Water Vapour Pressure

Programs for HP-41

Water Vapour Pressure

Postby mike-stgt » Thu Mar 30, 2023 9:34 pm

Highly likely nobody needs this on an HP41 or similar calculator any more. Honestly, to care anyway about such ancient stuff is complete waste of time -- it's nothing but sheer hobby.

This said, if you are still reading here, you probably know about the pros and cons of approximations like the formulas of Rankine, Antoine, August and Magnus. Digging through old rubbish -- ah, sorry, through Warren's archive -- I stumbled over one of them in "Prisma", Nr. 1, Jan. 1982, p. 7f.
Code: Select all
 28•LBL 00
ENTER^  ENTER^  7,5  *
X<>Y  238  +  /  10^X
6,107  *  RTN
to compute from °C the vapour pressure of water in mbar. A simple adjustment of the program saved one byte, a little change of the coefficients added two bytes, but the difference to observed values is now in the range from 0..100 °C below 0.3% instead of >0.8% before.
Code: Select all
 01•LBL "PSN"
7,463  X<>Y  ST* Y  236
+  /  10^X  6107 E-6  *
END
In contrast to the original program this one returns the result in bar.
Here a graph of the relative errors:
relerr of ps.jpg
Relative error of approximations of water vapour pressure vs a polynomial formula

The 'outlier' in black corresponds to the original program, blue my improvement, green what I used to use so far in my programs, and the red-dotted line the table in Cerbe-Hoffmann: "Wärmelehre", Westermann-Verlag (1968), all compared against this formula found here.
As I told you before, nothing special, simply hobby.
mike-stgt
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