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- Thread starter antonima
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I like Serena

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Welcome to PF, antonima!

Let's see.

I think we're talking about a release of 0.36 MJ in energy, of which part will be kinetic energy.

The volume that comes out is 18 L (assuming no change in temperature).

We would need the compressibility of water for this:

[tex]\beta = -{1 \over V} {\partial V \over \partial P}[/tex]

The change in volume (the water spewing out) is:

[tex]\Delta V = -\beta V \Delta P[/tex]

The energy that is released by the expansion to standard pressure is:

[tex]W = \int PdV = \int P \cdot -\beta V dP = -{1 \over 2} \beta V P^2 |_{P_1}^{P_2}[/tex]

At T=25 °C, we have:

β = 4.6 x 10^{-10} m^{2}/N

V = 0.982 m^{3}

P1 = 40 MPa

P2 = 100 kPa

This means W=0.36 MJ and ΔV=0.018 m^{3}

Let's see.

I think we're talking about a release of 0.36 MJ in energy, of which part will be kinetic energy.

The volume that comes out is 18 L (assuming no change in temperature).

We would need the compressibility of water for this:

[tex]\beta = -{1 \over V} {\partial V \over \partial P}[/tex]

The change in volume (the water spewing out) is:

[tex]\Delta V = -\beta V \Delta P[/tex]

The energy that is released by the expansion to standard pressure is:

[tex]W = \int PdV = \int P \cdot -\beta V dP = -{1 \over 2} \beta V P^2 |_{P_1}^{P_2}[/tex]

At T=25 °C, we have:

β = 4.6 x 10

V = 0.982 m

P1 = 40 MPa

P2 = 100 kPa

This means W=0.36 MJ and ΔV=0.018 m

Last edited:

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.36 MJ. I like that!

See, I have been learning about oceanography and how water compresses in the deeper parts of the ocean. At 4 km in depth, or 40 MPa water is compressed by 1.8%. I was thinking that maybe it could be sealed in a container which would keep it pressurized and raised to extract energy from the deep ocean.

Funny enough, to raise this water would at the very minimum require

(buoyancy at top - buoyancy at bottom * 1/2) * gravity * height

(basically using mass*gravity*height)

(18*1/2*4000*9.81) = .353 MJ !!

This is not counting friction, drag, or the energy required to raise the container which carries the water. It seems that the thermodynamics of this all works out so no energy is created, and energy cannot be continuously extracted from the ocean.

Your equation also agrees with the the pressure analysis. Pressure is just Newtons/meter squared. If water were to be a cube just short of 1 meter squared, it would expand ~1.8 cm to one side.

40,000,000 pascals *.5*.018 m = .36 MJ !

using

Force*distance

- #4

I like Serena

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Nice that it fits! :)

And pity that we can't extract energy this way. :(

And pity that we can't extract energy this way. :(

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