Cubic equation of state near critical point (~0.95 < Tr < 1)

In summary, cubic equations of state can have convergence issues when calculating vapor pressure near the critical point. This is demonstrated in experiments and discussed in a NASA report from 1970 and a journal article from 1985. This can lead to uncertainty when applying an equation of state in near-critical fluid conditions. Additionally, there is limited information available in the literature about describing properties of structural alloys in the range of 0.9 - 1 Tm.
  • #1
maistral
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Hi. I have read somewhere that cubic equations of state seem to have convergence issues when vapor pressure calculations are done near the critical point. Sadly, I have forgotten where I have have read it :(

I would like to ask some knowledgeable people regarding this, or can people point me I am the right direction about this topic?
 
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  • #2
Cubic equations (and even higher order polynomials) can be inadequate to describe properties near transitions such as the critical point.

See the NASA report, SURVEY OF HEAT TRANSFER TO NEAR-CRITICAL FLUIDS, November 1970
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710003560.pdf

. . . experiments demonstrate that, near the critical point, large relaxation times are required for a thermally disturbed system to return to
equilibrium. One consequence of this is that the near-critical fluid under the dynamic conditions of heat transfer can be expected to experience some degree of thermodynamic nonequilibrium. This, in turn, will result in some uncertainty in applying an equation of state.
from bottom of page 5 of the report.

See also - J. V. Sengers, "Transport properties of fluids near critical points," International Journal of Thermophysics, May 1985, Volume 6, Issue 3, pp 203–232

On a similar matter, I have a particular interest in describing properties of structural alloys in the range of 0.9 - 1 Tm. One finds scarce information in the literature.
 
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1. What is the Cubic Equation of State?

The cubic equation of state is a mathematical model that describes the relationship between pressure, volume, and temperature for a substance. It is often used to analyze the behavior of gases and liquids.

2. What is the critical point in the Cubic Equation of State?

The critical point is the temperature and pressure at which a substance transitions between the gas and liquid phases. At this point, the substance exhibits unique properties, such as having the same density for both gas and liquid phases.

3. How does the Cubic Equation of State behave near the critical point?

Near the critical point, the Cubic Equation of State predicts that the behavior of the substance will be highly non-ideal. This means that the substance will not follow the ideal gas law and its properties will be significantly affected by changes in temperature and pressure.

4. What is the range of reduced temperatures for the Cubic Equation of State near the critical point?

The range of reduced temperatures for the Cubic Equation of State near the critical point is typically between 0.95 and 1. This means that the temperature is very close to the critical temperature, which is the temperature at the critical point.

5. How accurate is the Cubic Equation of State near the critical point?

The accuracy of the Cubic Equation of State near the critical point depends on the specific substance being studied. For some substances, it may provide a good approximation of the behavior near the critical point, while for others it may not accurately predict the behavior. Other more complex equations of state may be needed for more accurate predictions.

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