Re: [Phys-l] Which is the most E efficient?

[Brian Whatcott <betwys1@sbcglobal.net>]

Bernard Cleyet wrote:
> Well, ...  since none of you answered my question on adding  
> dissipation to my equation of motion of a coupled cart oscillator, I  
> try again w/ another question.
>
> This one is easy, IT.
>
> Friend is poverty stricken retired school librarian (Seattle pub.  
> school -- was long ago Gate Keeper Seese's master teacher in SF)  
> wants to know if running a teakettle to humidify very dry ambience   
> instead of purchasing a pricey humidifier would be satisfactory.   
> Would aiming a fan at a wet towel dipped in pan of water be more or  
> less efficient?.  Assume both sources of "heat" are the same  
> (forsooth,  oil and electricity).
>
> bc  thinks an ultrasonic (most pricey?) would be the most efficient,  
> and thinks he knows all the factors to do the calc., but is lazy.
>   
'Fessing to feeling lazy is probably not the most attractive way of 
seeking responses - unless a person sees pleasure in making the 
comparisons. This is enough like working a criterion of merit for 
various materials and processes, that I am in this latter camp.

Visualizing the merits of literally thermodynamic versus mechanical 
methods, I can readily find specific energies for two representative 
processes:
boiling or evaporation: specific energy of vaporisation is around
540 cal/gm
2.27 kJ/gm
2.27 mJ/kg

mechanical spray methods:
given the surface energy of a water particle is
0.072 J/m^2 of surface
given the specific volume of water is (say)
1000 cc/kg
1E-3 m /kg
Suppose the number of spheres per kg is n
then  n = 1E-3/ (4/3 pi r^3)
leading to a surface area/size  relation of
3E-3/r   J/m for r radius of particle
which leads to a relation between surface energy and size of
SE = 2.16E-4/r   J/kg

For particle sizes smaller than some critical value, it is more energy 
intensive to mechanically divide water:
this would occur when the total specific surface energy
is equal to the  latent heat of a similar mass of particles.
Equating the values leads to a limiting radius of 95 nm
at the small end.   What is the large end, I wonder?

Perhaps the largest particle which can float for some reasonable period 
in air. NIOSH has an interest in airborne particles:
A searcher found that coal particles above 22 um diameter settled in 
under 150 meters, and rock dust above 18 nm diam settles in 60 meters.

It should be relatively safe to suppose that water particles under
10 nm can stay suspended for extended periods (though anyone who has run 
an oil drop charge experiment might well have a better feel for this.)

One concludes that a mechanical method that suspends particles between
200 nm and 15 um has an energetic advantage over evaporative methods.
The cost is the bodily  lofting of water contaminants too.
(It is not enough to cite a damp surface as being "cost-free" because 
people desire humidification to combat air which is dried by heating -
and they will necessarily pay to make good the heating which is lost by 
this "free" vaporization.)

It is not clear to me that ultrasonic dispersion is more energy 
efficient than other mechanical methods. It is clear that thermal 
evaporation and reverse osmosis are needed to provide contaminant free 
water, if many solids are present in the supply.
One could continue this line of study by evaluating a small pressure 
pump, a small r. osmosis membrane and either a fine spray head or an 
ultrasonic vaporizer....

Finally, it's amusing to note the powerful impact of assumptions on the 
outcome of comparisons.   You might well notice other important factors 
that I skipped....

Brian W