Matter and Motion, Spring Project 1999
Generating Water by using Electric Cooling Device
Tomoko Adachi, The Evergreen State College
May 24, 1999



 
 
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INTRODUCTION THEORY Calculations Glossaries REFERENCES Navigation Bar
ABSTRACT:

The project is to enhance the thermoelectric cooling (TEC) device system to condense water.  The TEC, thermoelectric heating, and cooling systems implement the well-known physics principle, the Peltier effect, which states that when a direct current is applied to an electric circuit made of two dissimilar materials, then one junction of the circuit becomes cold, the other hot.

The research has been done by other people:  Water Collection With Thermoelectric Coolers, by Tharald Nustad, 1996, and TEC Dehmidification, by Micah Dilley, 1996.  Both research papers were "alternative energy resource" oriented that the electricity is to be supplied by the solar panel.  My project does not discuss the source of electricity;  rather, it talks about the atmospheric condition and the properties of water vapor.  The two papers above discuss the energy input and output well enough.  This report focuses on other things such as the velocity and the mass of water vapor in order to estimate how much humidity or volume of the atmosphere is required to condense a cup of water that is about 200 ml.

Several experiments were conducted to analyze the relationship between the ambient and the cooling side temperatures.   It was difficult to set a consistent control environment due to the variations in the room's air conditioning, although the relationship could be analyzed by looking at graphs.

INTRODUCTION:

The project was to generate water using the TEC device. The model # 2CP 085 cascade type TEC is used, and it requires 10.3 ampere and 8.6 voltage to produce maximum temperature differences of 29 degree C.   It requires understanding the overall system that is the relationship between dew point, relative humidity, and ambient air temperature.  The paper discusses the relationship and makes a speculation for further improvement.

The assembling part was easy once you know the property of TEC.  (See diagram 1 in assembling section.)  The detail information of TEC can be obtained through Melcor Corporation  that manufactures TEC.  An information of semiconductor can be found in the physics textbook, Halliday, Resnick, Krane.

Water vapor molecule has its average speed of 640 meter per second at 25 oC.

With the formula Q = 3/2 kT;
where Q is thermal energy, k is the Boltzman's constant, and T is temperature, the mass of water vapor molecule was calculated.  The number of water vapor molecules, n were calculated by using Dalton's law of partial pressures: n1 = P1(V/RT).  From these values, the total mass of water vapor in a certain volume of air with relative humidity of 60% was obtained.  The value was used to postulate results of experiments that the device will produce a cup of water by providing about twenty cubic meter of air with relative humidity of 60%.
Several experiments were conducted with respect humidity and the ambient temperature.

Glossaries:
Semiconductor
RELATIVE HUMIDITY
HEAT TRANSFER THERMAL RADIATION

THEORY:

As discussed earlier in the abstract, the Peltier effect was the principle to generate temperature difference between the two surfaces of the thermoelectric cooling device. TEC is a semiconductor that utilizes the Peltier effect to move heat.  When current passes through the junction of two different types of conductors it results in a temperature change.   The semiconductor requires being a good electric conductor but poor heat conductor.

The TEC consists of a number of p- and n-type couples connected electrically in series and sandwiched between two ceramic plates.  When it connected to a DC power, current causes heat to move from one side of the TEC to the other.  This creates a hot side and a cold side.  The theory is to use this TEC's cold side to condense water from ambient air.  So the theory is simple.  However, since the whole system interacts with the atmosphere; in this case, the room temperature and the humidity, it is not so simple as it is seemed.  It also needs to include an account of a diffusion of gases that helps to create humidity of air relatively homogenous, but also it helps evaporation.

The principle at the heat sink is that it can dissipate the heat from the hot side of the TEC through heat sink that is made out of aluminum, and has a high thermal conductivity.  Twelve thin fins are attached to the plate.  The principle of hot side is simpler than the cooling side due to thermodynamics.  Heat flows from a higher temperature region to lower temperature region.  The temperature of the ambient air is usually cooler than the heat sink, so the heat sink dissipates its heat by convection and radiation.  It also is blown by a fan to improve the dissipation.  But the principle at the cooling side is more complicated because of the laws of thermodynamic. It demands warmer air at the cooling surface to achieve a large enough temperature difference between the surface and the air to condense water vapor.  But the warmer air increases the temperature at the cooling surface and the condensation produces the latent heat.  It is critical to keep the cooling surface below the dew point.

The voltage needs to be constantly increased to increase the temperature differences between the hot side and the cold side.  There is always an energy loss in the net heat exchange in the system.  The loss may be found as the voltage change.  The heat in the whole system flows towards thermal equilibrium so the initial temperature of the ambient air is better be not so high in terms of this phenomena.  But for the cold side the initial temperature is better be high in terms of dew point.   Warmer air can hold more water vapor.   In order to reach the dew point the warmer air needs to be cooled down.  The cooling surface is very sensitive to change.  Once the cooling surface is in contact with warm air, the temperature at the cooling surface increased and was taking much more time to be cooled down again.  (See experiment section)

Calculations:
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Velocity Calculation:

"Average speed of gas molecules at 25 C Water vapor: 640 m/sec.
 Average speed is proportional to square root of (Temp./molar mass)"
The Kinetic Model of Gas, Atkins and Jones. (page 167)


The following is an equation to calculate the velocity of gas:
 Q = 3/2 kT
       (Terrestrial Energies, winter '98 Mechanical energy, escape velocity, and atmospheric composition, by Dr. E.J. Zita).

         Q  =  K                             T:  Temperature in Kelvin
  K = 1/2 mv2                          k:  constant  1.38 x 10-23 J/K
          3/2 kT  =  * mv2                          m:  mass
          v2  =  3/2 kT 2/m
           v  =  sqrt(3kT/m)

Using value for speed of water vapor above to estimate the mass of the water vapor.
         m  =  3kT/v2 T = 25 oC + 273.15 =   298,15   Kelvin
  k =   1,38E-23   J/K
  v = 640 m/sec,   v2 = 409600   m2/sec2

m = 3*(1,38E-23J/K)(298,15K)/409600 m2/sec2
= 3.01 x 10-26   kg

The above calculation is confirmed by checking the units:

  kg m2/sec2  K
  * * *
mass  =                K                =  kg
  * * * **
        m2/sec2

The mass of water vapor molecule:     3,01 x 10-26 kg

Then with this mass, the velocity of water vapor at temperature 21oC can be calculated.

   T = 21oC + 273.15 = 294,15 K
    mass =   3,01E-26 kg
v  =  sqrt(3kT/m)    k =  1,38E-23 J/K
v = sprt[(3*1,38E-23J/K*294,15K)/3,01E-26kg]
 636 m/sec

The velocity of water vapor at the temperature 21oC is (the average temperature in the room 1234, LAB II)
 636 meters/sec

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The various velocities of water vapor were obtained as follows:


 



 

Temp.(C) Velocity (m/sec)  Temp.(K)
9 623 272.15
15 630 288.15
19 634 292.15
23 638 296.15
27 643 300.15
31 647 304.15
35 651 308.15

Relative Humidity and the mass of Water Vapors
 

  Partial pressure of water
       Humidity =       ******** **     x 100%
  Vapor pressure of water

Partial pressure can be obtained by algebraic manipulation of the above:

 Pp   =  Humidity x Vapor pressure
                              100%

Then it is converted into the atm units.

T: Temperature
Torr: Atmospheric pressure
pP Partial pressure
vP Vapor pressure
H: Humidity
 

T vP (millibar) pP(millibar) H pP (torr) pP (atm)
0 4,58 2,75 60% 2,75 0,0036
10 9,21 5,53 60% 5,53 0,0073
20 17,54 10,52 60% 10,52 0,0138
21 18,65 11,19 60% 11,19 0,0147
22 19,83 11,90 60% 11,90 0,0157
23 21,07 12,64 60% 12,64 0,0166
24 22,38 13,43 60% 13,43 0,0177
25 23,76 14,26 60% 14,26 0,0188
30 31,83 19,10 60% 19,10 0,0251
37 47,08 28,25 60% 28,25 0,0372
40 55,34 33,20 60% 33,20 0,0437
60 149,00 89,40 60% 89,40 0,1176
80 355,26 213,16 60% 213,16 0,2805
100 760,00 456,00 60% 456,00 0,6000


 The values except vapor pressure were estimated. The value of vapor pressure were taken from the Table 5.4 CHEMISTRY Molecules, Matter, and Change 3rd, by Atkins and Jones.

"In a closed container, water vaporizes until its partial pressure has reached a certain value, called its vapor pressure.  When there is another gas, such as air, in the container, water vaporizes in the same way, until its partial pressure equals its vapor pressure.  At this point, the gas holds as much water vapor as it can and is said to be saturated with water vapor." (page 162, Chemistry Molecules, Matter, and Change, Atkins and Jones.)
The vapor pressure of water varies with temperature, and some values are given in Table.
 


 "Diffusion helps to keep the composition of the atmosphere approximately constant,
because abnormally high concentrations of one gas diffuse away and disperse."
(Chemistry, Atkins and Jones)


 VAPOR PRESSURE OF WATER

Temperature, Vapor pressure, Partial pressure,
         oC millibar,          atm

   0 4.58 0.0036
 10 9.21 0.0073
 20 17.54 0.0138
 21 18.54 0.0147
 22 19.83 0.0157
 23 21.07 0.0166
 24 23.76 0.0177
 25 23.76 0.0188
 30 31.83 0.0251
 37 47.08 0.0372
 40 55.34 0.0437
 60 149.44 0.1176
 80 355.26 0.2805
        100 760.00 0.6000

(The vapor pressure is comverted into atm units by conversion factor:  l millibar = 1atm/760torr)

Ideal Gas Law says:

 PV = nRT
 n = PV/RT
 P = Pdry air  +  Pwater vapor
 P = P1 + P2 = n1RT/V  +  n2RT/V  = (n1 + n2)(RT/V)
Dalton's Law of Partial Pressure says:
 n1  =  P1(V/RT)
Since the partial pressure of water vapor is obtained above,
the numbers of mol of water vapor can be calculated.
 

    To obtain number of water vapor in the Volume of 1 cubic meters container
 Molar mass of water:    1,802 x 10-2 kg/mol   Useful conversions:
 Density of water =   1000 kg/meter cubed
 R, gas constant in Joules:  8.31   J/mol K
 R, the gas constant:  0,08206 L atm/K mol   Joules = Pa * m cubed
 Partial pressure of v.:  0,0138 atm  at 20oC   Pa = 1 kg/m s2  =  1 N /m squared
 Temperature:    293,15 K (20oC =20 + 273.15)  Joules = kg m2/s2

 n water vapor =  P water vapor (V/RT)
 Thus:
  0,0138 atm * 103 L
 n    = 0,08206 L atm * 293,15 K
  K mol
  = 0,5736 mol


From the mol value, the number of water molecules is calculated  using Avogadro's constant:
 Abogadro's constant:  6,02 x 1023 molecules/mol
 0,5736 mol  x (6,02 x 1023) molecules/mol
 = 3,453E+23 molecules
 Also, the total mass of water vapor in the volume of 1 m3 is obtained as follows:
 Molar mass of water:    1,802 x 10-2 kg/mol
 0,5736 mol x (1,802 x 10-2)
 = 1,033 x 10-2 kg that is also 10 ml

In order to generate a cup of water that is about 200 ml, the volume needs to be 20 times more.
 10 ml x 20  = 200 ml

 Since the 10 ml of water is generated in the volume of 1 m3, so 20 times it gives
 1 m3 x 20 = 20 meter cubed

In a practical use, the water vapor can be infinitely supplied when the device is implemented outdoors although humidity is still an issue.  It became easier to speculate to design a device in order to condense about 200 milliliter of water from about 20 cubic meters of air where less heat transfer must occur.   The values and number that were obtained above were to be analyzed to maximize the cooling surface area and to design a chamber to lessen heat transfer in order to maintain the cooling surface to be cooled.
 A kind of filter that can introduce water vapor into a cold side chamber, while it filter out any warmer air, needs to be invented.

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Link to the Evergreen State College: http://www.evergreen.edu
 

More about TEC: if you want to explore a lot more, then I listed some grossaries also.  Hope this will help you to enjoy.
 
Semiconductor
RELATIVE HUMIDITY
HEAT TRANSFER THERMAL RADIATION

Link to Melcor

EXPERIMENT:

The first experiments were conducted in a bathroom with the relative humidity of  60% to 70%.  It was found that the device worked well as a dehumidifier when the humidity was 70%.  Other experiments were conducted in the room 1234, LAB II, and the temperature and the humidity were respectively; about 17oC, and 21oC, and 60% to 70%.

Experiment 10B, C, D

The data is logged for 600 sec.  Three Vernier temperature probes were attached to the heat sink, cold surface and the ambient air.  (See the graphs in the next page)

 RESULTS:

CONCLUSIONS:
 

REFERENCES:

* Chemistry Molecules, Matter, and Change Third Edition 1997, Atkins and Jones
* Energy and Problems of a Technical Society, Second edition, 1993
* Clouds, Rain & Rainmaking, 1962, B. J. Mason
* Melcor Corporation, URL: http://www.melcor.com.
* TEC Dehumidification, 1996, Micah Dilley
* MRI, Thermoelectric Technology, Midwest Research Institute,
 URL:  http://www.mriresearch.org/ea/te.html
* Water Collection With Thermoelectric Coolers, 1996, Tharald Nustad.
*

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Glossaries:
 

SEMICONDUCTOR

It is intermediate between conductors and insulators such as silicon or germanium.  A typical semiconductor might contain 10^10 - 10^12 conduction electrons per cm^3.  One of the properties of semiconductors that makes them so useful is that the density of conduction electrons can be changed drastically by small changes in the conditions of the material, such as by introducing small quantities (less than 1 parts in 10^9) of impurities or by varying the applied voltage, the temperature, or the intensity of light incident on the material.
(Physics, Halliday, Resnick, Krane)

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RELATIVE HUMIDITY

Relative humidity, H, or the saturation ratio, S, of the air, is defined as the ratio of its actual vapor pressure, vP, to that required to saturate the air at the same temperature, partial pressure; pP, Thus H or S = vP/pP, and when the air achieves saturation, vP = pP and S = 1.  The relative humidity is commonly expressed as a percentage.

Air is saturated when there is no net transfer of vapor molecules between it and a plane surface of water at the same temperature.

The supersaturation s of the air is given by vP/pP - 1; this may also be expressed as a percentage by multiplying by 100.  Thus air which has a saturation ratio of 1.01 (corresponding to a relative humidity of 101%) has a supersaturation of  0.01 or 1%.
Clouds, Rain & Rainmaking, 1962, B. J. Mason

Droplet growth by condensation
the rate of increase of mass of a droplet of radius r is given by
dm/dt  =  4prD(r - rr)      (3.1, page 39, Clouds, Rain & Rainmaking)
where D is the diffusion coefficient of water vapor in air, r is the vapor density at distances remote from the droplet and rr the corresponding value at the surface of the droplet.
Since    dm/dt  = 4pr*rL dr/dt,  and r = pM/RT
where rL  is the density of water, p the vapor pressure, M the molecular weight of water, R the universal gas constant, and T the absolute temperature of the air, (3.1) may be re-written as
 r dr/dt = DM/rLRT(p - p*r) = DM/rLRT (Sp* - p*r)    (3.2, page 39)
where p*r is the vapor pressure at the droplet surface, p* the saturation vapor pressure at the air temperature T, and S = p/p* is the saturation ratio of the environment.

The growth rate of the droplet is controlled not only by the rate of condensation, which is limited by the rate at which the liberated heat of condensation can be dissipated.  Nearly all this heat is lost from the droplet surface by conduction through the air.  The equation describing the heat transfer from the droplet is very similar in form to (3.2) for the equilibrium vapor pressure p*r over the surface of a solution droplet
 r dr/dt = K/LrL (Tr - T)        (3.3, page 40)
K is the thermal conductivity of the air, L the latent heat of condensation and Tr the surface temperature of the droplet which is higher than the of its surroundings.

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HEAT TRANSFER:  CONDUCTION, CONVECTION AND RADIATION

Heat transfer occurs where there is any material medium between any tow points at differing temperatures.   Where there is the differing temperatures, then there is a potential.  Heat energy always flows from the higher temperature to the lower temperature.   These potential can be converted to power such as the horse power and  the electric power.  Although this paper does not discuss about the power.  We rather focus on the nature of heat.  There are three characteristics of heat transfer that are Conduction, Convection and Radiation.
 
 

Conduction

Thermal conduction will take place through any material medium between any two points at differing temperatures.  Heat energy will flow by conduction from regions of higher temperature to regions of lower temperature.  There is no heat transfer by conduction through empty space, such as in a vacuum chamber.  Thermal conduction proceeds by transferring the energy of vibrating atoms, molecules, and electrons to their less energetic neighbors.  The ability to conduct heat in this way varies enormously from one material to another, depending on, among other factors, the density of free electrons in the material.

Every material has an associated thermal conductivity, k, which is the rate of heat flow across a unit thickness per unit cross-sectional area per unit temperature gradient.  Appropriate units for thermal conductivity are:  Btu per hour per square foot per degree Fahrenheit across a 1-inch thickness (Btu * in./hr * ft* * *F) or, in metric terms, joules per second per square centimeter per degree Celsius across a 1-centimeter thickness (J * cm/sec * cm* * *C).  In the latter case, the thermal conductivity is equal numerically to the number of watts (or joules per second) conducted from one face of a cubic centimeter of some material to the opposite face when the two faces differ in temperature by 1 degree Celsius.

Thermal conductivity for several substances are given in Table A-1.  Note that the mechanisms for thermal conduction can be especially complex for porous materials, gases, and liquids because conduction, convection, and radiation processes are simultaneously present in the space occupied by the medium.  In the strictest sense, the term  " thermal conductivity* can apply only to solid media.  Nevertheless, the given values, which result from measurement under laboratory conditions, are useful in heat-transfer calculations.  They do represent how well heat is transmitted through the bulk of each material.

(Energy and Problems of a Technical Society, Second edition, 1993)

 Table A-1  Typical Values of Thermal Conductivity k near 20*C.

  J * cm Btu * in.
 Substance sec * cm* * *C hr * ft* * *F
 Metals
Silver  4.23 2930
Copper 3.85 2680
Gold 2.93 2030
Brass 1.09 750
Iron and steel 0.46 320
Aluminum 2.01 1390
Mercury, liquid 0.063 44
Nonmetallic solids
Brick, common 7.1 x 10** 5.0
Concrete 1.7 x 10** 12.0
Wood (across grain) 1.3 x 10** 0.9
Glass 5.9 x 10** 4.0
Ice 2.2 x 10** 15.4
Porous Materials
Fiber-blanket insulation 3.8 x 10** 0.27
Glass wool or mineral wool 3.8 x 10** 0.27
Sawdust 5.9 x 10** 0.41
Corkboard 4.2 x 10** 0.30
Liquids
Water 5.99 x 10** 4.15
Ethyl alcohol 1.76 x 10** 1.23
Gases
Air 2.34 x 10** 0.16
Hydrogen 1.7   x 10** 1.16

                                      (Energy and Problems of a Technical Society, Second edition, 1993)





A calculation of how much heat is conducted per unit time, Q/t (Btu/hr), through some material with a thickness of l (inches), an area A (ft*), and a thermal gradient of T* - T* (*F), can be carried out with the use of the following expression:

Q/t =  kA (T* - T*)
         l

(Energy and Problems of a Technical Society, Second edition, 1993)
 

 CONVECTION

Liquids and gases transfer heat principally by convection, which is motion of a medium, such as air, between regions at different temperatures, which thus transfers heat energy.  Convection may be forced, as by a blower for air or a pump for liquids, or it may be natural, driven by buoyancy.  When air warmed near the surface of a stove rises and cooler air near the inner surface of a window moves downward, natural convection takes place.  Connective heat transfer is difficult to analyze exactly; semiempirical rules are usually used.  The medium'* viscosity, specific heat, density, and thermal conductivity all influence the efficiency of heat transfer by this means.  Most of our space heating systems operate through connective heat transfer.
(Energy and Problems of a Technical Society, Second edition, 1993)
 
 

THERMAL RADIATION

All materials are constantly emitting and absorbing thermal radiation.  The sun*s light, the redness of a very hot stove, and the direct heat we feel from a campfire are all examples of thermal radiation.  The radiation is electromagnetic, in the same general class as radiowaves, microwaves, x-rays, and gamma radiation.  Thermal radiation has its origin in the motion of electrons.  These charged particles, in random motion, with abrupt changes in direction, radiate electromagnetic energy.  All electromagnetic radiation arises from the acceleration of electric charges.  The properties of thermal radiation are of particular importance to us because this is the means by which we receive the sun*s energy.

The intensity and wavelength distribution of the thermal radiation emitted by any body depend on the surface temperature and on a property of the surface known as the emissivity.  The heat energy radiated per unit area is given by Stefan*s law.

P
                *    = ** T*
A

where P/A is the heat energy in watts emitted per square meter, e is the surface emissivity, * = 5.67 x 10** W/m* * *K* is the Stefan-Boltzmann constant, and T is the surface temperature in degrees Kelvin.  Note that the radiated the heat energy increases dramatically with increasing temperature because of the fourth-power dependence.  A doubling of the absolute temperature produces a 16-fold increase in  the radiated power because 2* =16.

The emissivity, e, is a dimensionless factor that is related to the rate of thermal radiation from a particular surface.  It varies from a maximum of 1.0 down to very small values, close to zero.  It varies with surface temperature, roughness, color, and degree of oxidation.  Several values are shown in Table A-2.  It is interesting to note that most building materials have emissivities near 0.9, but that the aluminum foil commonly used in this layers on insulating panels has an emissivity of less than 0.10.  The low value obviously leads to reduced heat transfer by thermal radiation.  To perform a radiant heat-transfer calculation, it is also necessary to have another factor, absorptivity (a)-the fraction of the radiation impinging on a surface that is directly absorbed as heat.  Reflectivity ( r ) is the complement (r = 1 - a ) of absorptivity for opaque surfaces.
(Energy and Problems of a Technical Society, Second edition, 1993)

Table A-2  Emissivity of Surfaces near T = 300*K

Material e(T * 300symbol 176 \f "Symbol" \s 14*K)
Aluminum
 Polished 0.04
 Rough plate 0.06
 Oxidized 0.15
Cast iron 0.50
Sheet steel 0.70
Wood, black lacquer, white enamel, 0.90
plaster, roofing paper
Porcelain, marble, brick, glass, 0.94
rubber, water

                             (Energy and Problems of a Technical Society, Second edition, 1993)

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