# RESULTS AND DISCUSSION 8.3.1 Electrostatic Force Analysis

In an attempt to establish the proliferation of electric force around the plastic tank mathematically to tug the water down, the dynamic photon proliferation is solved through the integration of HSEF electric field created. Therefore, the local U(l) gauge invariant allowed the addition of mass term for gauge particles within 0' ->e'a^0. A covariant derivative using a special transformation rule can explain it in detail for the scalar field as expressed in [37,12,13]:

Whereby local U(l) gauge invariant HSEF suited to the complex scalar field is represented by:

Notably, the function jFl,vF,‘'’ represents the kinetic term for the gauge field, that is, heating photon, and V (0) represents the extra term contained in the HSEF. Such means V(0*0) =ai2(0*0)+A (0*0)2-

Thus, the HSEF (//), when subject to perturbations in the quantum field, start with massive scalar particles 0, and ф2 together with a mass /.i. The consequent situation /.r < 0 involves countless quantum, and every one meets the condition ф2 = -q2 / Я =v2 and the fj via the covariant derivatives that also use the shifted fields q and | that the quantum field defines as фо =-L[(o+7j)+i|].

Kinetic term is represented as fjhn(v>%) = (^‘фУ(Э^ф)

Potential term includes V(r),E,)=kv1r1, and it applies up to the second order in various fields. The complete HSEF can, therefore, be presented as:

In this case, massive is represented as q. massless as | (as previously done) and a mass term for quantum Af which is fixed in number up to dt,a as Eq. (8.14) demonstrates. A,, and ф vary simultaneously, and therefore, it is possible to redefine them to incorporate the heating photon particle spectrum that falls in the quantum field through the expression:

Therefore, the expansion term in the fj linked to the scalar field suggests that HSEF electric field is ready to start the propagation of static electricity to create a quantum field capable of tugging the water down.

Confirming the tugging down of water requires calculations of isotropic spread of movement on the differential cone taking into account angle в and remaining in the range between 0 and в + сЮ constitutes j sinOdO and with a differential static electric force density recorded at energy e and angle в as shown:

Therefore, the calculation of the function that the high static electricity force plays takes into account the directional form of с (1 - cos#), calculating the absorption level of water vapor for each unit as:

In an effort to modify the functions to realize an integration rather than s rather than в by (8.3) and (8.5), the calculation of determining the accuracy are as follows:

in which,

The results obtained emerge as a dimension variable (p together with dimensionless cross section a. Calculations of the variable s0 < 10. The functional asymptotic calculation made for

had to be reliable whereby s0 - 1«1 and s0 » 1 is expressed as:

where

It would be appropriate to write the last integral as where

Ultimately, the expression of the tug down water using static electricity force can be detailed readily by implementing the calculations of (p |.v0] to confirm the expected .v„ value to capture water vapor. Therefore, this study uses the corrective functional asymptotic formulas as provided below:

The function is therefore illustrated as 1 < s0 < 10. In case of the larger 50, it has a natural logarithmic that is s0 for confirming the tug down of 100% water vapor that the HSEF direct to the plastic tank.

In typical daily life, every person requires an average of 100 gallons of water every day. Therefore, for 1 year, l()()?w„„/Day/Person x 4persons x 365(/„„, which amounts to 146,000 gallons of water that a family of four would require annually. Normally, a standard oak tree transpires an approximately 151,000 liters or 40,000 gallons of water annually. This means that only four standard oak trees would be needed to satisfy the family’s water demand if the HSEF manages to tug down 100% of the water vapor. If the family has 6 standard oak trees, it can rely four to meet its water domestic water demands and the others for generating clean energy for the home through the electrolysis process.

# ELECTROLYSIS FOR HYDROGEN ENERGY PRODUCTION

In the current model, it is easy to conduct water-splitting reactions for H, production because (a) the H, evolution reaction tends to have the lowest over-voltage losses, which lowers the need to have a catalyst and, therefore, facilitates an optimized counter electrode for use in more sophisticated 02 evolution reactions, and (b) under illumination, which requires the semiconductor surface to be protected cath- odically [30,31,32]. Figure 8.5 illustrates photocurrent-voltage curves applicable to p-GaInP2(Pt)/TJ/GaAs and p-GaInP,(Pt) electrodes assessed in a two-electrode configuration. In the dark, the open circuit voltage is expected to be -0.75 V and —0.64 for /?-GaInP2(Pt)/TJ/GaAs and /;-GaInP,(Pt) electrodes respectively. Notably, the dark reduction current is to remain in the microampere range for the two electrodes. The /j-GalnP, (Pt) while under illumination is to be started to produce hydrogen at

FIGURE 8.5 Electrical current via a single-level molecular junction as Eq. (8.18) (broadened molecular level) and Eq. (8.19) (zero-width molecular level) express. The parameters that the calculations use include e = 0.4 eV, // = 0.5, Va = 0, and у, = уR = 1 meV for (a-c) and yL = yR= 10 meV for (d). These parameters are typical values in the molecular junction of the current work.

a 500 mV negative with 0 V bias. Such implies that additional external voltage will have to be provided for the semiconductor to manage splitting the water. Whereas, p-GalnP, (Pt)/TJ/GaAs electrode exhibits an open circuit voltage of -0.55 V when under illumination. That suggests that the GaAs cell generates the extra voltage. H, evolution begins directly and at 400 mV positive of a short circuit. The density of photocurrent is to be met at a limiting value of 120 mA/cm2 and at ~0.15 V. This would remain constant with rising bias. Numerous gas bubbles are to be seen at the semiconductor surface. Because the gas bubbles are able to reach a size that they can sufficiently act as miniature lenses to pit the semiconductor electrode, that means that 0.01 M of the surfactant Triton X-100 is chosen as the solution of facilitating the formation of smaller bubbles, which leaves the sample surface faster. The less saturated photocurrent applicable in p-GalnP, (Pt)/TJ/GaAs electrode in comparison to the />-GaInP2 electrode is considered in showing that the pin GaAs bottom cell constitutes the current-limiting junction (Figure 8.5).

The collection and analysis of products of photoelectrolysis will be conducted by mass spectrometer. The calculations of the efficiency of generating H2 will follow the equation: Efficiency = (power out)/(power in). Hereby, the input power constitutes the incident light intensity of approximately 1190 mW/cm2 (Figure 8.6a). In case of the output power, taking the assumption of 100% efficiency in photocurrent electrolysis, the H, generation photocurrent of 120 mA/cm2 get multiplied with 1.23 V that constitutes the ideal fuel cell limit achieved at 25°C to arraign the highest efficiency in H2 energy generation; 25°C is the lowest heating value of hydrogen (Figure 8.6b).

The calculated estimate shows that a gallon of water can yield 0.42 kg of hydrogen. In the proposed PEM electrolyzers, the ideal figure would be 44.5 kWh/kg-H2. Thus, the yields amount to 16.7 kWh. Notably, a kilowatt hour constitutes 3600 kilojoule and the enthalpy of forming hydrogen energy derived from liquid water and at 25°C amounts to -286 kJ/mol, while a gallon of water constitutes 3785 mL. Taking into account that water ought to be 18 mL/mol, which is approximately 210 mol of

FIGURE 8.6 (a) Current-voltage attributes for curve 1 (/?-GaInP,(Pt)/TJ/GaAs) and curve 2 (p-GalnP,) electrodes in 3MH 2S04 when placed under white light illumination, (b) A photocurrent time profile recorded at short circuit for photoelectrochemical/photovoltaic (PEC/PV) tandem cell in 3MH 2S04 using 0.01 M Triton X-100 when placed under tungsten-halogen white light illumination. The recorded efficiency of 5120 mA/cm2 31.23 V 3100/1190 mW/cm2 at current density were observed.

water, the calculation 286 x 210.3/3600 will imply that 116.7-kilowatt-hours energy is generated. On average a small family of four requires 30 kWh daily. As a result, two gallons of water would be sufficient to meet their daily energy demands if done on daily basis. Thus, the amount water vapor that a small oak tree can generate would be sufficient if electrolysis applies.

# CONCLUSION

Plants play the major role in balancing the global environmental equilibrium. Nevertheless, the process of transpiration uses only a mere portion of the ground water and releases rest of the water into the air. Simply, the hydraulic conductivity that the soil has together with the scale of pressure gradient via the soil affects the large amount of water that gets to the plant leaves from the roots. The cohesive attribute of the water enables tension to pass through leaf cells to both the leaf and stem xylem. From this, a momentary negative pressure results on the pulling of water from the roots and up the xylem. Surprisingly, plants’ metabolism only uses 0.5% and the remaining portion of 99.5% evaporates through transpiration through the stomatal cell. Ultimately, there is continuous water flowing through plants leading to loss of considerable amounts of ground water that creates significant roles in global potable water crises throughout the world. As a way of mitigating this issue, the transpiration mechanism is suggested to be useful in transforming and converting the transpiration water vapor into clean energy and clean water and consequently mitigate global potable water crisis. The adoption of this technology promises to be a revolutionary field of science that humans can use to tackle the global potable water and global energy crisis in the hope of establishing the best-balanced Earth and a humane civilization.

# ACKNOWLEDGMENTS

Green Globe Technology offered support in preparing this research under grant RD-02017-06 aiming to build a better environment. The author came up with all the findings, assumptions, conclusions, and prediction in the article and there was no conflict of interest in choosing to publish the research in a journal.

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