Boyle’s Gas Tube Experiment
Robert Boyle (1627 – 1691) established the law that, for a given quantity of a gas (ideal) at a fixed
temperature, the pressure is inversely proportional to the volume: P = A/V, where A is a parameter whose
value is to be estimated from experimental measurements of pairs of values of P and V. By pouring mercury
into the open top of the long side of a J-shaped tube, Boyle increased the pressure of the air trapped in the
short leg. The volume of the trapped air would be V = h*cross section of short leg, where h is the height of
the air in the short leg. If y = height of mercury in long leg – height of mercury in short leg, then we have
Y = 0 + 1x, where x = 1/h. Due to the fact of experimental error, the model should be written as
Yi = 0 + 1xi + i, where i = random error associated with ith measured pair of values of x and y. In his
experiment, Boyle took 25 measurements of y at 25 specific different values of x. The data are shown
below, together with the SAS program which analyzes the data.
data one;
input h y;
x = 1/h;
prod = h*y;
label x = "Reciprocal of Height in Short End"
y = "Height in Long End";
cards;
48 29.4375
46 30.5625
44 31.9375
42 33.5000
40 35.3125
38 37.0000
36 39.3125
34 41.6150
32 44.1875
30 47.0625
28 50.3125
26 54.3125
24 58.8125
23 61.3125
22 64.0625
21 67.0625
20 70.6875
19 74.1250
18 77.8750
17 82.7500
16 87.8750
15 93.0625
14 100.4375
13 107.8125
12 117.5625
;
proc print;
Title "Data from Boyle's Gas Tube Experiment";
;
proc plot;
plot y*(x prod);
Title "Scatterplot of Height in Long End vs. Reciprocal of Height in Short End";
Title2 "And vs. the Product of the Heights";
;
proc corr;
var h x y prod;
Title "Correlations Among Variables";
Title2;
;
proc reg;
model y = x;
plot predicted.*x;
plot residual.*y;
Title "Analysis of Boyle's Data on Gas Pressure vs. Volume";
;
run;