<p>First, let's explain what compressibility is. <a href="http://en.wikipedia.org/wiki/Compressibility" rel="nofollow noreferrer">Compressibility</a> is defined as a measure of the relative volume change of a parcel of fluid as a response to a pressure change. </p>

<p>When I calculate the compressibility of seawater using Matlab and the <a href="http://www.marine.csiro.au/datacentre/processing.htm" rel="nofollow noreferrer">seawater package</a> (equivalent to <a href="http://agris.fao.org/agris-search/search.do?recordID=AV20120150138" rel="nofollow noreferrer">Fofonoff &amp; Millard, 1983</a>), I obtained that the compressibility increases at cold temperatures for salty, brackish, and fresh water. In fact, water has a minimum compressibility at 46.5°C (<a href="http://dx.doi.org/10.1063%2F1.1679903" rel="nofollow noreferrer">Fine &amp; Millero, 1973</a>). As pressure increases the compressibility decreases for any of the salinities considered. 
<img src="https://i.sstatic.net/DsUB4.png" alt="Compressibility for a range of pressures and temperatures"></p>

<p>As can be seen in the figure the compressibility is maximum at low temperatures for any salinity (not just seawater) and pressure. So in general, the compressibility of water is maximum at low temperatures due to the internal structure of water. The inverse relationship with temperature seems well accepted (<a href="http://dx.doi.org/10.1063%2F1.1679903" rel="nofollow noreferrer">Fine &amp; Millero, 1973</a>) and has a direct relation with other properties like the speed of sound.</p>

<p>In a typical liquid, the compressibility at low temperatures is reduced as the structure becomes more compact. In water, there is a change at low temperatures toward more open-structure <a href="http://www1.lsbu.ac.uk/water/clusters.html" rel="nofollow noreferrer">clusters</a> (expanded icosahedral water cluster) versus denser clusters (collapsed icosahedral water cluster). As the water structure at lower temperatures is more open, the capacity for it to be compressed increases. </p>

<p>As cold liquid water is heated it shrinks, it becomes less easy to compress, the speed of sound within it increases, gases become less soluble and it is easier to heat.</p>

<p>The compressibility above is calculated using the formula in the figure (same as in the <a href="http://en.wikipedia.org/wiki/Compressibility" rel="nofollow noreferrer">wiki article</a>) and I have included the code to reproduce the results:</p>

<pre><code>T=-2:1:30;
P=0:10:1000;
S=35;
for i=1:length(T)
    for j=1:length(P)
        dens(i,j)=sw_dens(S,T(i),P(j));
        dens15(i,j)=sw_dens(15,T(i),P(j));
        dens0(i,j)=sw_dens(0,T(i),P(j));
    end
end
spvo=1./dens;
spvo15=1./dens15;
spvo0=1./dens0;    
for i=1:length(T)
    for j=1:length(P)-1
%        Ev2(i,j)=-(1./spvo(i,j))*(spvo(i,j+1)-spvo(i,j))./(P(j+1)-P(j));
        Ev35(i,j)=(1-spvo(i,j+1)/spvo(i,j))/(P(j+1)-P(j));
        Ev15(i,j)=(1-spvo15(i,j+1)/spvo15(i,j))/(P(j+1)-P(j));
        Ev0(i,j)=(1-spvo0(i,j+1)/spvo0(i,j))/(P(j+1)-P(j));
    end
end
figure(1);clf
for j=[1,20,100]
    line(T,Ev35(:,j),'Color','k','LineWidth',2);
    line(T,Ev15(:,j),'Color','b','LineWidth',2);
    line(T,Ev0(:,j),'Color','r','LineWidth',2);axtt
end
text(T(20),Ev35(20,1),['P=',num2str(P(2)),'dbar'])
text(T(20),Ev35(20,20)*.99,['P=',num2str(P(21)),'dbar'])
text(T(20),Ev35(20,100)*.98,['P=',num2str(P(101)),'dbar'])
text(T(15),Ev0(15,1),['P=',num2str(P(2)),'dbar'],'Color','r')
text(T(15),Ev0(15,20)*.99,['P=',num2str(P(21)),'dbar'],'Color','r')
text(T(15),Ev0(15,100)*.99,['P=',num2str(P(101)),'dbar'],'Color','r')
xlabel('Temperature (degC) ')
ylabel('Compressibility (1/dbar) ')
legend('35 PSU','15 PSU','0 PSU')    
text(7,5e-6,'$c_w=-{1\over V}({dV\over dp})$','Interpreter','latex','FontSize',20,'FontWeight','bold')
</code></pre>

CC BY-SA 3.0
2014-10-03T16:55:58.720Z
I agree with your math and coding, but what is the actual physical reason why water is more compressible at lower temperatures? You said "So in general, the compressibility of water is maximum at low temperatures due to the internal structure of water." What is it about the internal structure of water that changes with temperature that affects compressibility?
pocketlizard
CC BY-SA 3.0
2014-10-03T17:33:41.633Z
I hope the modified answer better addresses your concerns
arkaia
CC BY-SA 3.0
2014-10-03T17:42:40.683Z
Answered my question perfectly!
pocketlizard
CC BY-SA 3.0
2014-10-04T03:12:53.260Z
+1 It would be great if you could include the actual code rather than the screen capture.
milancurcic
CC BY-SA 3.0
2014-10-04T18:46:31.667Z
Do you mean copy and paste the code? I don't know if there is anyway to upload a file that is not a figure
arkaia
CC BY-SA 3.0
2014-10-06T17:30:45.610Z
@aretxabaleta When editting the answer, use the preformatted text (Ctrl-k) to insert monospace code.
milancurcic
CC BY-SA 3.0
2014-10-03T16:45:21.223Z
2014-10-06T17:40:15.997Z
2014-10-06T17:40:15.997Z
arkaia
<p>I know compressibility is related to the pressure and temperature of the water parcel, but what is the physical/molecular reason as to why colder water is more compressible?</p>

CC BY-SA 3.0
2014-09-26T00:07:40.187Z
It seems counter-intuitive to me that colder water is more compressible (more dense, sure, but that's different). Do you have a link to an example of this claim?
naught101
CC BY-SA 3.0
2014-09-26T00:39:09.940Z
Actually the computations were part of a homework problem. I asked the professor why cold water was more compressible after and he said he wasn't sure about the specifics. The homework involved plugging in values into an equation of state calculator and determining various things about the sensitivity of density to pressure. Set salinity to 35ppt, look at the density at pressures of 0dbar and 1000dbar, and try different temperatures using this online calculator: http://www.es.flinders.edu.au/~mattom/Utilities/density.html
You'll find that colder temperatures have higher compressibilities!
pocketlizard
<ocean><oceanography><temperature>
Why is colder seawater more compressible?
pocketlizard
# Why is colder seawater more compressible?

(Asked by: username_0 on 2014-09-24)

I know compressibility is related to the pressure and temperature of the water parcel, but what is the physical/molecular reason as to why colder water is more compressible?

**Tags:** ocean, oceanography, temperature

> **Comments:**
> **username_1**: It seems counter-intuitive to me that colder water is more compressible (more dense, sure, but that's different). Do you have a link to an example of this claim?  
> **username_0**: Actually the computations were part of a homework problem. I asked the professor why cold water was more compressible after and he said he wasn't sure about the specifics. The homework involved plugging in values into an equation of state calculator and determining various things about the sensitivity of density to pressure. Set salinity to 35ppt, look at the density at pressures of 0dbar and 1000dbar, and try different temperatures using this online calculator: http://www.es.flinders.edu.au/~mattom/Utilities/density.html You'll find that colder temperatures have higher compressibilities!  

---

## 1 answers

### Answer by username_2 on 2014-10-03. Score: 8 | Accepted answer

First, let's explain what compressibility is. [Compressibility](http://en.wikipedia.org/wiki/Compressibility) is defined as a measure of the relative volume change of a parcel of fluid as a response to a pressure change.

When I calculate the compressibility of seawater using Matlab and the [seawater package](http://www.marine.csiro.au/datacentre/processing.htm) (equivalent to [Fofonoff & Millard, 1983](http://agris.fao.org/agris-search/search.do?recordID=AV20120150138)), I obtained that the compressibility increases at cold temperatures for salty, brackish, and fresh water. In fact, water has a minimum compressibility at 46.5°C ([Fine & Millero, 1973](http://dx.doi.org/10.1063%2F1.1679903)). As pressure increases the compressibility decreases for any of the salinities considered.
![Compressibility for a range of pressures and temperatures](https://i.sstatic.net/DsUB4.png)

As can be seen in the figure the compressibility is maximum at low temperatures for any salinity (not just seawater) and pressure. So in general, the compressibility of water is maximum at low temperatures due to the internal structure of water. The inverse relationship with temperature seems well accepted ([Fine & Millero, 1973](http://dx.doi.org/10.1063%2F1.1679903)) and has a direct relation with other properties like the speed of sound.

In a typical liquid, the compressibility at low temperatures is reduced as the structure becomes more compact. In water, there is a change at low temperatures toward more open-structure [clusters](http://www1.lsbu.ac.uk/water/clusters.html) (expanded icosahedral water cluster) versus denser clusters (collapsed icosahedral water cluster). As the water structure at lower temperatures is more open, the capacity for it to be compressed increases.

As cold liquid water is heated it shrinks, it becomes less easy to compress, the speed of sound within it increases, gases become less soluble and it is easier to heat.

The compressibility above is calculated using the formula in the figure (same as in the [wiki article](http://en.wikipedia.org/wiki/Compressibility)) and I have included the code to reproduce the results:

```
T=-2:1:30;
P=0:10:1000;
S=35;
for i=1:length(T)
    for j=1:length(P)
        dens(i,j)=sw_dens(S,T(i),P(j));
        dens15(i,j)=sw_dens(15,T(i),P(j));
        dens0(i,j)=sw_dens(0,T(i),P(j));
    end
end
spvo=1./dens;
spvo15=1./dens15;
spvo0=1./dens0;    
for i=1:length(T)
    for j=1:length(P)-1
%        Ev2(i,j)=-(1./spvo(i,j))*(spvo(i,j+1)-spvo(i,j))./(P(j+1)-P(j));
        Ev35(i,j)=(1-spvo(i,j+1)/spvo(i,j))/(P(j+1)-P(j));
        Ev15(i,j)=(1-spvo15(i,j+1)/spvo15(i,j))/(P(j+1)-P(j));
        Ev0(i,j)=(1-spvo0(i,j+1)/spvo0(i,j))/(P(j+1)-P(j));
    end
end
figure(1);clf
for j=[1,20,100]
    line(T,Ev35(:,j),'Color','k','LineWidth',2);
    line(T,Ev15(:,j),'Color','b','LineWidth',2);
    line(T,Ev0(:,j),'Color','r','LineWidth',2);axtt
end
text(T(20),Ev35(20,1),['P=',num2str(P(2)),'dbar'])
text(T(20),Ev35(20,20)*.99,['P=',num2str(P(21)),'dbar'])
text(T(20),Ev35(20,100)*.98,['P=',num2str(P(101)),'dbar'])
text(T(15),Ev0(15,1),['P=',num2str(P(2)),'dbar'],'Color','r')
text(T(15),Ev0(15,20)*.99,['P=',num2str(P(21)),'dbar'],'Color','r')
text(T(15),Ev0(15,100)*.99,['P=',num2str(P(101)),'dbar'],'Color','r')
xlabel('Temperature (degC) ')
ylabel('Compressibility (1/dbar) ')
legend('35 PSU','15 PSU','0 PSU')    
text(7,5e-6,'$c_w=-{1\over V}({dV\over dp})$','Interpreter','latex','FontSize',20,'FontWeight','bold')

```

> **Comments:**
> **username_0**: I agree with your math and coding, but what is the actual physical reason why water is more compressible at lower temperatures? You said "So in general, the compressibility of water is maximum at low temperatures due to the internal structure of water." What is it about the internal structure of water that changes with temperature that affects compressibility?  
> **username_2**: I hope the modified answer better addresses your concerns  
> **username_0**: Answered my question perfectly!  
> **username_3**: +1 It would be great if you could include the actual code rather than the screen capture.  
> **username_2**: Do you mean copy and paste the code? I don't know if there is anyway to upload a file that is not a figure  
> **username_3**: @aretxabaleta When editting the answer, use the preformatted text (Ctrl-k) to insert monospace code.  

---

