Physics help? CRITICAL THINKING?

Question

What is compressibility of water at critical point?
Why?

tinkertail:

What is specific heat of water at 50C? According to your logic it is zero, since once you begin heating water, it is no longer at point 50C.

Answer 1

I think the compressibility of water (and any other substance) at the critical point is infinite.

Consider the critical as limiting case of the vaporization process. At subcritical vaporization the average density (mixture of liquid and vapor) changes along a line of constant pressure and temperature. That means for the phase transition volume changes at constant pressure.
the following pVT diagram illustrates this:
http://www.taftan.com/thermodynamics/PVT.GIF

At the critical point the density difference between vapor and liquid vanishes. But as limiting case of phase transition you have volume change at constant pressure.
Therefore the critical isotherm, which is in contradiction to the subcritcal isotherms a smooth curve, has a saddle point at the critical point. Hence:
(∂p/∂V)tc = 0

On the other hand isothermal compressibility is defined by:
κ = - (1/V) · (∂V/∂p)t

So if you try to calculate the critical compressibility you need to divide by zero:
κ_c = -(1/V_c) · (∂V/∂p)t_c) = -(1/V_c) / (∂p/∂V)t_c = -(1/V_c) / 0 = ∞

Answer 2

The compressibility of water is dependent on pressure; see the reference. Liquid water IS compressible, but less so than, say, steel. I'm also a little confused as to why you're asking about the compressibility of water at the critical point, as the critical point is where the liquid phase can no longer exist. Did you mean triple point?

Answer 3

It may depend on how pedantic one is with the definition of critical "point" one could make the case that as the critical point the compressibility is zero because if one compressed the water it would no longer be at the critical point.

Answer 4

water in its liquid form, is, like most liquids
incompressible.
so its compressibility would be 0 i guess.
Most liquids are incompressible, just try to compress a sealed can of soft drink.