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

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SUMMARY

The discussion centers on the applicability of the adiabatic gas equation to liquid compression at high pressures, specifically at 7000 bar. The participants conclude that while the adiabatic gas equations (T2 = T1(v1/v2)^(y-1) and P2 = P1(v1/v2)^y) are not suitable for liquids due to their incompressibility, an alternative approach using the pressure-volume equation for liquids (V = V0e^(-βP)) is recommended. The bulk modulus (β) and the relationship between compressional work and temperature change (CpΔT) are essential for accurate calculations in this context.

PREREQUISITES
  • Understanding of thermodynamics principles, particularly the concepts of adiabatic processes.
  • Familiarity with the bulk modulus and its application in fluid mechanics.
  • Knowledge of the specific heat capacities (Cp and Cv) and their significance in thermodynamic equations.
  • Basic mathematical skills for manipulating exponential equations and understanding pressure-volume relationships.
NEXT STEPS
  • Research the bulk modulus of various liquids and its implications for high-pressure scenarios.
  • Study the derivation and application of the pressure-volume equation for liquids.
  • Explore the differences between compressible and incompressible fluid dynamics.
  • Learn about the principles of compressional work and its relation to temperature changes in fluids.
USEFUL FOR

Engineers, physicists, and researchers involved in high-pressure fluid dynamics, particularly those working with liquid systems in thermodynamic contexts.

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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