 |
| Fig. 1 |
In this post the blanks are filled in with the relevant temperatures that take the perplexing reality out of thermal expansion and contraction.
The graphics I have used in this series show that it is no longer a mystery.
It is a scientific fact that the maximum density temperature is also a border line that activates an eye catching transition in seawater.
But more than that the not-often-discussed border line is instructive for those who would try to figure out the dynamics of temperature change induced volume change (thermal expansion and contraction) in seawater they are studying.
To make it easier to comprehend two HTML tables are provided below to show the mysterious event in two temperature paths; one from warm to cold and the other from cold to warm.
The only change in the relevant operative variables is the in situ temperature (T) which begins at +19 deg. C and ends at -10 deg. C in one experiment (Fig. 1), but is reversed (begins at -10 deg. C and ends at +19 deg. C) in the other experiment (Fig. 2).
Here are the two HTML tables:
Table 1
The HTML table below details the results of a C++ test program which calculates volume and density as the Conservative Temperature (CT) changes. The constant values are: depth (30m), lat (30 N), lon (10 W), SP (salinity 32). T (in situ temperature) varies. The bold line is maximum density.
| Row | CT | T | density | volume |
| 1 | 19.0767 | 19 | 1022.87 | 9.77644 x 10-4 |
| 2 | 18.0723 | 18 | 1023.11 | 9.77408 x 10-4 |
| 3 | 17.068 | 17 | 1023.35 | 9.77181 x 10-4 |
| 4 | 16.0638 | 16 | 1023.58 | 9.76963 x 10-4 |
| 5 | 15.0597 | 15 | 1023.8 | 9.76754 x 10-4 |
| 6 | 14.0558 | 14 | 1024.01 | 9.76554 x 10-4 |
| 7 | 13.052 | 13 | 1024.21 | 9.76363 x 10-4 |
| 8 | 12.0484 | 12 | 1024.4 | 9.76181 x 10-4 |
| 9 | 11.0448 | 11 | 1024.58 | 9.76009 x 10-4 |
| 10 | 10.0414 | 10 | 1024.75 | 9.75847 x 10-4 |
| 11 | 9.03806 | 9 | 1024.91 | 9.75695 x 10-4 |
| 12 | 8.03483 | 8 | 1025.06 | 9.75554 x 10-4 |
| 13 | 7.0317 | 7 | 1025.2 | 9.75422 x 10-4 |
| 14 | 6.02866 | 6 | 1025.32 | 9.75302 x 10-4 |
| 15 | 5.02568 | 5 | 1025.44 | 9.75192 x 10-4 |
| 16 | 4.02276 | 4 | 1025.54 | 9.75093 x 10-4 |
| 17 | 3.01988 | 3 | 1025.63 | 9.75007 x 10-4 |
| 18 | 2.01702 | 2 | 1025.71 | 9.74931 x 10-4 |
| 19 | 1.01416 | 1 | 1025.78 | 9.74869 x 10-4 |
| 20 | 0.0112749 | 0 | 1025.83 | 9.74818 x 10-4 |
| 21 | -0.991654 | -1 | 1025.87 | 9.74781 x 10-4 |
| 22 | -1.99466 | -2 | 1025.9 | 9.74757 x 10-4 |
| 23 | -2.99777 | -3 | 1025.91 | 9.74747 x 10-4 |
| 24 | -4.00103 | -4 | 1025.9 | 9.74751 x 10-4 |
| 25 | -5.00446 | -5 | 1025.88 | 9.7477 x 10-4 |
| 26 | -6.00812 | -6 | 1025.85 | 9.74804 x 10-4 |
| 27 | -7.01203 | -7 | 1025.79 | 9.74855 x 10-4 |
| 28 | -8.01627 | -8 | 1025.72 | 9.74921 x 10-4 |
| 29 | -9.02086 | -9 | 1025.64 | 9.75005 x 10-4 |
| 30 | -10.0259 | -10 | 1025.53 | 9.75107 x 10-4 |
 |
| Fig. 2 |
Table 2
The HTML table below details the results of a C++ test program which calculates volume and density as the Conservative Temperature (CT) changes. The constant values are: depth (30m), lat (30 N), lon (10 W), SP (salinity 32). T (in situ temperature) varies. The bold line is maximum density.
| Row | CT | T | density | volume |
| 1 | -10.0259 | -10 | 1025.53 | 9.75107 x 10-4 |
| 2 | -9.02086 | -9 | 1025.64 | 9.75005 x 10-4 |
| 3 | -8.01627 | -8 | 1025.72 | 9.74921 x 10-4 |
| 4 | -7.01203 | -7 | 1025.79 | 9.74855 x 10-4 |
| 5 | -6.00812 | -6 | 1025.85 | 9.74804 x 10-4 |
| 6 | -5.00446 | -5 | 1025.88 | 9.7477 x 10-4 |
| 7 | -4.00103 | -4 | 1025.9 | 9.74751 x 10-4 |
| 8 | -2.99777 | -3 | 1025.91 | 9.74747 x 10-4 |
| 9 | -1.99466 | -2 | 1025.9 | 9.74757 x 10-4 |
| 10 | -0.991654 | -1 | 1025.87 | 9.74781 x 10-4 |
| 11 | 0.0112749 | 0 | 1025.83 | 9.74818 x 10-4 |
| 12 | 1.01416 | 1 | 1025.78 | 9.74869 x 10-4 |
| 13 | 2.01702 | 2 | 1025.71 | 9.74931 x 10-4 |
| 14 | 3.01988 | 3 | 1025.63 | 9.75007 x 10-4 |
| 15 | 4.02276 | 4 | 1025.54 | 9.75093 x 10-4 |
| 16 | 5.02568 | 5 | 1025.44 | 9.75192 x 10-4 |
| 17 | 6.02866 | 6 | 1025.32 | 9.75302 x 10-4 |
| 18 | 7.0317 | 7 | 1025.2 | 9.75422 x 10-4 |
| 19 | 8.03483 | 8 | 1025.06 | 9.75554 x 10-4 |
| 20 | 9.03806 | 9 | 1024.91 | 9.75695 x 10-4 |
| 21 | 10.0414 | 10 | 1024.75 | 9.75847 x 10-4 |
| 22 | 11.0448 | 11 | 1024.58 | 9.76009 x 10-4 |
| 23 | 12.0484 | 12 | 1024.4 | 9.76181 x 10-4 |
| 24 | 13.052 | 13 | 1024.21 | 9.76363 x 10-4 |
| 25 | 14.0558 | 14 | 1024.01 | 9.76554 x 10-4 |
| 26 | 15.0597 | 15 | 1023.8 | 9.76754 x 10-4 |
| 27 | 16.0638 | 16 | 1023.58 | 9.76963 x 10-4 |
| 28 | 17.068 | 17 | 1023.35 | 9.77181 x 10-4 |
| 29 | 18.0723 | 18 | 1023.11 | 9.77408 x 10-4 |
| 30 | 19.0767 | 19 | 1022.87 | 9.77644 x 10-4 |
The numbers in the HTML tables are generated by the free TEOS-10 C++ software library.
I only furnish the constant values and the beginning "T" (in situ temperature) which is iterated by the C++ program that is using the TEOS-10 library functionality.
In other words the event horizon for the maximum density temperature is a result or discovery of the Gibbs function "built into" the TEOS-10 library.
As has been indicated previously on Dredd Blog, Gibbs was the correct choice to consider when TEOS-10 was developed:
'Albert Einstein called him 'the greatest mind in American history.' Gibbs’s studies of thermodynamics and discoveries in statistical mechanics paved the way for many of Einstein’s later discoveries.'
'TEOS-10 is based on a Gibbs function formulation from which all thermodynamic properties of seawater (density, enthalpy, entropy sound speed, etc.) can be derived in a thermodynamically consistent manner.'
(In Search Of Ocean Heat - 5). Thus, the Dredd Blog assertion that whether seawater will increase in volume (thermal expansion) or decrease in volume (thermal contraction) depends on the temperature of the seawater at the time the temperature changes.
On to the next subject.
The previous post in this series is here.
Ode To The Warming Commentariat:
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