Bob loves to cook and eat eggs. He just had a plate full of fried eggs, followed by a bowl of scrambled. Now he wants some poached eggs, or maybe hard boiled, but in spite of cooking them for a very very long time, they are still not done. Where is Bob?
between 62.2° C and 65° C while egg yolk protein coagulates between
65° C and 70° C. So, if Bob's water boils below 70 C, he will have a hard time.
The density and pressure of the Troposphere drops exponentially with
altitude (since the pressure is governed by the overhead mass of air).
The simple relationship is: p = exp (- g h M / T0 R0), with g the
acceleration of gravity, h the height, M the molar weight of dry air,
T0 the sea level temperature and R0 the Universal gas constant. M = 0.029 kg/mole.
Likewise the Clausius-Clapeyron Equation (CCE) relates boiling
point of a liquid to its latent heat of evaporation (delta_H) and ambient pressure:
ln P = delta_H/R0/(R0 ,T) + Const, so, ln(P1/P2) = (delta_H/R0) (1/T1 - 1/T2)
Note, delta_H = 4410 J/mol. Here T1 = 373.15 K (100 C, normal boiling)
and P1 = 1013.14 hPa (1 Atm).
Alt. [m] P [hPa] Boil T [C] Comment
---------------------------------------
0. 1013. 100. Sea Level
400. 964. 99.
800. 917. 97.
1200. 872. 96.
1600. 830. 95.
2000. 789. 94.
2400. 751. 92. airplane cabin
2800. 714. 91.
3200. 679. 90. Dome A Antarctica
3600. 646. 89.
4000. 614. 87.
4400. 584. 86.
4800. 556. 85.
5200. 529. 84. TAO Obs (Chile)
5600. 503. 82.
6000. 478. 81.
6400. 455. 80.
6800. 433. 79.
7200. 412. 78.
7600. 392. 77.
8000. 373. 75.
8400. 354. 74.
8800. 337. 73. Everest Summit
9200. 321. 72.
So I am not sure where Bob will have trouble since he
can cook eggs on the summit of Everest. I checked the
space station and they run at 1 atm so that will work too.
Finally - cooking tip - adding a lot of salt to the water will raise the
boiling point a couple of degrees,
allowing for hotter liquid water for cooking.
Here is the code
program pa
implicit none
real term,term2,p,g,h,m,T0,T1,T2,Tc,R0,p0,dH
integer i
dH=44010.
p0=1013.25
T0=273.15
T1=373.15
g=9.8
M=0.028979
R0=8.3145
do i=0,92,4
h=i*100.
term=g*h*M/(T0*R0)
p=p0*exp(-term)
term2 = (R0/dH)*log(p/p0)
T2 = 1. / ( (1./T1) - term2 )
Tc = T2 - 273.15
print 7,h,p,Tc
7 format(f8.0,2x,f7.0,3x,f7.0)
enddo
end
Edited on March 5, 2025, 1:16 pm
soln and cooking hint
