You are presented with a beaker of a fluid that you think is olive oil (which ca

Question

You are presented with a beaker of a fluid that you think is olive oil (which can have a specific gravity of 0.91 - 0.92 depending upon the "grade" of the oil). You are also given a block of paraffin wax that is 2mm x 5 mm x 10mm in shape, that has a specific gravity of 0.82 - 0.96. Report all calculation results to 3 significant digit accuracy. First, you place the block of paraffin into a beaker of distilled water (SG=1), with the 2mm side perpendicular to the surface of the water - greatest surface area parallel to the water's surface, and note that only 0.3 mm remains above the surface of the water. What is the actual specific gravity of your sample based on this measurement? You now place the paraffin block in the oil, again with the 2mm side perpendicular to the fluid's surface. The block sinks into the oil with only 0.15 mm above the surface of the water. What is the specific gravity of your oil sample, and is it, indeed, olive oil? If the paraffin block were to sink until it's top surface were just at the level into which you submerged it; i.e., it was totally submerged, but not below the surface of the fluid, what can you say about the relationship between the paraffin block and the fluid?

Explanation / Answer

a) SGolive = dolive / dwater

0.91-0.92 = dolive / dwater

similarly,

SGparaffin = dparaffin / dwater

0.82-0.96 = dparaffin / dwater

Now, when parafin wax is immersed,

Volume of water displaced by wax sample = 1.7x5x10 mm3 = 85x10-9 m3

mass of water displaced = 85x10-9 x1000 = 8.5x10-5 kg

mass of paraffin = 0.82-0.96x1000x2x5x10 mm3 = 0.82-0.96x1000x100x10-9 =0.82-0.96x10-4 kg

Actual SGparaffin = 0.85

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