Density by Archimedes' Principle Using a Top Loading Balance In a well known method for measuring density of a liquid,' a smooth bob is suspended from one arm of' s balance. The bob is massed while susoended in air, and again while suspended in the'liquid. Then density p of the liquid a t temperature T is calculated using the equation
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Twonn)u
Am
(1) Vo[l + a ( T - To)] in which Am is the difference in the two mass readings; Vo, the volume of the bob a t some refer,m 140. ,u ence ternoerature To: and u. the coefficient of eu..., ., v. h i d exninsion far the bob'over the temoerature Figure 1. (len) Setup for measuring range 'fo to T. The volume Vo is determined by density using a top loading balance. measuring Am using water a t TO as the liquid, looking up p in a handbook a t To, and calculating V e usingeqn. (1). LOADIN6 Figure 2. (above) Density of volatile In recent years top loading balances have oil. BALANCE come into common use. It seems worth pointing out that a revised version of the above method msv, he used with a ton loadine balance. A diagram of the experimental. setup is shown in Figure 1. A beaker of liquid a t temperature T is massed. A smooth bob is then suspended from a rigid support so that it is immersed in the liquid, and the beaker of liquid is again massed. By Archimedes principle, the liquid buoys up the bob so that the mass reading with bah will be greater than the mass reading without hob by the mass of a bob's volume of liquid. The density of the liquid is again calculated using eqn. (1). This revised Archimedes method is rapid, and of good accuracy ~rovidedthat a large bob is used with an accurate balance, and that the temperature is well controlled. It is well adapted for measuring density a t elevated temperatures; it is only necessary to enclose the beaker in a heated, insulated mantle. I t is well adapted for measuring density of volatile andlor corrosive liquids whose vapors would tend t o condense on the beam of an ordinary, overhead balance. It is also well adspted for measuring density of viscous liquids or of suspensions for which pycnometers may not be applicable. The bob material should be such that corrosion will not occur, such that a is known, and such that theliquid wets the solid so as to avoid holdup of air bubbles on the bob surface when the bob is immersed. In one application of the method, the bob was of 316 stainless steel with a = (4.8)(10-9 sC-',2 and Vo = 29.24 cm3 a t T
