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Energy requirements for heating a liquid under different pressures

  1. Aug 24, 2011 #1
    Hello,

    I am interested to know how pressure affects how much energy is needed to heat up a liquid, if at all.

    For example, does it require less energy to heat up water at sealevel compared to the energy needed to do the same at the bottom of the sea?

    Cheers,
    klillas
     
  2. jcsd
  3. Aug 24, 2011 #2
    Basic energy to heat water:

    Q = mass * cp * Temperature Difference

    If mass and Temperature Difference remain constant, the heat will vary with the specific heat. Some data for water:

    At 60 F and 14.7 psia, cp = 0.999237 BTU/lb-R
    At 60 F and and 3000 psi (about 7000 ft deep) cp = 0.983650 BTU/lb-R

    So it will require about 2% less energy to heat water in the depths of the ocean.
     
  4. Aug 24, 2011 #3
    Thanks!
    I would like to keep going until I get a correct understanding of how this works if you have the patience :)

    Let's say I have a bucket upside down filled with water just below sea level and an identical bucket in the depths of the ocean. I use the same amount of energy to heat the water in the two buckets. The water expands (a little) which generates two lifting forces on the buckets.
    How will the two forces compare to each other? Is one greater than the other?

    Cheers,
    klillas
     
  5. Aug 25, 2011 #4
    I think the difference would be small but you could estimate as follows:

    The density difference will generate the buoyancy force. Assume you heat liquid from 60 F to 200 F. So compare:

    * density (14.7 psia, 60 F) - density (14.7 psia, 200F)

    to,

    * density (3000 psia, 60 F) - density (3000 psia, 200F)

    The one with the larger difference would make more force.
     
  6. Aug 25, 2011 #5
    Thank you,

    If I read the following table correctly, it would seem that you get a larger buoyancy force at high pressures than at lower pressures if using the same amount of energy to heat the water. I simply compared the volume changes from 0C to 50C at different pressures.

    http://www.nist.gov/srd/upload/NISTIR5078-Tab3.pdf

    My full thought experiment is the following:

    Consider that the bucket at sealevel is heavy enough to be dragged down to the bottom of the sea. While at sealevel, the bucket has a potential energy which could be stored as electrical energy in a battery while the bucket goes down to the bottom.

    Using the stored energy to heat the water in the bucket would generate a lifting force that would drag the bucket back up to the surface. The bucket would have to be insulated enough for the heat to not exit the bucket before reaching the surface.

    Now, if we always needed a constant amount of energy to generate the same lifting force independent on how far down the bucket is, then we could keep going down until we have more energy stored than we need to get back up to the surface again.

    I thought that the higher pressure would result in more energy needed to generate the same lifting force. If that is not the case, then how does this work? In what way do I need more energy at greater depths to get back up again using this method of heating water? Or, and this seems more and more likely, have I completely misunderstood something?
     
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