Does the Adiabatic Gas Equation Apply to Liquid Compression at High Pressures?

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Discussion Overview

The discussion revolves around the applicability of the adiabatic gas equation to the compression of liquids at high pressures, specifically at 7000 bar. Participants explore whether the equations typically used for gases can be adapted for liquids and how to calculate the resulting temperature changes under such conditions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the suitability of the adiabatic gas equation for liquids, suggesting that most liquids are essentially incompressible and that gas equations may not accurately model liquid behavior.
  • Another participant acknowledges that while liquids are nearly incompressible, at 7000 bar, this may not hold true, and expresses a need to determine the temperature rise despite limited knowledge of thermodynamics.
  • A different approach is proposed involving the pressure-volume equation for liquids, suggesting the use of the bulk modulus to calculate compressional work and relate it to temperature change.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of the adiabatic gas equation to liquids under high pressure. There are competing views regarding the behavior of liquids and the appropriate methods for calculating temperature changes.

Contextual Notes

There are limitations regarding the assumptions made about liquid compressibility at high pressures and the dependence on specific definitions of thermodynamic properties. The discussion does not resolve these complexities.

bootsnbraces
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Hi all,
Hope you can help I am trying to figure out the temperature rise in a liquid subject to high pressures (7000bar in this case)

Is the below adiabatic gas equation still suitable? or is there another way of working this out for liquids?

T2 = T1(v1/v2)^y-1
P2 = P1(v1/v2)^y
Were y = Cp/Cv

I tried working this out backwards from the theory that pressure = f/a = energy/volume but i got a bit lost along the way lol
 
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Most liquids are essentially incompressible, so I wouldn't expect a great rise in temperature. And I wouldn't think that using gas equations to model liquid behavior would be accurate, either.
 
unfortunately nearly incompressible doesn't count at 7000 bar, i don't expect the rise to be to great but i need to figure out what it will be and don't know enough about thermodynamics to get there!
I did stumble across the answer on a different forum a few months ago but I am damned if i can find it now!
 
Try starting out with the pressure-volume equation for a liquid: V=V0e-βP where β is the bulk modulus, and V0 is the volume at low pressure. Use this to calculate the compressional work done. That should be equal to CpΔT.
 

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