Thermodynamics and Chemistry

CHAPTER 2 SYSTEMS AND THEIR PROPERTIES

2.3 SOMEBASICPROPERTIES ANDTHEIRMEASUREMENT 44

ideal behavior only in the limit of low pressure, it is necessary to make a series of the paired
measurements, changing the amount of gas in the bulb before each new pair so as to change
the measured pressures in discrete steps. Thus, the operational equation for evaluating the
unknown temperature is

T 2 DT 1 lim

p 1! 0

p 2 V 2

p 1 V 1

(2.3.6)

(gas)

(The ratioV 2 =V 1 differs from unity only because of any change in the bulb volume whenT
andpchange.) The limiting value ofp 2 V 2 =p 1 V 1 can be obtained by plotting this quantity
againstp 1 ,1=Vm, or another appropriate extrapolating function. Note that values ofnand
Rare not needed.
Another method is possible if the value of the second virial coefficient at the reference
temperatureT 1 is known. This value can be used in the virial equation (Eq.2.2.2) together
with the values ofT 1 andp 1 to evaluate the molar volumeVm. Then, assumingVmis the
same in both equilibrations of a measurement pair, it is possible to evaluatep 2 Vm=Rat
temperatureT 2 , andT 2 can be found from

T 2 D lim

p 2! 0

p 2 Vm

R

(2.3.7)

(gas)

Constant-volume gas thermometry can be used to evaluate the second virial coefficient
of the gas at temperatureT 2 if the value atT 1 is known (Prob. 2. 3 ).
The principles of measurements with a gas thermometer are simple, but in practice great
care is needed to obtain adequate precision and accuracy.^8 Corrections or precautions are
required for such sources of error as thermal expansion of the gas bulb, “dead volume”
between the bulb and pressure measurement system, adsorption of the thermometric gas on
interior surfaces, and desorption of surface contaminants.
The national laboratories of several countries, including the National Institute of Stan-
dards and Technology in the United States, maintain stable secondary thermometers (e.g.,
platinum resistance thermometers and thermocouples) that have been calibrated according
to the ITS-90. These secondary thermometers are used as working standards to calibrate
other laboratory and commercial temperature-measuring devices.

Practical thermometers

Liquid-in-glass thermometersuse indicating liquids whose volume change with temperature
is much greater than that of the glass. A mercury-in-glass thermometer can be used in the
range 234 K (the freezing point of mercury) to 600 K, and typically can be read to0:01K.
A Beckmann thermometer covers a range of only a few kelvins but can be read to0:001K.
Aresistance thermometeris included in a circuit that measures the electric resistance.
Platinum resistance thermometers are widely used because of their stability and high sen-
sitivity (0:0001K). Thermistors use metal oxides and can be made very small; they have
greater sensitivity than platinum thermometers but are not as stable over time.

(^8) In 1899 H. L. Callendar, the British physicist who introduced the platinum resistance thermometer, wrote
(Ref. [ 26 ]) “It is impossible for those who have never worked with a gas-thermometer to realize the extent of
its shortcomings.”