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Homework Help: Water expansion and pressure

  1. Sep 13, 2008 #1
    hey.. i have a question that i am not 100% sure on...

    suppose a beaker of water was heated from 10 degrees to 90 degrees. does the pressure at the bottom of the beaker increase, decrease, or stay the same?

    any help here would be greatly appreciated!!

  2. jcsd
  3. Sep 13, 2008 #2
    To a good approximation, it stays the same if the top of the beaker is open and the water is allowed to expand. If the beaker is closed and the water volume is kept constant then the pressure will increase.

    To see this, you should write down the condition for mechanical equilibrium: The water in the beaker is not accelerating, so the total force exerted on the water must be zero. But gravity exerts a force on it, and there are presure forces acting on the water. The bottom of the beaker exerts an upward force on the water equal to the pressure times the area. And the air on top of the beaker exerts a downward force on the beker equal to atmospheric pressure times area (if the two areas of the top and botom are not the same, then that means that the sides of the beaker are not oriented vertically and the pressure forces acting there then have a vertical component as well, the net effect is then that only the pressure difference of top and bottom matters)

    If the temperature of the wate is increased, the water expands, but the mass stays the ame (ignoring relativistic corrections). So, the force of gravity stays the same. There is then a very slight decrease in pressure due to the fact that the water level has now risen a bit and the atmospheric pressure at that slightly higher level is slightly less (equivalently, you can also say that the buoyancy force has increased a bit due to the slightly larger volume).
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