Page 41 - Essentials of physical chemistry

Ideal and Real Gas Behavior 3

Bent glass
tube

L air
L Hg

Mercury
FIGURE 1.2 A schematic of the J-tube Sir Robert Boyle used to study the PV relationship.

Boyle’s ‘‘J-tube’’ is a very ingenious device, which is simple and accurate. Today this would be
called a manometer, which is a device to measure pressures in a laboratory. In Figure 1.2, the
difference between the two heights of mercury is given in ‘‘inches of mercury’’ but modern
measurements including blood pressure measurements from an arm cuff are usually given in
‘‘mm of mercury’’ and 1 atm of air pressure on planet Earth is standardized as 760 mm of mercury
at sea level (since the pressure varies with height above sea level). Please note that 1 in. is exactly
2.54 cm. (If you ever work on a car or machine with metric dimensions you will find the 13 mm
wrench works great on a ½ in. bolt but few others are interchangeable. A Ford Pinto 2000 engine
has SAE (Society of Automotive Engineers) bolts externally but internal metric dimensions as built
in Germany. This modern example shows that we need to be prepared to convert data in inches as
evident in Boyle’s data to scientific centimeter units. If we standardize on 760 mmHg as 1 atm
(earth) we can also relate the height of 29 11=16 in. of Hg to yet another set of units as

11
29 in: (25:4 mm=in:) ¼ 754:0625 mm
16
so

754:0625 mmHg=(760 mmHg=atm) ¼ 0:9921875 atm:

This brings up a problem having to do with experimental measurements in terms of how accurate we can
carry out calculations with data that are only good within 1=16 in. or at best 1=32 in. ( 0.079375 cm)
according to Boyle’s (subjective) eyes. In fact all experimental data will have some uncertainty. We will
postpone the treatment of experimental uncertainty for a few pages so that we do not lose sight of the
problem at hand, but we will say here that quoting the value in atmospheres to seven significant figures is
artificially precise when the data are good to only the nearest 1=16 in. (0.156875 cm). Here we show
some of the actual data from Boyle’s 1662 book ‘‘New Experiments Physico-Mechanical, Touching the
Spring of Air, and its Effects. . . .’’ The data in Table 1.1 lead to an important phenomenological
observation in that the product of the pressure (P) and volume (V ) is essentially constant! Although
there is some variation in the PV product, a wise observer can see the values are nearly constant allowing