3
$\begingroup$

My textbook states that liquids (say water for example) can sustain "negative pressures" because of their intermolecular attractive forces. The text depicts this concept with the following image

Text

The author then also states that "in gases, pressure can only be positive". This statement gives me problems though. If the attractive intermolecular forces of a liquid are what allow liquids to sustain negative pressures, then surely real gases (as opposed to ideal gases) can in fact sustain negative pressure because the molecules in a real gas can be either attractive (when their internal pressure is positive: $\pi_T>0$) or repulsive (when $\pi_T < 0$). The case when $\pi_T>0$, meaning attractive intermolecular forces, should in theory allow for gases to sustain negative pressures? Is this true? Can gasses sustain negative pressures just like liquids (albeit at a reduced strength relative to liquids)?

$\endgroup$
5
  • 1
    $\begingroup$ I suspect that gases condense to liquids precisely when the attractive forces become strong enough to make negative pressures possible. Thus gases cannot sustain a negative pressure because any gas that could immediately condenses to a liquid. But proving this is going to be tricky. $\endgroup$ Aug 3 '21 at 11:41
  • $\begingroup$ @JohnRennie A gas above its critical temperature cannot condense. $\endgroup$ Aug 3 '21 at 12:16
  • $\begingroup$ A liquid cannot sustain a pressure less than its equilibrium vapor pressure without forming a 2nd phase. In the picture, even though the liquid pressure may be less than atmospheric, it is still under positive absolute pressure. Thus, although the gauge pressure may be negative, the absolute pressure is positive. $\endgroup$ Aug 3 '21 at 12:42
  • 1
    $\begingroup$ @ChetMiller Gauge pressure is not an issue. The picture correctly depicts a situation with absolute negative pressure. The parallel with solids is also correct. However, .. there is a however. I'll try to explain with an answer. But I can't do it immediately. I'll be back to this problem in a few hours. $\endgroup$
    – GiorgioP
    Aug 3 '21 at 12:52
  • $\begingroup$ In the diagram in the question, the piston could also be held up if the chamber was filled with a gas. It is atmospheric pressure exerting a force on the outside of the piston which keeps it up. $\endgroup$ Aug 3 '21 at 15:36
1
$\begingroup$

The stretched, negative-pressure states of liquids are not so well-known as the supercooled and the superheated metastable states. Even today, many physicists believe that pressure cannot be negative. Interestingly, in the first decade of the present century, a NATO Advanced Research Workshop, held in Budapest in 2002, was entirely dedicated to Liquids under negative pressure. A recent paper on the subject starts its abstract as follows:

Although pressure is usually believed to be an always positive quantity, negative pressure states exist since the beginning of the Universe, and they have been studied since Huygens.

The key point with negative pressure states of solids and liquids is that they are metastable with respect to a stable liquid-vapor (or solid-vapor) phase coexistence. However, nucleation processes driving the system towards the stable state may be very inefficient, and the metastable state may last unperturbed for hours or days. Each liquid has a lower limit for negative pressures. Below that limit, the metastable state becomes unstable, and cavitation (i.e., the formation of vapor bubbles) becomes unavoidable. Notice, however, that the negative pressure limit may reach values of $-100$ MPa (for water). Obviously, such values are genuine negative values of the absolute pressure (no gauge pressure).

So, what about negative pressures in gases? Two important factors make the situation of gases very different.

The first is the average larger distance between molecules in vapor with respect to the case of a liquid (almost one order of magnitude larger for the vapor coexisting with the liquid close to the triple point. Larger distances mean that the attractive tail of the intermolecular interactions, responsible for the cohesive force, is significantly weaker than in the case of liquids.

A second related factor is a fundamental asymmetry between the process of stretching a liquid or a gas. In the case of a starting stable liquid state, stretching implies driving it in the metastable region. If we start with a stable vapor phase and increase the volume, we go from a stable phase to another stable phase with a lower density (and still positive pressure).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.