I wrote an article for the PCA Bulletin a couple of years ago which covered in passing some of the issues in this thread about measuring density. I have set out an expanded version below. My belief is that for anyone trying this at home, the 'weight in air and weight in water' method is easier and more accurate than measuring the mass and the volume separately.
Density and Specific Gravity, and the accuracy of measurements
Specific Gravity (SG) is a measure of how the weight of something compares to the weight of exactly the same volume of water, and is a pure number. Density is a measure of the mass of a substance in a given volume, measured for example in grammes per cubic centimetre (g/cc). Because the density of water at 4 deg C is 1.000 g/cc, the numeric value of density and specific gravity is the same at 4 deg C. So we do not really need to worry too much about the difference when talking about paperweights. It is easier to type or say ‘density’ than ‘specific gravity’ !
The commonest method of measuring the SG of paperweights is to measure the weight in air, and then the weight when immersed in water. This allows us to calculate the SG: the apparent change in weight is due to the upthrust from the displaced fluid, and is equal to the weight of the same volume of water as the paperweight. There is a very small upthrust from the air when measuring the weight in air, but this is tiny, and we can ignore it. This method has the advantage that the measuring scales need not be accurate, provided they are linear and correctly zeroed! Linear means that if you weight two laboratory 1000g weights and get 1000g for each, you ought to get 2000g for the pair weighed together. The reason that the absolute value does not matter is that the calculation depends upon the ratio of two measurements - so they can be eg 2% wrong, and it has no effect on the calculated SG. The absolute method - ie weighing the item in air and determining the volume by displacement of liquid - is fine theoretically, but requires an absolute measurement in each case. The scales must be spot on - if they read 2 % wrong, then your density will be 2% wrong. And the difficulty of making an accurate determination of the volume has been rehearsed earlier in this thread - it is fraught with inaccuracies.
It is not difficult to overcome some of the difficulties described for the immersion method. I use a rod fixed to a pivot at one end, resting part way along on a knife edge on a pair of electronic scales. The item is suspended in a cradle of plastic coated garden wire at the free end. The reading on the scales is adjusted by moving the knife edge so that the highest reading possible is obtained in air - that way the errors are reduced. The plastic coated wire does not absorb water. And when the apparatus is ready to go, you 'tare' the scales to zero. Then add the item - you get a 'weight in air reading (A)'. The bring a jug of water up from below to immerse the item - you get a 'weight in water (W)' reading. The SG is calculated as A/A-W. eg A=500, W=350, SG = 3.33. If the item is the same density as water, then W will be zero, and you get SG =1.00. Note that units are cancelled out, and absolute measurements are not required - suject to the caveats above.
What about the effect of water temperature? At 20 deg C, the density of pure water has reduced to 0.9982 g/cc, because water expands as it gets warmer. So too does the glass of a paperweight, but water expands more rapidly than glass at temperatures around 20 deg C. So, for example, if a paperweight and a jug of water are warmed from 20 deg C to 25 deg C, the water will expand more than the glass, and the density of the water will decrease more. A paperweight at 25 deg C immersed in water at 25 deg C displaces slightly more water (the paperweight increases in volume by around 135 parts per million) but because the water is less dense, the upthrust from the water decreases by 1050 parts per million. So the apparent weight in water is greater, leading to a higher calculated specific gravity figure (915 parts per million) – roughly one part in a thousand for a 5 deg C change in temperature. But as long as we know the water temperature we can adjust our measurements – and anyway, a couple of degrees will not make a significant difference.
What about the purity of the water? Water does vary in density depending what salts are dissolved in it, but the difference between distilled water and typical tap water is very small – about 30 parts per million at room temperature, and can be ignored for the purposes of this article.
Measurement accuracy. This is very important. A typical Old English paperweight weighs about 500g, and has a density of about 3 g/cc. The apparent weight when submerged in water will be about 330g. Provided we take care to minimise systematic errors, then the greatest accuracy we might achieve in an individual measurement using non-specialised equipment is a tenth of one gram: if the true SG were 3.000, our measured value could then vary between 2.997 and 3.003. That is about plus or minus one part in a thousand – similar to a 5 deg C change in water temperature. If our accuracy is no better than about half a gram, our measured value would vary between 2.985 and 3.015. That is about plus or minus 5 parts in a thousand, and is far larger than any of the other factors discussed above. This range can be reduced somewhat by taking the mean of several repeated measurements, but accuracy and reproducibility are the most important factors when measuring SG. Indeed, repeating measurements from time to time on the same weight is a good test of the reproducibility of the measurement system, and I have done this with satisfactory results.
Alan
Topic: Testing densities (split from Re: Black & White Hound Dog) (Read 3470 times)
