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

[Gil]

HP49-50G :
Water boiling temperature
= f(altitude + temp.air )

Water density
(already published, but now included in
the directory WATER)

Water boiling temperature
= f(altitude + temp.air )

Here two programs are given:
- one when you have the altitude [in m] AND the air temperature at that altitude [in degrees C] as inputs ;
- another, using a different formulae, to be used only with altitude [in m] as single argument (without the air temperature).

Code 1
'MT—>BOIL.H²O'
\<< "2 Arg:
. alt [m]
. temp.air [\^oC at alt]
" DROP 273.15 + 100. 273.15 + 9.80665 28.9647 18.0153 2257000. \-> h Tair T0 g \Gmair \GmH\178O q12
\<< "At " h + "m/" + Tair 273.15 - + "\^oC" + 'T0*Tair*q12*\GmH\178O/(q12*\GmH\178O*Tair+\Gmair*g*h*T0)' \->NUM 273.15 - "\^oC H\178O boiling" \->TAG
\>>
\>>

Code 2
'M—>BOIL.H²O'
\<< "1 Arg only:
. alt [m]
" DROP DUP .3048 / \-> alt.m ft
\<< "At " alt.m + "m" + '29.921*(1.-.0000068753*ft)^5.2559' EVAL \-> HG
\<< '(49.161*LN(HG)+44.932-32.)/1.8' EVAL \->NUM "\^oC H\178O boiling" \->TAG
\>>
\>>
\>>

Code for density of water:
'—>DENS.H²O'
\<< "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
\>>
\>>

Example
Boiling temperature at Everest, 8848 m, and local temperature - 20 degrees Celsius : 68.842 degrees Celsius.

And using the program without giving the local/unknown temperature returns 68.048 degrees Celsius.

Just download the Directory-file Water
in your HP49-50G and use one of the 3 files given above.

Regards,
Gil

[Gil]

I hope that the directory/file WATER.doc will be included now.

Regards,
Gil [/align]

[Albert Chan]

(08-13-2021 09:38 PM)Gil Wrote:  Boiling temperature at Everest, 8848 m, and local temperature - 20 degrees Celsius : 68.842 degrees Celsius.

And using the program without giving the local/unknown temperature returns 68.048 degrees Celsius.

What local temperature will the 2 results match ?

How does local temperature affect boiling point of water ?

What direction is the effect ?
And, by how much ? (is it always within 1 degree Celsius ?)

Can you provide source of formulas ? Thanks.

[Gil]

Boiling temperature (of water)
=f(pression), without inclusion of air.Temp.
See:
https://www.omnicalculator.com/chemistry...t-altitude


But pression =g(altitude, air.Temp), so that
Boiling temperature (of water)
=f(altitude, air.Temp).
See:
https://planetcalc.com/275/

Greater pression —> Higher boiling temperature.

Greater local temperature —> higher pression —> Higher boiling temperature.

A must, therefore, to calculate "more or less accurately" boiling temperature is to have both altitude and local temperature, in order to get first the pression, which enables then to reckon the local estimated boiling temperature.

Another way is to introduce directly the effective measured pression at Altitude h, as suggested in the second reference given above.

Note that g is taken as a constant, which is not absolutely true.

So that the final result is more an indication.
Degree of accuracy is beyond my scope, perhaps 1/10 or 1/100 of Celcius degree?

I included the references in the new version.

Regards,
Gil

[Gil]

As for the program without the input 'local temperature', it is supposed that temperature decays 6.5 degrees every 1000 m.

The formulae uses feet (0.3048m) and inches.

The final given pressure is in INCHES (2.54 cm) of HG
(76 cm HG <=> 1013325 Pascals).

See also Paragraph
"Gradients de température typiques"
in https://fr.m.wikipedia.org/wiki/Formule_...3%A9trique

[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

[Gil]

Completely new versions, following questions of Albert CHAN.

My thanks to him.

The 3 old ones, with inconsistent results between themselves, are named now with ...BOIL.OLD (with capital letters & OLD-suffix); they are to be found at the end of the directory WATER; the best would be to delete them.

The 1st new program 'MT—>Boil.H²O' means:
- Give in stack level 1 the altitude (M stands for meters);
- Or give in stack level1, in {}, the altitude & the local air temperature (T stands fort Temperature, that is to be entered in degrees Celsius), to get the corresponding boiling temperature of water.

Its code is:
\<< "1 stack Arg:
. 
Alt

. or 
{Alt T.Air}

with 
{}


Alt in [m]
T.air in [\^oC]

" DROP STD DUP TYPE 5 ==
IF
THEN OBJ\-> DROP NEG 15 + OVER /
ELSE .0065
END .0289644 9.80665 8.31446261815 \-> a M g R
\<< 'Alt.m' STO "At " Alt.m + "m:" + 15 a Alt.m * - 1 RND "Air [\^oC]" \->TAG DUP 'T.Air' STO '101325*(1-a*Alt.m/(15+273.15))^(M*g/(R*a))' \->NUM P\->Boil.H\178O
\>>
\>>

The 2nd program 'P—>Boil.H²O'
is to be used directly (without using 'MT—>Boil.H²O')
when already knowing the local pressure (independently of altitude and temperature).
- Give the pressure in Pascals, to get the corresponding boiling temperature of water.

Its code is:
\<< "1 Arg:
. 
Pressure
 in [Pa]

" DROP STD "P [Pa]" \->TAG DUP 'P' STO "
GOFF.GRATCH 1984
\->" 'LOG(P/100)=-(7.90298*(373.15/(T1+273.15)-1))+5.02808*LOG(373.15/(T1+273.15))-.00000013816*(10^(11.344*(1-(T1+273.15)/373.15))-1)+.0081328*(10^(-3.49149*(373.15/(T1+273.15)-1))-1)+LOG(1013.246)' 'T1' 100 ROOT "Boil.\^oC H\178O" \->TAG "
ARDEN
 
BUCK 1996
\->" 'P=611.21*e^((18.678-T2/234.5)*(T2/(257.14+T2)))' 'T2' 100 ROOT "Boil.\^oC H\178O" \->TAG 3 FIX
\>>

The references
are under the program REFER.

The two used formulae used here for boiling temperature of water =f(pressure) are:
- Arden Buck equation, 1996;
- Goff-Gratch equation, 1984.

Both formulae give quite similar boiling temperatures to 0.03 degrees Celsius.

Example Everest, altitude 8848 meters.
1)Type 8848
2)ENTER
3)Press MT—>Boil.H²O

Result
"At 8848m:"
:Air [°C]: -42.500
[Pa]: 31444.626
"
GOFF.GRATCH 1984—>"
:Boil.°C H²O: 70.205
"
ARDEN
 
BUCK 1996—>"
:Boil.°C H²O: 70.180

Suppose you will travel in summer to Everest.
You could check that average temperature is then equal to -19 degrees Celsius, and not -42.5.
Then
1) Write {8848 -19} (don't forget the {})
2)ENTER
3)Press MT—>Boil.H²O

The new results are:
"At 8848m:"
:Air [°C]: -19.000
[Pa]: 33184.930
"
GOFF.GRATCH 1984—>"
:Boil.°C H²O: 71.457
"
ARDEN
 
BUCK 1996—>"
:Boil.°C H²O: 71.432

Of course, in both cases the calculated pressure is an approximation.
It seems that, at Everest, the mean pressure in July is about 253 torrs.
101325 PA —> 760 torrs.
253 torrs = 101325/760 torrs×253=33731.
In that case we should use
directly the program Press P—>Boil.H²O.
1)Write 33731
2)ENTER
3)Press P—>Boil.H²O

The corresponding results are then:
[Pa]: 33731
"
GOFF.GRATCH 1984—>"
:Boil.°C H²O: 71.839
"
ARDEN
 
BUCK 1996—>"
:Boil.°C H²O: 71.814

For the time being, I let g as a constant, but it should diminish with the altitude: g=go×(Re/Re+h)².

Regards and enjoy!
Gil

[Gil]

HP49-50G

New version 5

As always, 3 programs
- MTBoil.H²O P
- Boil.H²O
- DENS.H²O

regarding 2 distinct topics on water:
- water boiling temperature = f(altitude + temp);
- water density=w[/align](pressure, temperature, water pureness[not from tap / from tap] ).

New calculation here:
Added the classical Clausius-Clapeyron equation relative to boiling temperature.

Example result:

P [Pa]: 150000
"
CLAUSIUS-CLAPEYRON
" :Boil.°C H²O: 111.518
"
GOFF.GRATCH 1984
" :Boil.°C H²O: 111.374
"
ARDEN
 
BUCK 1996
" :Boil.°C H²O: 111.420

Conclusion

GOFF.GRATCH 1984
& "
& "
ARDEN
 
BUCK 1996
"
give very similar results, meanwhile Clausius-Clapeyron output differ somewhat more from Goff-Gratch & "
ARDEN
 
BUCK"

New code for :

P—>Boil.H2O

\<< "1 Arg:
. 
Pressure
 in [Pa]

" DROP STD "P [Pa]" \->TAG DUP 'P' STO "
CLAUSIUS-CLAPEYRON
\->" 8.31446261815 40650 \-> R \GDHvap
\<< 'LN(P/101325)=-(\GDHvap/R*(1/(T1+273.15)-1/(100+273.15)))' 'T1' 100 ROOT
\>> "Boil.\^oC H\178O" \->TAG "
GOFF.GRATCH 1984
\->" 'LOG(P/100)=-(7.90298*(373.15/(T2+273.15)-1))+5.02808*LOG(373.15/(T2+273.15))-.00000013816*(10^(11.344*(1-(T2+273.15)/373.15))-1)+.0081328*(10^(-3.49149*(373.15/(T2+273.15)-1))-1)+LOG(1013.246)' 'T2' 100 ROOT "Boil.\^oC H\178O" \->TAG "
ARDEN
 
BUCK 1996
\->" 'P=611.21*e^((18.678-T3/234.5)*(T3/(257.14+T3)))' 'T3' 100 ROOT "Boil.\^oC H\178O" \->TAG 3 FIX
\>>

Regards,
Gil

[Gil]

Water.05.hp
with .hp ending.