atom888 said:
I just did a rough calculation of air ratio by your value given.
Alright, giving 14.7 g of air going into combustion. The oxygen is 3 gram and 11.7 gram of mostly nitrogen. The energy loss to nitrogen is the different in enthalpy between nitrogen at ambient temperature and nitrogen enthalpy of exhaust (I lost my thermal book to look up table value). Let say we introduce 2.5 gram of electrolysis gas. The ratio is .5g of hydrogen and 2g of oxygen. The gas intake now is offset by 14.7 - 2.5 = 12.2g .
Continue with his later I gtg...
This is way too much gas from electrolysis in 1 second though. I'll give a description of some important ideas for determining how much additional gas products that we can put in using electrolysis.
First, let's calculate the theoretical work (energy) needed to produce 1 gram of hydrogen. Our chemical equation is the following:
2(H20) (l) ---> 2(H2) (g) + (O2) (g) dH = 483.6kJ
Since this equation produces four grams of hydrogen, multiply it by 1/4.
1/2(H20) (l) ---> 1/2(H2) (g) + 1/4(O2) (g) dH = 120.9kJ
Now the amount of work we need to input into the system to split water is given by the Gibbs Free Energy equation:
dG = dH - TdS
where dG is the change is free energy, dH is the change in enthalpy, T is the temperature in kelvins, and dS is the
change in entropy.
Let's now compute dS. dS is given by
dS = SUM[nS(products)] - SUM[mS(reactants)]
where n and m are the coefficients of the substances in the chemical equation. My chemistry textbook gives values the following values in units of J/(mol*K):
H2 (g) -- 130.7
O2 (g) -- 205.2
H20 (l) -- 69.9
If you solve for dS, you should find dS = 0.0817
kJ/(mol*K)
Substituting our computed dH and dS values into the Gibbs Free Energy equation, we have
dG = 120.9 - T*(0.0817)
in units of kJ. It is evident that as temperature increases, the input energy (work) is reduced--the temperature of the water will rise because of heat dissipation due to various car components and inherent resistances.
Assuming the standard condition temperature of T = 298 K, you will find that the theoretical work needed to produce 1 gram of hydrogen is dG = 96.55 kJ.
Now let's assume some efficiencies. Assuming that the electrolysis device ranges from 60-80% efficiency and that the electrical energy generation and mechanical efficiency of the automobile is 30%, our total range of efficiency is 18-24% (I quoted these values on a previous post from a journal article). Taking these efficiencies into account gives the following values at 298 K:
18% efficiency -- dG = 536.39 kJ
24% efficiency -- dG = 402.29 kJ
Now divide these values by 3600 seconds to find the joules per second or watt-hours needed to produce the gram of hydrogen:
18% efficiency -- 149.00 W*h
24% efficiency -- 111.75 W*h
So how much hydrogen then can we produce in hour. This is where my results become speculative. An alternator can typically supply a maximum current of 100 amps and has voltage at about 14.4 volts. If the head lights and all accessories are off, then the car typically needs less than 10 amps to operate the necessary electrical devices (ignition coil, etc.). So let's assume that 90 amps are available for electrical work, then by the relation P=I*V,
P=1,296W*h.
This is the upper ceiling for the power that we can use to produce hydrogen while keeping the battery charged. However, I can't say for certain if the battery can output this amount power any given moment--the cold cranking amps commonly have values above 100 amps--because it may be constrained by the internal chemical reactions. Let's assume that it does, so that we can calculate the maximum amount of hydrogen that can be produced via electrolysis. Before we do, note the following: since we are looking at the power from the alternator being transferred into work at the electrolysis device, we don't have to take the 30% efficiency value from earlier (it is still important though) but only the efficiency of electrolysis. If you take our theoretical work energy needed 94.55 kJ from earlier and apply the electrolysis efficiency range using similar manipulations from above, you find the following work requirements.
60% electrolysis efficiency -- 44.70 W*h
80% electrolysis efficiency -- 33.52 W*h
If we divide our maximum output power from the alternator/battery by these values we find the maximum number of grams of hydrogen that can be produced in one hour:
60% electrolysis efficiency -- 28.99 g/hr
80% electrolysis efficiency -- 38.66 g/hr
Multiply these values by a factor of 8 to find the number of grams of oxygen produced.
Now we are ready to look at the maximum amount of hydrogen that we can put into the engine for combustion each second. Divide by 3600 seconds:
60% electrolysis efficiency -- 8.1 x 10^-3 g/s
80% electrolysis efficiency -- 1.1 x 10^-2 g/s
A good approximation for the amount of gasoline used each second by a car is 1.0-1.5 grams. The best case scenario for this analysis is 1.1% mass fraction of hydrogen relative to gasoline. You can determine the rest of your values from here.
As a last analysis, let's determine how many grams of gasoline we need to produce 1 gram of hydrogen. The combustion energy per kilogram of stoichiometric mixture is 2.79 MJ. The stoichiometric ratio of air to gasoline is 14.7:1, so the amount of gasoline needed to produce 2.79 MJ of energy can be found from the relation
x + 14.7x = 1000 grams
which shows that x = 63.69 grams of gasoline
We can now determine our objective from the following relation:
grams of gas to produce 1 gram of hydrogen = (Work to produce 1 gram H2) * (gasoline mass per combustion energy ratio)
Note that we do not need to consider the efficiencies if we use one of dG values that already includes them. For example, we previously determined that we need dG = 536.39 kJ based on an 18% total efficiency:
grams of gas to produce 1 gram of hydrogen = [(536.39 kJ) / (1 gram of hydrogen)]*[(63.69 g gasoline)/(2.79MJ)] =
12.23 grams of gasoline
This amount will obviously be consumed over whatever time interval is necessary to produce 1 gram of hydrogen. It also doesn't imply that the idea works, only that the gas consumption to produce one gram of hydrogen is not very much (about .5% of a gallon of gasoline, or a reduction of .15 miles per gallon if you get 30 miles per gallon).