The Battery

Battery driven vehicles are becoming compulsory very soon, but how good are they when compared to petrol-driven vehicles?

Input Energy Capacity:
element   J/kg
Deuterium5863118.68377495
Helium2941284.32702004
Lithium848061.55668485
Beryllium653159.83021088
Boron362984.66483210
Carbon326730.62435714
Nitrogen105063.92056926
Oxygen92015.18265725
Fluorine61967.26393213
Neon116679.53963537
Sodium85348.03762644
Magnesium80729.55173763
Aluminium62332.51857463
Silicon59882.40261192
Phosphorus47511.14390782
Sulphur45894.24033174
Chlorine18448.19672038
Argon16372.38205486
Potassium30110.74785834
Calcium29374.69566819
Scandium23806.74052725
Titanium22358.90455922
Vanadium19258.67666817
Chromium18868.06659522
Manganese16484.00858812
Iron16215.71922450
Cobalt14268.92836769
Nickel14327.22604720
Copper12350.93793462
Zinc11999.15458107
Gallium10553.18055905
Germanium10133.58226303
Arsenic9243.22344950
Selenium8770.47986315
Bromine8185.37142481
Krypton7805.00630478
Rubidium7249.75434263
Strontium7071.67945909
Yttrium6620.93131661
Zirconium6452.68269858
Niobium6034.12890323
Molybdenum5843.32992341
Technetium5410.44790183
Ruthenium5294.61603115
Rhodium4974.08260804
Palladium4809.81448808
Silver4547.52131533
Cadmium4363.74499600
Indium4101.37453357
Tin3967.57621700
Antimony3719.09351758
Tellurium3548.58648719
Iodine3435.88589815
Xenon3305.65622639
Caesium3163.60001426
Barium3061.71987038
Lanthanum2922.55018077
Cerium2897.30147973
Praseodymium2784.98967939
Neodymium2720.64857873
Promethium2617.28074740
Samarium2525.72117883
Europium2420.96617659
Gadolinium2339.58476349
Terbium2244.77247102
Dysprosium2195.39217341
Holmium2099.42322914
Erbium2070.19380121
Thulium1991.10318574
Ytterbium1943.85947591
Lutetium1869.04935882
Hafnium1832.15843556
Tantalum1758.42619801
Tungsten1730.66917506
Rhenium1663.79500826
Osmium1628.60893183
Iridium1570.44602633
Platinum1547.41397720
Gold1494.26267175
Mercury1466.53925580
Thallium1404.91533524
Lead1385.81675886
Bismuth1341.29594571
Polonium1341.28554816
Astatine1303.82274273
Radon1233.17172277
Francium1199.72837025
Radium1183.77799418
Actinium1152.35815552
Thorium1127.47676925
Protactinium1107.75091192
Uranium1075.20649030
Table 1
the workings of a dry-cell battery
Fig 1. Lithium Ion Battery

Definitions

The following are CalQlata’s definitions for a typical lithium-ion battery (Fig 1).
anode: negatively charged electrode (lithium alloy (Lᵢ.Sᵢ or Lᵢ.C₆))
cathode: positively charged electrode (lithium cobalt oxide (Lᵢ.Cₒ.O₂))
electrolyte; Lithium hexafluorophosphate (Lᵢ.PF₆)
electrolyte shield; solid electrolyte interphase (sei)
positive electrolyte shield; positive solid electrolyte interphase (sei⁺)
transition metal oxides (TMO)
positive lithium ions (Lᵢ⁺)
graphite (C)
separator; permeable membrane (manganese dioxide (Mₙ.O₂))
Note: the separator only allows the flow of positive lithium ions. It does not allow the flow of electrons.

Battery Charging

Connect one end of a charging device to the anode of the battery, the other end to the cathode and switch it on (activate). The process goes something like this:
1) The charging device pulls electrons from the lithium atoms in the cathode making them positively charged; positive ions.
2) These electrons are dragged by the charging device through the activated circuit and pushed into the anode, making it negatively charged.
3) The electrons in the anode cannot pass through the separator, so they pull the positively charged ions through the electrolyte into the anode intercalating them within the graphite lattice structure neutralising the electrons and the ions in the anode.
4) This process continues until the graphite can accommodate no more ions; it is 'full'. When this happens, and the flow of positive ions has ceased, the battery is fully charged.

Discharging

The discharging cycle is almost identical to the charging cycle, but the process is reversed.
Connect the negative end of an external circuit to the cathode of the battery, the positive end to the anode and switch it on (activate). The process goes something like this:
1) The electrical circuit pulls electrons (via a conductor) from the lithium atoms in the anode creating positive ions from its lithium atoms. Some electrons are normally lost to the circuit in this process.
2) These electrons flow through the circuit to the cathode, making it negatively charged.
3) The electrons in the cathode cannot pass through the separator, so they pull the positively charged ions through the electrolyte into the cathode neutralising the electrons and the ions in the cathode.
4) When the flow of ions from the anode to the cathode ceases; (emptying the graphite of lithium atoms), the battery is fully discharged.

Relative Efficiency

Petrol possesses 4.8E+07 J/kg of releasable energy.

There are 8.60882E+25 atoms in one kg of lithium.
The kinetic energy in the outer-shell electron of a lithium atom at 300K is 9.85107E-21 J.
Giving a total energy capacity for lithium at room-temperature of 8.48062E+05 J/kg (Table 1).
But because a lithium-ion battery contains only 12% (per unit mass) lithium, a lithium-ion battery can hold no more than 101767.44 J/kg.
And because you need to input potential energy (Voltage) to release kinetic energy (current), which applies to both charging and discharging, electrical [operational] energy release of a lithium-ion battery is only 25% efficient, giving it an effective energy capacity of 25441.8467005455 J/kg.
Added to which, we must also take into account the efficiencies of the driven system. At best, a battery driven motor (for example), cannot be greater than 0.04% efficient when compared with a petrol-driven motor.

When compared with petrol-power, battery efficiency is; ξ = 2.54418467005455E+04 ÷ 4.8E+07 = 0.053003847% (or petrol is 188,665.55% more efficient than an equivalent battery pack).
However, this result is only valid if 100% of all the lithium in a battery is mobile, which is not the case. To this must be added losses due to the electrical circuitry and the driven system.

In addition to the above, battery driven vehicles are at least 30% heavier than petrol driven vehicles, reducing their efficiency still further:
KE = ½.m.v²
(KEb - KEp) ÷ KEp = 0.302362205 (Ford Focus)
ξp = 1886.6555 ÷ 0.302362205 = 6239.720013
making the petrol driven vehicle 623,972% more efficient than the battery driven vehicle.

Energy Cost

Next we must compare the cost of energy production. For this exercise we will look at the cost of domestic supply in the UK:
Petrol is charged £1.50 per litre at the pump, but 60% of this is excess tax (over and above normal national taxation), which must be ignored as it has nothing to do with the cost of production.
Electricity sells at 24.5p/kWh, the tax on which is in accordance with the national average.

Ignoring the excess tax on UK petrol, a comparison of cost to the consumer will give us a good indication of the relative cost of energy production.
Petrol: cost = 0.4 . £1.5 /SG /4.8E+07 = £1.56250E-08 per Joule
electricity: cost = £0.245/1000/3600 = £6.80556E-08 per Joule
making electricity 4.36 times more expensive to generate than it costs to recover and refine petrol.

Transport Cost

Next we must consider container costs. A battery pack is no more than the electrical equivalent of a petrol tank.

A replacement fuel tank for a Ford Fiesta costs ≈£125
carrying capacity 42 litres, which = 42 . 0.8 . 4.8E+07 = 1.6128E+09 Joules
the carrying capacity cost = 125 / 1.6128E+09 = 7.7505E-08 £/Joule
a modern petrol tank will last 20 years, so the overall cost will be 7.7505E-08 / 20 = 3.87525E-09 £/J/yr

A replacement battery pack for an electric Ford Fiesta costs ≈£87/kWh
carrying capacity = £87 / 1000 / 3600 Joules = 2.41667E-05 £/Joule
a battery pack will last anything between 1 and 3 years at maximum carrying capacity; cost = 8.05556E-06 £/J/yr

Making the battery pack ≈2,079 times more expensive than a petrol tank.

Battery Problems

Due to battery cost and the pollution they create, it is essential to prolong their life, which is already considerably less than that of a petrol tank.
Maximising battery life relies almost entirely on ensuring ion mobility does not exceed that of the separator and electrolyte shields, as excessive charging rates will result in premature damage to both, dramatically reducing the battery's useful life.
The potential damage is listed below:
    electrode cracking; reducing ion mobility,
    shield disruption; reducing ion mobility,
    dendrite generation; shorting the battery,
    island generation; reducing effective battery capacity,
    electrode plating; reducing ion mobility and battery capacity.
    memory loss; reducing battery capacity.
This is why you must always fully drain and fully charge a battery, and never charge it faster than its ion mobility allows.

In addition to the above, one must take into consideration the fact that batteries lose power with reducing temperature. For example; a lithium-ion battery will lose 10% of its energy capacity from 23°C to 0°C.

A runaway battery fire is virtually impossible to extinguish, making it far more dangerous than a petrol fire, which can be put out with a conventional fire extinguisher.

Conclusion

Is there any benefit for battery-driven vehicles over those fueled by petrol?

Even taking the improved efficiency of the electric motor over the internal combustion engine;
assume electrical efficiency of 100% (impossible) and a conservative 33% for an internal combustion engine; (ξ = ξp/3 / ξb/1)
the energy in petrol is more than 207,990.67% more efficient, 4.36 times cheaper to generate, and 2,079 times less expensive to contain than in a battery.

Given that transport technology is today quite rightly focusing on reduced weight, and the public is already struggling with the cost of electricity, it would appear that the internal combustion engine scores heavily over every aspect of the battery driven vehicle.
It is extremely difficult to find a reason why anyone would want to drive a vehicle using battery power, let alone impose it as a matter of decree.

Yes, batteries and their charging facilities are improving, but until they achieve similar levels of efficiency, safety, cost, pollution and convenience, they shouldn't be imposed on the public.

Battery or Petrol?

In comparison with a petrol driven system, battery power doesn't look too promising; does it!

Given the difficulty every country is having with electrical energy generation, surely it would be a good idea to ensure that battery-power is actually better than petrol before imposing it on any nation?

Newton-Coulomb Atom Verification

'thundersaidenergy' claims that lithium has an energy capacity of between 200 and 300 W.h/kg {J/s . hr/kg}, so let's assume 250;
Eₜ = 250 x 3600 = 9E+05 J/kg

The ionisation energy in a lithium atom at 300K according to Newton-Coulomb is calculated as follows:

The temperature of the proton-electron pair (Ṯ̱ₛ), the electron of which is orbiting in lithium's outer shell (shell-2; N=2);
Ṯ̱ₛ = Ṯ/N = 150 K

The orbital velocity of the electron in lithium's outer shell (according to Newton-Coulomb) is calculated thus;
v² = Ṯₛ/X (m/s)²

Its kinetic energy is therefore;
KE = Nₑ . ½.mₑ.Ṯₛ/X J
where Nₑ is the number of electrons in the outer shell (1 or 2). In the lithium atom; Nₑ = 1
KE = 1 . ½.mₑ.150/X = 9.85107E-21 J

The ionisation energy capacity of lithium is therefore;
Eₙ = KE/mₐ = 848061.5567 J/kg
where; mₐ is the atomic mass (1.161598961557E-26 kg)

The ratio of the 'thundersaidenergy' estimate and Newton-Coulomb's calculation is ...
Eₜ:Eₙ = 9E+05/848061.5567 = 1.061243719

... yet further vindication of the Newton-Coulomb atom.

Further Reading

You will find further reading on this subject in various specialist locations, but CalQlata suggests Stanford University's; Oliver Friedman for its operational aspects.

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