Conversion from Kilowatt-hours to Electronvolts

Information about the Kilowatt-hour (kWh)

The kilowatt-hour is a unit of energy equal to the energy delivered by one kilowatt of power flowing for one hour, or exactly 3.6 million joules. Its symbol is kWh. It is the unit in which virtually all electricity in the world is bought and sold.

Its form explains its usefulness. Power multiplied by time gives energy, so a device rated in watts and a duration in hours produce a figure that can be read straight off a bill. A two-kilowatt heater running for three hours consumes six kilowatt-hours, and no conversion is needed between the rating on the appliance and the number on the meter.

Domestic consumption sits at a comprehensible scale. A typical European household uses somewhere between 2000 and 5000 kilowatt-hours a year, an American one closer to 10,000. A kettle boiling once costs about 0.1, a load of washing about 0.7, and a modern refrigerator around 200 a year. Those figures make the unit an effective tool for reasoning about where energy actually goes in a home.

Electric vehicles brought it to a new audience. Battery capacity is quoted in kilowatt-hours, typically between 40 and 100 for a passenger car, and efficiency is expressed as kilowatt-hours per hundred kilometres, the electrical analogue of litres per hundred kilometres. Charging power in kilowatts then determines how long a given amount of energy takes to deliver.

The unit is not SI and is sometimes criticised for compounding a prefixed unit with a non-SI time unit. The megajoule is the formally correct alternative, and some countries do bill gas in megajoules or gigajoules, but the kilowatt-hour's direct link to appliance ratings has kept it dominant for electricity everywhere.

Larger multiples run the electricity industry. A megawatt-hour is the unit of wholesale trading, a gigawatt-hour describes the output of a power station over a day, and a terawatt-hour is used for national annual consumption.

Tariffs have turned the unit into a signal as much as a measurement. Time-of-use pricing charges different amounts per kilowatt-hour by hour of the day, wholesale markets settle in half-hourly blocks, and in periods of high wind and low demand the price has gone negative, so that generators pay to keep supplying. Households with a battery or an electric car respond by shifting consumption into the cheap hours, which flattens the load on the network. The kilowatt-hour is also the unit in which the carbon intensity of electricity is reported, in grams of carbon dioxide per kilowatt-hour, which lets a country's generation mix be judged on one number.

One kilowatt-hour equals 3.6 million joules, 3600 kilojoules, or about 860 kilocalories.

Information about the Electronvolt (eV)

The electronvolt is a unit of energy equal to the work done on a single electron moved through a potential difference of one volt. Its symbol is eV. Since the 2019 redefinition of the SI it has an exact value, 1.602176634 times ten to the power minus nineteen joules, because the elementary charge itself is now a defined constant.

It exists because the joule is hopelessly large for the atomic world. A single visible photon carries between about 1.6 and 3.3 electronvolts, and expressing that in joules requires nineteen leading zeros. Working in electronvolts lets a physicist state the energy of a chemical bond, an atomic transition or a subatomic collision as a number between one and a few, which is what a unit is supposed to do.

The scale organises whole disciplines. Chemistry lives at a few electronvolts, the energy of bonds and of the visible and ultraviolet photons that break them. X-rays occupy kiloelectronvolts. Nuclear physics works in megaelectronvolts, the scale of binding energies and radioactive decay. Particle physics uses gigaelectronvolts, where the proton's rest mass is 0.938, and teraelectronvolts at the Large Hadron Collider, whose protons carry 6.8 each.

Mass is quoted in the same unit through the mass-energy relation. A particle's rest mass is given in electronvolts divided by the speed of light squared, and physicists routinely drop the divisor and simply say that the electron is 511 kiloelectronvolts. The Higgs boson is 125 gigaelectronvolts on the same convention.

Semiconductor engineering depends on it. The band gap that determines what a material does electrically and optically is an energy in electronvolts: about 1.1 for silicon, 3.4 for gallium nitride, and this single number decides whether a device is a solar cell, a transistor or a blue light-emitting diode.

Astronomy inherits the convention for high-energy photons, so gamma-ray telescopes report observations in gigaelectronvolts and teraelectronvolts rather than in wavelengths.

Particle accelerators are named after the energies they reach, which is why their names track the prefixes. The Cockcroft-Walton machine that first split a nucleus in 1932 worked at a few hundred kiloelectronvolts; the Bevatron of the 1950s reached billions and found the antiproton; and the Large Hadron Collider brings protons to 6.8 teraelectronvolts each. Cosmic rays put all of this in perspective by arriving with energies up to 10 to the twentieth electronvolts, tens of millions of times more than any machine can produce, though only a handful of such particles strike the Earth in a century over a square kilometre.

One electronvolt equals about 1.602 times ten to the power minus nineteen joules, or roughly 3.83 times ten to the power minus twenty calories.