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

[bootsnbraces]

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

 

[SteamKing]

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.

 

[bootsnbraces]

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!

 

[Chestermiller]

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 C_pΔT.

 

[PJC01]

Hello,

Thank you for your question. Adiabatic liquid compression is a complex phenomenon that requires a thorough understanding of thermodynamics and fluid mechanics. The adiabatic gas equation you have mentioned is only applicable to ideal gases, and cannot be used for liquids.

For liquids, the temperature rise under high pressures can be determined using the Joule-Thomson coefficient, which is a measure of the change in temperature with respect to pressure at constant enthalpy. This coefficient can be calculated using the Clausius-Clapeyron equation and the compressibility factor of the liquid.

Alternatively, you can also use the isentropic compression equation, which takes into account the specific heat capacity of the liquid and the change in volume under compression. This equation is more accurate for non-ideal liquids.

I would recommend consulting a thermodynamics textbook or seeking assistance from a fluid mechanics expert to accurately calculate the temperature rise in your specific case. I hope this helps. Best of luck with your research!