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If we speak about vacuum above -25mbar, does it mean that it shall be deeper than -25mbar, i.e., for example, -40mbar?

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My gut feeling for this question as it is worded is that yes, a vacuum above -25 mbar means that it shall be deeper than -25 mbar, e.g. -40 mbar.

When measuring a vacuum the scientific community (to the limit of my experience) would normally use absolute values, so between 0 bar and 1 bar. A total vacuum is considered to be 0 bar. By comparison, atmospheric pressure at STP (standard temperature and pressure) is 1 bar. The vacuum of space is just slightly above 0 bar. (Also in my experience it would be measured in Pa, but that's not in scope here.)

When vacuums are referenced as negative values this often refers to a suction pressure value as it is referenced to atmospheric pressure. This can also be slightly variable since local atmospheric pressure is variable, unless it is a controlled environment.

This also leads to the uncertainty of the meaning as you have asked due to the ambiguity in definition.

Consider this:
A suction pressure of 25 mbar gives a vacuum of -25 mbar when referenced to atmospheric pressure.

But... a suction pressure greater than 25 mbar gives a vacuum below -25 mbar. A suction pressure of 30 mbar gives a vacuum pressure of -30 mbar, which is lower than -25 mbar, but which might also be considered to be above -25 mbar, and could also be spoken of as being greater than -25 mbar. Which all just leads to confusion, which leads scientists to sometimes go to great pains to be precise in their meaning, but that meaning can be sometimes quite different to the everyday meaning, which brings us back to square one (if we are not aware of this).

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