## Energy Units

**Energy**is generally defined as the potential to do work or produce heat. This definition causes the SI unit for energy is the same as the unit of work – the

**joule (J)**. Joule is a derived unit of energy and it is named in honor of

**James Prescott Joule**and his experiments on the mechanical equivalent of heat. In more fundamental terms, 1 joule is equal to:

**1 J = 1 kg.m ^{2}/s^{2}**

Since energy is a fundamental physical quantity and it is used in various physical and engineering branches, there are many **energy units** in physics and engineering. These units are summarized in following points:

- 1 joule = 0.239 Calories
- 1 joule = 9.48 x 10
^{-4}BTU - 1 joule = 2.778 x 10
^{-7}kWh

**Examples of Energy of 1 Joule:**

One joule in everyday life and in science corresponds to approximately:

- The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.
- The kinetic energy of a 50 kg object (e.g. human) moving very slowly – approximately 0.72 km/h.
- The energy required to lift a medium-size apple (100 g) 1 meter vertically from the surface of the Earth.
- The heat required to raise the temperature of 1 g of water by 0.24 °C.
- The heat required to evaporate of 0.00044 g of liquid water at 100°C.
- The amount of electricity required to light a 1 watt LED for 1 s.
- Is released by approximately
**3.1****⋅****10**^{10}**fissions**in a nuclear reactor.

**Calorie (unit: cal)**. Calorie is a traditional unit of heat. It is part of the

**International System of Units**(SI). It is defined to be the amount of heat that must be absorbed by 1 gram of water to raise its temperature by 1 °C. Its counterpart in the British Imperial system of units is the BTU, which is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. But we have to distinguish between small calorie and large calorie. The large calorie (unit: Cal) is defined in terms of the kilogram rather than the gram. It is equal to 1000 small calories and it is i.e. 1 kilocalorie (unit: kcal). It is used by nutritionists to characterize the energy-producing potential in food.

- 1 calorie = 4.184 J
- 1 calorie = 0.00397 BTU
- 1 calorie = 1.16 x 10
^{-6}kWh

**British Thermal Unit (unit: BTU)**. British Thermal Unit is a traditional unit of heat. It is part of the British Imperial system of units. It is defined to be the amount of heat that must be absorbed by a 1 one pound of water to raise its temperature by 1 °F at the temperature that water has its greatest density (approximately 39 degrees Fahrenheit). Its counterpart in the

**International System of Units**(SI) is the calorie, which is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius.

- 1 British Thermal Unit (BTU) = 1055 J
- 1 British Thermal Unit (BTU) = 252 calories
- 1 British Thermal Unit (BTU) = 0.000293 kWh

**Foot-pound force (unit: ft.lbf)**. Foot-pound force is a derived unit of work and energy. It is equal to the energy transferred to an object when a force of one pound-force (lbf) acts on that object in the direction of its motion through a distance of one foot. The corresponding SI unit is the joule. The foot-pound is often used in ballistics, especially in the United States. Typically muzzle energies of bullets are given in foot-pound force.

- 1 foot-pound force = 1.356 J
- 1 foot-pound force = 0.324 cal
- 1 foot-pound force = 0.00129 BTU

**Kilowatt-hour (unit: kWh)**. Kilowatt-hour is a derived unit of energy. It is used to measure energy, especially electrical energy in commercial applications. One kilowatt-hour is equal to one kilowatt of power produced or consumed over a period of one hour (kilowatts multiplied by the time in hours). The kilowatt hour is commonly used by electric utilities as a billing unit for energy delivered to consumers. 1kW . h = 1kW . 3600s = 3600kWs = 3600kJ = 3600000J. One kilowatt-hour corresponds to the heat required to evaporate of 1.58 kg of liquid water at 100°C. A radio rated at 100 watts operating for 10 hours continuously uses one kilowatt hour.

- 1 kWh = 3.6 x 10
^{6}J - 1 kWh = 8.6 x 10
^{5}cal - 1 kWh = 3412 BTU

**Megawatt-day (unit: MWd)**. Megawatt-day is a derived unit of energy. It is used to measure energy produced, especially in

**power engineering**. One megawatt-day is equal to one megawatt of power produced by power plant over a period of one day (megawatts multiplied by the time in days).

**1 MWd = 24,000 kWh**. At nuclear power plants there are also gigawatt-days, because it approximately corresponds to energy produced by power plant over a period of one day. This unit (MWd) was also used to derive unit of

**fuel burnup**. The most commonly used measure of fuel burnup is the fission energy release per unit mass of fuel. Therefore fuel burnup of nuclear fuel is normally have units of megawatt-days per metric tonne (

**MWd/MTU**), where tonne refers to a metric ton of uranium metal (sometimes MWd/tU HM as Heavy Metal). In this field, the megawatt-day refers to the thermal power of the reactor, not the fraction which is converted to electricity. For example, for a typical nuclear reactor with a thermal power of

**3000 MWth**, about

**~1000MWe**of electrical power is generated in the generator. For example, a reactor with 100 000 kg of fuel operating at 3000MWth power level for 1000 days would have a burnup increase of 30,000 MWd/MTU. In words of fissions, fissioning of about 1 g of U-235 produces about 1 MWd of thermal energy (see: Energy Release per Fission).

- 1 MWd = 8.64 x 10
^{10}J - 1 MWd = 2.06 x 10
^{10}cal - 1 MWd = 8.19 x 10
^{7}BTU

**Electronvolt (unit: eV)**. Electronvolts are a traditional unit of energy particularly in atomic and nuclear physics. Electronvolt is equal to energy gained by a single electron when it is **accelerated** through **1 volt** of **electric potential** difference. The work done on the charge is given by the charge times the voltage difference, therefore the work W on electron is: W = qV = (1.6 x 10^{-19 }C) x (1 J/C) = **1.6 x 10 ^{-19} J**. Since this is very small unit, it is more convenient to use multiples of electronvolts: kilo-electronvolts (keV), mega-electronvolts (MeV), giga-electronvolts (GeV) and so on. Since Albert Einstein showed that mass and energy are

**equivalent and convertible**one into the other, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c

^{2}, where c is the speed of light in vacuum (from E = mc

^{2}). For example, it can be said the

**proton**has mass of

**938.3 MeV**, although strictly speaking it should be

**938.3 MeV/c**. For another example, an electron–positron annihilation occurs when a negatively charged electron and a positively charged positron (each with a mass of 0.511 MeV/c

^{2}^{2}) collide. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc

^{2}formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

**e**^{−}** + e**^{+}** → γ + γ (2x 0.511 MeV)**

- 1 eV = 1.603 x 10
^{-19}J - 1 eV = 3.83 x 10
^{-20}cal - 1 eV = 1.52 x 10
^{-22}BTU

**Example of Energies in Electronvolts**

**Thermal neutrons**are neutrons in thermal equilibrium**with a surrounding medium of temperature 290K (17 °C or 62 °F)**. Most probable energy at 17°C (62°F) for Maxwellian distribution is**0.025 eV**(~2 km/s).- Thermal energy of a molecule is at room temperature about
**0.04 eV**. - Approximately
**1 eV**corresponds to an**infrared photon**of wavelength 1240 nm. - Visible light photons have energies in range 1.65 eV (red) – 3.26 eV (violet).
- The first resonance in n +
^{238}U reaction is**at 6.67 eV**(energy of incident neutron), which corresponds to the first**virtual level in**^{239}**U**, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10^{-14}s. - Ionization energy of atomic hydrogen is
**13.6 eV**. - Carbon-14 decays into nitrogen-14 through beta decay (pure beta decay). The emitted beta particles have a maximum energy of 156 keV, while their weighted mean energy is
**49 keV**. - High energy diagnostic medical x-ray photons have kinetic energies of about
**200 keV.** **Thallium 208,**which is one of nuclides in thedecay chain,^{232}U**emits****gamma rays****of 2.6 MeV which are very energetic and highly penetrating.**- Typical kinetic energy of
**alpha particle**from radioactive decay is about**5 MeV**. It is caused by the mechanism of their production. **The total energy released**in a reactor is**about 210 MeV**per^{235}U fission, distributed as shown in the table. In a reactor,**the average recoverable energy**per fission is**about 200 MeV**, being the total energy minus the energy of the energy of antineutrinos that are radiated away.- Cosmic ray can have energies of
**1 MeV – 1000 TeV**.

## Examples of Energy of 1 Joule

**One joule**in everyday life and in science corresponds to approximately:

- The kinetic energy of an object with mass
**1 kg**moving at √2 ≈**1.4 m/s**. - The kinetic energy of a
**50 kg**object (e.g. human) moving very slowly – approximately**0.72 km/h**. - The energy required to lift a medium-size apple (
**100 g**)**1 meter vertically**from the surface of the Earth. - The heat required to raise the temperature of
**1 g of water by 0.24 °C**. - The heat required to
**evaporate**of**0.00044 g of liquid water**at 100°C. - The amount of electricity required to light a
**1 watt LED**for**1 s**. - Is released by approximately
**3.1****⋅****10**^{10}**fissions**in a nuclear reactor.

**Reactor Physics and Thermal Hydraulics:**

- J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
- J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
- W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
- Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
- Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
- Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
- Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
- Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
- U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

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