ASTM D1217 Standard Test Method for Density and Relative Density (Specific Gravity) of Liquids by Bingham Pycnometer
11. Calculation
11.1 Calculate the true density of the sample as follows:
where:
Ws = weight in air of sample contained in the pycnometer at the test temperature, g,
Ww = weight in air of the water contained in the pycnometer at the calibration temperature, g,
dw = density of water at the calibration temperature, as obtained from Table 1,
da = density of air in balance case at the time of weighing, as calculated from 10.3,
dwt = density of weights used in weighing the sample and water (brass = 10.4 g/mL, stainless steel = 7.75 g/mL), and
ds = approximate density of sample or
(Ws x d)/Ww
11.2 The equation assumes that the weighings of the pycnometer empty and filled are made in such a short time interval that the air density has not changed. If significant change should occur, the calculated apparent weight of the sample, Ws, in this equation, must be corrected for the difference in air buoyancy exerted on the pycnometer as follows:
where:
W2PS = weight of pycnometer and contained sample under second or final air density,
W'P = weight of pycnometer in air of first density,
d'a = density of air when weighing empty pycnometer,
da2= density of air when weighing filled pycnometer, and
dwt and 2.2 = density of weights and borosilicate glass, respectively.
Likewise, if the pycnometer, empty and filled with water for calibration, is weighed under different air densities a similar correction for different air buoyancies shall be applied.
11.3 Calculate the relative density (specific gravity) of the sample by dividing the density as obtained in 11.1 by the relative density of water at the reference temperature obtained from Table 1.
11.4 Calculate the density of air in the balance room as follows:
where:
B = barometric pressure, mm Hg, corrected to 0°C,
H = relative humidity, decimal fraction,
p = vapor pressure of water at temperature t, mm Hg, and
t = room temperature, °C.
NOTE 6 - If this test method is to be used frequently, a considerable amount of calculation can be avoided by use of a gas density balance to determine the air density. Weigh a sealed 250-mL glass bulb at several different air densities and plot the weight against the air density. To determine the air density at some later time, weigh the bulb and read the air density from the point on the curve corresponding to the weight.
11.5 To calculate the density or relative density (specific gravity) at any test temperature, t, other than the calibration temperature, t c(to correct for the cubical coefficient of thermal expansion of borosilicate glass), divide the value obtained in 10.1 or 10.2 by the following expression:
