Density and Buoyancy – A Simulated Experiment copyright 2001 Gary L. Bertrand

http://web.mst.edu/~gbert/balance/ABal.html

Instructions

Specific Gravity of a Solid: The specific gravity (SG) of a material is the ratio of its density to that of water at the same temperature and pressure. The difference between the weight of a solid in air and under water is equal to the weight of water displaced by the volume of the sample:

SG = (weight in air)/(weight in air – weight under water) Eq 1

These values are normally reported to only three significant digits.

1. Select water as the liquid and select a solid sample. 2. Tare the balance. 3. Select sample position as weigh in air and record the value. 4. Select sample position as weigh under liquid and record the value. 5. Repeat steps 2-4 at least twice and calculate values for SG with Eq 1. 6. Average your results and estimate the uncertainty of this value.

Volume of a Solid and Density of a Solid:

All fluids, including air, exert a buoyancy effect. The weight of a solid immersed in a fluid (WF) is related to the weight in vacuum (WVac) by the volume (V) of the sample and the density of the fluid (DF):

WF= WVac- VDF .

The volume may be determined by weighing the solid in two fluids of known density , such as water (WW, DW) and air (WA, DA):

V = (WA-WW)/(DW – DA) Eq 2.

Values for the density of water at various temperatures are provided by the link density of water. The density of air may be estimated at temperature (t, oC) and 1 atm pressure: DA = 0.353/(t + 273.15) .

1. Select water as the liquid and select glass as the solid sample. 2. Tare the balance. 3. Select sample position as weigh in air and record the value. 4. Select sample position as weigh under liquid and record the value. 5. Repeat steps 2-4 at least twice and calculate values for V to four significant digits with Eq 2. 6. Average your results and estimate the uncertainty of this value.

The density of the glass sample can be calculated by correcting the weight in air to the weight in vacuum and dividing by the volume:

Dsample = (WVac/V) = (WA/V) + DA Eq 3.

The densities of other solids may be determined to about ± 0.1% by this method.

Density of a Liquid: After determining the volume (V) of the glass sample (or any other solid), the densities of other liquids (DL) may be determined by the difference between the weight of the glass sample in air (WA, DA) and when immersed in the liquid (WL):

DL = DA + (WA – WL)/V Eq 4.