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Mass stays the same:volume-density weight?

  1. Sep 30, 2004 #1
    Hi ya'll,
    We debated in class...Dr Mir had clearly stated during his lecture that the mass, of water won't change even if the temp does. He said "yes the volume will expand and contract, with temp change, but the MASS won't" Anyway he assigned this question: 'What is the difference in weight of 50 gal of water at 39F and at 77F?'

    Well we've been doing a lot of interpolation this week finding the density of water at diff temps, so it was automatic for most of us to start messing with the convertion to celcius then to find the density at each temp using the table, and interpolating....some of us began to wonder if we even needed to do anything.

    Is it safe to say that since: wt=mg, and if the m has not changed the wt too remains the same? Then we debated over gamma=wt/volume. But density and volume directly relate to eachother in an oppisite fashion with temp change would they still need to be concidered or can we ignore the density and volume...well ignore all the values the question states? Are we completely over thinking a trick question? Or were we on the right track to begin with?

    Thanks vm,
  2. jcsd
  3. Sep 30, 2004 #2
    Well what's that? Sorry I'm only a second yr student, and have had just basic physics. This is for engineering (hydraulics) I'm sure we'll get to that, but havn't yet. is e=energy? LOL and is c celcius? NO laughing please lol
  4. Sep 30, 2004 #3
    Or would you just say the weight stays the same? Knowing what little we have learned, do you think that's the answer?
    btw thanks ; )
  5. Sep 30, 2004 #4

    Claude Bile

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    You hit the nail on the head in your initial post, if the mass is invariant with temperature, then the weight will also be invariant because weight is just mass times the acceleration due to gravity. You can ignore density and volume in this instance.

  6. Sep 30, 2004 #5


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    The volume, however, isn't invariant with temperature. I'm not sure why you think you can ignore volume, when the prof. said to compare the weight of 40 gallons of water at two temperatures. I would interpret this statement as holding the volume constant. (Assuming we've been given an accurate quote on this key remark). Holding the volume constant means the mass must vary.
  7. Sep 30, 2004 #6
    Volume is everything...

    Yep, you are right, this is a trick question in the sense the Dr. is holding volume constant, so you were thinking on the right track but were not seeing the clue element in the question... "Volume" is constant.
  8. Oct 1, 2004 #7
    Well he only 'mentioned' the fact that mass never changes (just the volume) He told us that about 45 minutes before he assigned the questions and left. (we have lab time he uses to make us work on concepts)
    I think it was a suttle hint knowing what he was going to assign.

    Anyway we all agreed in class that the volume could/would change, but some of us were wondering just exactly they were doing with the density and the volume if it had nothing to do with the weight of the water. They argued that it did. Some of them seem to think that the water would have a different weight.

    The assignment question that I posted earlier is word for word exactly how it reads.

    So if wt=mg and m stays the same no matter what the volume or density does (I'm assuming about the density) there's no reason to find density of these temps, or even to convert our F degrees to C degrees. Right?

    Thanks tons guys! I'm flippen never right! Sounds like maybe I was this time eh?
  9. Oct 1, 2004 #8
    'What is the difference in weight of 50 gal of water at 39F and at 77F?'

    Well, you need to consider the densities. Here's Why.

    Take 50 Gallons of water at 39F (sample A). It has a certain mass. ( density at 39F * 50 gallons ).

    Now, take 50 Gallons of water at 77F. It will have a different mass. Because at 77F, Sample A will increase in volume due to heating. So, you'll have remove water from it to bring it back to 50 Gallons. So, you are decreasing its mass. It means that

    mass(50 Gallon at 39F) > mass(50 Gallon at 77F)

    and the difference is

    ( density at 39F * 50 gallons ) - (density at 77F * 50 Gallons )

    Multiply by g ( invariant with temp!!! ) and get the answer.

  10. Oct 1, 2004 #9
    Aww man now I'm confused. Yeah that's what our debate was all about. They said what equals mass? and considering that made me wonder. But proof? Sure I can do the math and get the difference, but am I gonna be right? Can I proove it to myself with the results?
    Thanks again,
  11. Oct 1, 2004 #10
    Well if you want an easy way to understand it maybe this well help. Start with the 50g barrel filled with water @ 77F. Now if we cool this water to 39F we will see that we don't have 50 gallons anymore. As the water cools it loses energy which lets the molecules get closer together. So now we have at add more water to compensate for the loss in volume. That will result in an increase in weight and mass.
  12. Oct 1, 2004 #11

    Doc Al

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    volume kept constant, not mass

    It is true that weight = mg, but you are not comparing the same mass at different temperatures, you are comparing the same volume. Since the density depends on temperature, the same volume will have a different mass at each temperature---and thus a different weight.

    I suspect the difference in weight will be small. :smile:
  13. Oct 1, 2004 #12


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    Actually, this may just come down to a wording issue with the question. What exactly does the question say?

    If it says you're taking 50 gal of water at one temperature and changing that container's temperature without regard to what that does to its volume, you'll end up with a different volume at the same mass (weight).

    If it says you're taking 50 gal at one temperature and still 50 gal at another, then you'll end up with the same volume and a different mass (weight).
  14. Oct 1, 2004 #13

    Sounds like the number 50g has to remain constant to me.
  15. Oct 1, 2004 #14
    Here's the question exactly how it reads in the handout:
    'What is the difference in weight of 50 gal of water at 39F and at 77F?'
  16. Oct 2, 2004 #15
    the question can be answered either way, depending on how you run the experiment. The question isn't worded clearly enough so that the required experiment is unambiguous.

    The first way to run the experiment:
    Take 50 gallons of water at 39F and measure it's weight. Heat that same water until it's temperature is 77F and weigh it again. The weight has not changed.

    The second way to run the experiment:
    Take water at 39F and measure off 50 gallons of it. Weigh it and record the results. Throw that water out, and from a resevoir of water at 77F measure out another 50 gallons. Weigh that and you'll get a different result (as given by factoring in the different densities of water at various temperatures).

    I strongly suspect your teacher meant for you to run experiment two.

    For more advanced information, water is a very complicated liquid, and unlike most other sbstances it expands as it gets gets colder. The curve of density over termperature is not a straight line, nor even a simple curve, and there might be two specific temperatures where the density is equal. I believe water is least dense a few degrees above freezing, which might be why 39F was chosen.
  17. Oct 3, 2004 #16

    I disagree that the question is worded as to imply that both experiments are valid. For one thing they don't tell you what the temperature of the water is to begin with (which we would need to know to do the first experiment you suggest).
    Thinking about this some more I guess it wouldn't matter as the answer will always be equal weight. However I still think you have to work with 50g of water each time and not a 50g container where the water level changes.

    Also you say that water gets less dense as it get cooler. Is this true? Maybe you can explain this in more detail?
    Last edited: Oct 3, 2004
  18. Oct 3, 2004 #17


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    Water does NOT expand as it gets colder! As it freezes it suddenly expands but as long as it is still more that about 3 degrees celcius, it contracts like everything else.

    What has happened here is that this poor student has run into a teacher who assumes the students have actually LEARNED what they were taught in previous years: that density is mass divided by volume. The original poster told us that they had a table giving the density at different temperatures and that they were given the volume. Since density= mass/volume, mass= density*volume and you can find the weight from that.
  19. Oct 3, 2004 #18
    This is what I thought too. Isn't the reason that it takes up more space when frozen because the molecules, having less energy, are drawn into bonds that align them differently?
  20. Oct 3, 2004 #19


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    Yeah, I think you're right - I didn't realize that was it for the question didn't see the quotes.
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