Slice of solid 0.000001 liters of copper as a battery
Calculations
Q - electric charge = number of added or subtracted electrons / m^3 × volume x elementary charge of electron = 8.46753969×10^28 m^-3 × 0.000000001 m^3 × 1.602176634×10^−19 C = 8.46753969×10^28 × 0.000000001 × 1.602176634×10^−19 = 13.5664942388 coulombs C
Side length of a piece of copper block = Cube root of 0.000000001 m^3 = cbrt(0.000000001) = 0.001 m or 1 millimeter mm
0.001 m × 4,391,225,573.3491 atoms/m = 4,391,225.5733491 atoms
Based on the ionization energy, I assume the ionization voltage of 1 copper atom is 7.72638 V. You can also check the voltages of 4.53 - 5.10 V based on the work function.
4,391,225.5733491 atoms × 7.72638 V = 33,928,277.445413 V
13.5664942388 C × 33,928,277.445413 V = 13.5664942388 × 33,928,277.445413 = 460,287,780.4956 joules J
A 100 kWh battery has 360,000,000 joules J
460,287,780.4956 J ÷ 360,000,000 J = 460,287,780.4956 ÷ 360,000,000 = 1.278577168 times greater/higher capacity, so we calculate how much we can reduce the ionization voltage and the dimensions of the copper piece to maintain 100 kWh of capacity. √(√(1.278577168)) = 1.0633634685 times
33,928,277.445413 V ÷ 1.0633634685 = 31,906,566.710697 volts V, therefore, the copper piece is smaller than 0.000001 liters, i.e. 0.000001 × 8.935 kg/L = 0.000008935 kg = 0.008935 g or many smaller pieces of copper may one day replace other batteries at voltages as low as 31,906,566.710697 volts V
5 Liter Copper Block as a Battery
CalculationsQ - electric charge = number of electrons added or subtracted / m^3 × volume x elementary charge of the electron = 8.46753969×10^28 m^-3 × 0.005 m^3 × 1.602176634×10^−19 C = 8.46753969×10^28 × 0.005 × 1.602176634×10^−19 = 67,832,471.193928 C
Side length of the copper block = Cube root of 0.005 m^3 = cbrt(0.005) = 0.1709975947 m
0.1709975947 m × 4,391,225,573.3491 atoms/m = 750,889,010.82782 atoms
750,889,010.82782 atoms × 7.72638 V = 5,801,653,835.4799 V
67,832,471.193928 C × 5,801,653,835.4799 V = 67,832,471.193928 × 5,801,653,835.4799 = 3.93540517 × 10^17 J
A 100 kWh battery has 360,000,000 joules J
3.93540517 × 10^17 J ÷ 360,000,000 J = 3.93540517 × 10^17 ÷ 360,000,000 = 1,093,168,102.7778 times greater/higher capacity, so we calculate how much we can reduce the ionization voltage and the dimensions of the copper piece to maintain 100 kWh of capacity: √(√(1,093,168,102.7778)) = 181.8325954245 times
5,801,653,835.4799 V ÷ 181.8325954245 = 31,906,566.707336 volts V, so the copper block 6,011,947.9690954 times smaller than 5 liters, i.e. 5 ÷ 6,011,947.9690954 × 8.935 kg/L = 0.000007431 kg = 0.007431 g or many smaller pieces of copper may one day replace other batteries with voltages of 31,906,566.710697 volts V
Calculations for a battery voltage of 1000, 2000, 3000, 4000, 5000, ... volts V
1000 V / 7.72638 V = 129.4267172984 atoms
129.4267172984 atoms × thickness of 1 atom in a copper block 0.227726857 × 10^-9 m = 29.4739395×10^-9 m or about 30 nanometers
(29.4739395×10^-9)^3 × 8.46753969×10^28 m^-3 = 2,168,062.5322705 atoms and electrons in a cube with sides 30 nanometers
Charge = 2,168,062.5322705 × 1.602176634×10^-19 = 3.47361913×10^-13 coulombs C
Capacity = Charge × Voltage
3.47361913×10^-13 × 1000 = 3.47361913×10^-10 joules J
A 100 kWh battery has 360,000,000 joules J
360,000,000 ÷ (3.47361913×10^-10) = 1.03638305×10^18 or a quintillion nano pieces of copper
2000 V ÷ 7.72638 V = 258.8534345968 atoms
258.8534345968 atoms × thickness of 1 atom in a copper block 0.227726857 × 10^-9 m = 58.9478791×10^-9 m or about 59 nano meters
(58.9478791×10^-9)^3 × 8.46753969×10^28 m^-3 = 17,344,500.346435 atoms and electrons in a cube with sides 58.9 nano meters
Charge = 17,344,500.346435 × 1.602176634×10^-19 = 2.77889532×10^-12 coulombs C
Capacity = Charge × Voltage
2.77889532×10^-12 × 2000 = 5.55779064×10^-9 joules J
A 100 kWh battery has 360,000,000 joules J
360,000,000 ÷ (5.55779064×10^-9) = 6.47739405×10^16 or about 65 quadrillion nano pieces of copper
1 cent for less than 1 grams of copper + cost of ionizer, inverter and other accessories
This is calculated for a discharge to the ground - if it is not possible to discharge to the ground, you need to divide this piece of the block into 2 parts or add a second piece of the block.
3000 V ÷ 7.72638 V = 388.2801518952 atoms
388.2801518952 atoms × thickness of 1 atom in a copper block 0.227726857 × 10^-9 m = 88.4218186×10^-9 m or about 88.4 nanometers
(88.4218186×10^-9)^3 × 8.46753969×10^28 m^-3 = 58,537,688.569913 atoms and electrons in a cube with sides 88.4 nanometers
Charge = 58,537,688.569913 × 1.602176634×10^-19 = 9.37877168×10^-12 coulombs C
Capacitance = Charge × Voltage
9.37877168×10^-12 × 3000 = 2.81363150×10^-8 joules J
A 100 kWh battery has 360,000,000 joules J
360,000,000 ÷ (2.81363150×10^-8) = 1.27948525×10^16 or about 12.8 quadrillion nano pieces of copper
4000 V ÷ 7.72638 V = 517.7068691936 atoms
517.7068691936 atoms × thickness of 1 atom in a copper block 0.227726857 × 10^-9 m = 117.895758×10^-9 m or about 117.9 nano meters
(117.895758×10^-9)^3 × 8.46753969×10^28 m^-3 = 138,756,002.06531 atoms and electrons in a cube with sides 117.9 nano meters
Charge = 138,756,002.06531 × 1.602176634×10^-19 = 22.2311624×10^-12 coulombs C
Capacity = Charge × Voltage
22.2311624×10^-12 × 4000 = 8.89246496×10^-8 joules J
A 100 kWh battery has 360,000,000 joules J
360,000,000 ÷ (8.89246496×10^-8) = 4.04837131×10^15 or about 4 quadrillion nano Copper pieces
5 Liters of copper × 8.935 kg/L = 44.675 kg
44.675 kg × 80 PLN/kg = 3,574 PLN + the cost of the ionizer, inverter, and other accessories