container. Pressure in this experiment will be measured in
Torr. A table of common pressure units is shown in Table 6.1
In a gas bulb thermometer the pressure, p, increases with the temperature, T, of the gas
if the volume, Vconstant , is constant. The ideal gas law:
pVconstant = nRT
(6.1)
describes the relationship between pressure (p), temperature (T) and volume (Vconstant )
which is constant in this case. In addition, n is the number of moles of gas and R is the
J
).
’ideal gas law constant’ (8.315 molK
Equation 6.1 displays the proportionality between p and T. We can rewrite equation 6.1
as
p=(
nR
Vconstant
)T = CT
(6.2)
where C is a constant since the volume is constant.
As temperature decreases, molecular velocities decrease. Absolute zero is that temperature for which the molecular velocities reach zero and molecular motion ceases. (In quantum
mechanics, there is a small residual molecular motion even at absolute zero.) Figure 6.1
displays the p and T behavior of equation 6.1. Note that as p → 0, then T → absolute zero.
6.3
Equipment:
Gas thermometer, helium supply, vacuum pump, 3 temperature baths, graph paper.
6.4
Procedure
Special Cautions:
• The temperature of liquid nitrogen is 77 K (-196o C). Direct contact with skin will
burn.
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pressure
−273 oC
o
temperature ( C)
Figure 6.1: Plot of temperature vs pressure for an ideal gas
Figure 6.2: The gas thermometer with the pressure gauge.
• Do not exceed a pressures of 1060 Torr in the gas thermometer. Hold the stem or
handle of the bulb firmly while it is in the bath.
In this experiment we will show the linear dependence of p on T for the gas bulb thermometer. We will also find the numerical value (in degrees Celsius) of absolute zero temperature. The gas thermometer is shown in figure 6.2
• With the help of your teaching assistant, pump out and fill the gas thermometer with
helium. Attach the gas thermometer to the vacuum pump hose. Open the valve,
turn on the vacuum pump and remove the air from the gas thermometer. When the
pressure reads zero, close the valve and remove the vacuum pump hose. Attach the
helium regulator hose to the gas thermometer and fill the gas thermometer to a pressure
of 1060 Torr.
• Record the initial (room-temperature) pressure of the helium filled gas thermometer.
• Place the bulb of the thermometer in each of the three baths beginning with the liquid
nitrogen and ending with the boiling water. This avoids formation of a layer of ice
around the bulb that could result in errors. Jiggle the bulb around the bath until it
reaches thermal equilibrium. Record the reading of the pressure gauge in each bath in
a table like Table 6.2.
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Bath
liquid nitrogen
ice water
boiling water
Kelvin(K) Celsius (o C)
77
-196
273
0
373
100
Pressure
Table 6.2: Table of temperature and pressure values
Pressure
Temperature (K)
Tap Water
Room Air
Table 6.3: Table for temperature measurements
• Using graph paper, plot pressure on the y-axis and temperature on the x-axis. Draw the
’best fit’ straight line for the three data points. Extrapolate the line to zero pressure.
The value where the pressure is extrapolated to zero is absolute zero (-273o or 0 K).
Calculate the percentage error of the standard value of absolute zero (-273o) and your
extrapolated value.
• Now use your gas thermometer to measure the temperature of tap water. Read first
the pressure of the bulb when placed in tap water and then use your graph to tell you
the waters temperature. Record the values in a table like Table 6.3. Next use your gas
thermometer to measure the temperature of the room air. Wait for a few minutes for
your gas thermometer to come to equilibrium with the room air. Record the pressure
and find the temperature from your graph.
6.5
Questions
• What would our graph look like if we had filled the bulb with a gas which condenses
at, say, 10C ?
• Why do you think helium was used in our thermometer?
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