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From Wiki and from physics fundamentals lections I received info that pressure is scalar value. But in definition you have relation between projections of two vector values to normal axe-force and surface area with normal orientation. Are you interesting only in absolute values of this two vectors? (if so then the pressure is always positive.)

Can pressure be negative?

I don't want to discuss the averaged model of the pressure compare to tension elastic model. At current moment from the post answers and comments I realized that pressure scalar field can be defined so:

enter image description here

$f$ is support force to support equilibrium in $ds$ surface under other molecules attack. pressure scalar value in some circumstances can be negative. If smth. was wrong here please let me know!


marked as duplicate by CuriousOne, John Rennie, Martin, Kyle Kanos, ACuriousMind Jun 10 '15 at 18:42

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Your sources were probably trying to keep you from getting confused when they threw in a minus sign later. Typically you deal with a positive scalar pressure which doesn't have a direction. But like if you're doing a fluid mechanics problem and you've just calculated one pressure and you've got other areas of interest, say the other side of a divider, and the teachers throw in the negative.. It tells you which direction the pressure acts. Also you would typically think of pressures as resulting from a gass or a liquid trying to expand in some container. But as noted here Is negative 20 psi / 1.5 bar possible? it'd be reasonable to consider something pulling in on the walls and you could call that a negative pressure.

  • $\begingroup$ So your answer is: "yes, it can be. You take in account signs of projections"? p.s. Thanks for link. $\endgroup$ – bruziuz Jun 10 '15 at 10:07
  • $\begingroup$ I can't type equations in latex in comments, so I'll type it in question $\endgroup$ – bruziuz Jun 10 '15 at 12:31

From the definition of temperature from statistical physics and thermodynamics we have:

$$P=T{\partial S(E,V,N) \over \partial V} |_{E,N}$$ where P is the pressure, T is the temperature, E is the energy of the system. So the temperature will have a negative value if

1)The derivative of entropy over volume change is negative, or

2)The absolute temperature is negative

As for the 1), i don't know if it's sign can become negative(an increase in volume meaning a decrease in entropy or the opposite). But for the second, there is an enteire research going on for negative temperatures which suggest also negative pressures.

Hope this helps.

Note: See,if you are interest: http://arxiv.org/abs/1211.0545 , http://physicscentral.com/explore/action/negative-temperature.cfm , Showing existence of negative temperature for a quantum system, Are negative temperatures typically associated with negative absolute pressures?


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