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  1. #1
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    Thermal expansion formula



    Liquid 100% R134a trapped between 2 valves at 10°C and heated up to 35°C. Let's say volume can't change, what is the equation to calculate final pressure?


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  2. #2
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    Re: Thermal expansion formula

    Often wondered about this. A question for a someone who is knowledgeable about Physics I fear. I think if there is 100% liquid the pressure would be enormous!

  3. #3
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    Re: Thermal expansion formula

    I think the answer is at the end of this Youtube vid.
    Although it shows Enthalpy difference equation, it can be transposed to find the pressure difference.
    https://youtu.be/V77rmiRf2qE

  4. #4
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    Re: Thermal expansion formula

    Is it something that can be read off a pressure enthalpy chart if you know the density of the liquid at the 10 DegC?

    or maybe,

    https://www.theleeco.com/support-res...etric%20strain.

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  5. #5
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    Re: Thermal expansion formula

    I thought I could find the solution somewhere in the logp/h but couldn't bind it. This question was from one of my students and I couldn't give him an answer. I hope I find between the help of my colleagues somewhere the right answer.
    I will post another one which is not quite clear for me.
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  6. #6
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    Re: Thermal expansion formula

    Quote Originally Posted by seanf View Post
    Is it something that can be read off a pressure enthalpy chart if you know the density of the liquid at the 10 DegC?

    or maybe,

    https://www.theleeco.com/support-res...etric%20strain.

    .
    .
    .
    .
    I think this is what I was looking for.. now find he cubical thermal expansion for R134a ...found it for water whic was 4 or 5 times
    It's better to keep your mouth shut and give the impression that you're stupid than to open it and remove all doubt.

  7. #7
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    Re: Thermal expansion formula

    Found after your help with the correct English expressions this https://pressbooks.bccampus.ca/colle...s-and-liquids/
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    Re: Thermal expansion formula


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    Re: Thermal expansion formula

    it's it's 100% full and 100% liquid... then it'll stay liquid no matter the temperature?

    so

    pressure1 x volume1 / temperature 1

    equals

    pressure2 x volume2 / temperature 2



    (sorry I'm not very good at typing equations!)

  10. #10
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    Re: Thermal expansion formula

    I think PV/T might be for ideal gas only.

  11. #11
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    Re: Thermal expansion formula

    As simple as this? Never noticed and also never saw a log p/h where the lines of constant volume went up in the liquid phase
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    Re: Thermal expansion formula

    Quote Originally Posted by Peter_1 View Post
    As simple as this? Never noticed and also never saw a log p/h where the lines of constant volume went up in the liquid phase
    I dont know for sure.
    Seem to be half the charts that came up on a search do have the lines that far to the left.

  13. #13
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    Re: Thermal expansion formula

    Quote Originally Posted by seanf View Post
    I dont know for sure.
    Seem to be half the charts that came up on a search do have the lines that far to the left.
    I think you're spot on Sean
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  14. #14
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    Re: Thermal expansion formula

    Not so good with the Charts and Math myself, so help me out here.
    As I understood the original question (which drew my interest) it was how much pressure liquid would develop if it was trapped and could not expand when heated. (As if Refrigerant was trapped between two valves)
    The amount of increase in Temperature would of course be a factor in the pressure,, but I do not think that can be used to determine the final pressure.
    I did find this quote. It refers to freezing water, but I think this might be similar.
    Freezing force of water: as the water-ice temperature continues to drop to 0°F the forces involved range between 25,000 psi and can continue to reach 114,000 psi.
    I found this at https://inspectapedia.com/plumbing/F..._Water_Ice.php
    Looking forward to more discussion!

  15. #15
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    Re: Thermal expansion formula

    I stopped being lazy (retirement does that to one!) and found this.
    http://www.svasd.com/wp-content/uplo...ppedLiquid.pdf

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    Re: Thermal expansion formula

    Quote Originally Posted by NH3LVR View Post
    I stopped being lazy (retirement does that to one!) and found this.
    http://www.svasd.com/wp-content/uplo...ppedLiquid.pdf
    Thanks NH3LVR

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    Re: Thermal expansion formula

    Quote Originally Posted by NH3LVR View Post
    I stopped being lazy (retirement does that to one!) and found this.
    http://www.svasd.com/wp-content/uplo...ppedLiquid.pdf
    Very interesting lecture which I saved for my students (and myself) but there's still no connection to some formula ...seems not that easy to find some explanation for this phenomena
    It's better to keep your mouth shut and give the impression that you're stupid than to open it and remove all doubt.

  18. #18
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    Re: Thermal expansion formula

    Quote Originally Posted by knighty View Post
    it's it's 100% full and 100% liquid... then it'll stay liquid no matter the temperature?

    so

    pressure1 x volume1 / temperature 1

    equals

    pressure2 x volume2 / temperature 2



    (sorry I'm not very good at typing equations!)
    This is the gas law and not valid for liquids... I guess

    After posting, found this where it seems you're right
    https://www.eng-tips.com/viewthread....3D%20T2P1%2FT1.
    Last edited by Peter_1; 07-11-2022 at 08:22 PM.
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  19. #19
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    Re: Thermal expansion formula

    Last edited by Peter_1; 07-11-2022 at 08:33 PM.
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  20. #20
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    Re: Thermal expansion formula

    If the volume of the space is 100% liquid and can not change, pressure is not defined, because pressure has to be measured by measuring force (per area). At least an infinite small change (e.g. dV ) has to be thought of. In this small dV, there will be gas at preassure of 9bar (see above), same pressure everywhere inside the liquid. At 10°C it was 5bar.

    Maybe you have difficulties to imagine this, because you think of liquid!=gas, but because liquid and gas have 2nd Order Phase Transition and strictly speaking (at >0K) there is no pure liquid or pure gas anyway, this small dV has also measurable realisation (or just find the gas bubble...).

    Change of liquid density tabulars dont help here and are not necessary for the same reason.

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