(49g) (50g) Water boiling temperature = f(altitude/pressure + temp); Water density

[Gil]

HP49-50G
New version 3b
Used the SI units.
Tried to have in the several programs the same names.
Added boiling temperature of water = f(pressure).
The latter is derived from boiling temperature of water = g(altitude).
So that g(altitude) gives a temperature, a pressure p_alt and boil.temp1.
Now f(pressure p_alt) will give a boil.temp2 = boil.temp1.

Unfortunately, I could not get these formulae to give the same boiling temperature when you have as argument both altitude and local temperature.

Changing the the constants did not help.

Example 1
MT—>(2000 m, 2 degrees C) = 93.059 degrees C
But M—>(2000) = 93.215 degrees C

Example 2
MT—>(5077 m, -18 degrees C) = 82.641 degrees C
But M—>(5077) = 81.595 degrees C

Question
Is there a way to have both approches to be compatible with the final results ?

Thanks in advance for your insight.

'MT\->BOIL.H\178O'
\<< "2 Arg:
. 
alt
 [m]
. 
temp.air
 [\^oC at alt]
" DROP 273.15 + 100 273.15 + 9.80665 28.9644 18.015257 2256400 \-> h Tair T0 g \Gmair \GmH\178O q12.\GDHvap
\<< "At " h + "m/" + Tair 273.15 - + "\^oC" + 'T0*Tair*q12.\GDHvap*\GmH\178O/(q12.\GDHvap*\GmH\178O*Tair+\Gmair*g*h*T0)' \->NUM 273.15 - "\^oC H\178O boiling" \->TAG
\>>
\>>

[/b]
'P\->BOIL.H\178O'
\<< "1 Arg only:

P
 [Pressure, Pa]
" DROP 101325 .0289644 9.80665 .0065 8.31446261815 40650 "Or 40650" DROP \-> P P0 M g a R \GDHvap
\<< "At " P + "Pa" + '(1/(100+273.15)-R*LN(P/P0)/\GDHvap)^-1-273.15' \->NUM "\^oC H\178O boiling" \->TAG
\>>
\>>

[b]'M\->BOIL.H\178O'
\<< "1 Arg only:

alt
 [m]
" DROP .0289644 9.80665 .0065 8.31446261815 40650 "Or 40660" DROP \-> alt M g a R \GDHvap
\<< "At " alt + "m:" + 15 a alt * - 1 RND "\^oC / " + '101325*(1-a*alt/(15+273.15))^(M*g/(R*a))' \->NUM 101325 \-> P P0
\<< P 0 RND + "Pa" + '(1/(100+273.15)-R*LN(P/P0)/\GDHvap)^-1-273.15' \->NUM "\^oC H\178O boiling" \->TAG
\>>
\>>
\>>



'\->DENS.H\178O'
\<< "3 Arg:
\[] temp [\^oC]
\[] pressure [PA]
\[] 1/0
[1 for tap water]
[0 for pure water]

According to Tanaka
0 < t.C < 40 \^oC
" DROP ROT DTAG ROT DTAG ROT \-> t.C p.PA tap.wat
\<< t.C "t.C" \->TAG p.PA "p.PA" \->TAG -3.983035 301.797 522528.9 69.34881 tap.wat 1 == 999.972 999.97495 IFTE 5.074E-10 -3.26E-12 4.16E-15 \-> a1 a2 a3 a4 a5 c1 c2 c3 'a5*(1.-(t.C+a1)^2.*(t.C+a2)/(a3*(t.C+a4)))*(1.+(c1+c2*t.C+c3*t.C^2.)*(p.PA-101325.))' EVAL tap.wat 1 ==
IF
THEN "Tap H\178O"
ELSE "Pure H\178O"
END ", w/o air" + \->TAG DUP '-.004612+.000106*t.C' + EVAL tap.wat 1 == "Tap H\178O" "Pure H\178O" IFTE ", 100% air" + \->TAG
\>>
\>>

Regards,
Gil