Simple question, can gasoline be compressed? Is it compressible as in how water is incompressible. Would one be able to store x gallons of gasoline in a pressurized container that is x-y size. For example could you store 100 gallons of gasoline in a pressurized 98 gallon container?
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2$\begingroup$ Not strictly an answer, but gasoline's incomprehensibility is used in submersible devices. en.wikipedia.org/wiki/Bathyscaphe Everything is compressible to some extent, but Gasoline is fairly resistant to compression. $\endgroup$– userLTKSep 18, 2015 at 5:27
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$\begingroup$ Gases are compressible. As a first approximation, liquids are incompressible. Solids are also volumetrically incompressible to a first approximation, unless they have large gas inclusions (think foam or cork.) $\endgroup$– Level River StSep 18, 2015 at 12:55
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1 Answer
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The resistance of a material to compression is given by its bulk modulus.
Suppose the initial volume of out object is $V$ (100 gallons in this case) and we compress it by a small amount $dV$ (2 gallons) then the pressure needed to do this is:
$$ P = K\frac{dV}{V} $$
where $K$ is the bulk modulus.
The bulk modulus of gasoline is $1.3 \times 10^9$ Pa, so in your example the pressure needed to compress the gasoline is:
$$ P \approx 1.3 \times 10^9 \frac{2}{100} \approx 2.6 \times 10^7 \,\text{Pa} $$
One atmosphere is 101325 Pa so the pressure is about 260 atmospheres, which actually isn't that much. Industrial processes routinely work at these sorts of pressures.
Note that I used the approximately equal sign, $\approx$, in my equation. The bulk modulus is usually a function of the amount of compression rather than a constant, so my first equation is true only for an infinitesimally small compression $dV$ rather than the 2% compression you give. However the bulk modulus probably doesn't change that much over a 2% compression and the pressure I've calculated will be a good approximation.
answered Sep 18, 2015 at 5:22
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1$\begingroup$ That's a surprisingly small pressure. Thanks for the back of the envelope. $\endgroup$ Sep 18, 2015 at 5:39
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3$\begingroup$ @CuriousOne: I was a bit surprised too, though if a Haber process pressure vessel went bang next to us I suspect we'd feel otherwise :-) $\endgroup$ Sep 18, 2015 at 5:45
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3$\begingroup$ You are right, we have become too accustomed to calculated pressures inside neutron star cores to have any reverence for such "trivial" things as industrial pressure vessels. $\endgroup$ Sep 18, 2015 at 5:49
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$\begingroup$ So the Challenger Deep would have compressed the Trieste about 10%! $\endgroup$ Sep 18, 2015 at 12:53
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1$\begingroup$ @WetSavannaAnimalakaRodVance: even water is compressed by about 5% at the deepest points in the ocean! $\endgroup$ Sep 18, 2015 at 14:49