## Law of Conservation of Energy

**The law of conservation of energy** is one of the basic laws of physics along with the** conservation of mass **and the conservation of momentum. **The law of conservation of energy** states that energy can **change** from one** form** into another, but it** cannot be created or destroyed**. Or the general definition is:

The total energy of an isolated system remains constant over time.

**Energy** can be defined as the **capacity for doing work**. It may exist in a variety of forms and may be **transformed** from one type of energy to another in hundreds of ways.

For example, burning gasoline to power cars is an energy conversion process we rely on. The **chemical energy** in gasoline is** converted** to** thermal energy**, which is then converted to **mechanical energy** that makes the car move. The **mechanical energy** has been converted to **kinetic energy**. When we use the brakes to stop a car, that** kinetic energy** is converted by friction back to heat, or **thermal energy**.

A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind, which produces work without the input of energy, cannot exist.

The concept of** energy conservation** is widely used in many fields. In this article the following fields are discussed:

**Conservation of Mechanical Energy****Conservation of Energy in Fluid Mechanics****Conservation of Energy in Thermodynamics**- Conservation of Energy in Electrical Circuits
- Conservation of Energy in Chemical Reactions
**Conservation of Energy in Special Relativity Theory****Conservation of Energy in Nuclear Reactions**

## Law of Conservation of Mass-Energy – Mass-Energy Equivalence

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its **absoluteness**. One of the striking results of **Einstein’s theory of relativity** is that **mass and energy are equivalent and convertible** one into the other. **Equivalence** of the mass and energy is described by Einstein’s famous formula **E = mc ^{2}**. In words,

**energy**equals

**mass**multiplied by the

**speed of light squared**. Because the speed of light is a very large number, the formula implies that any small amount of matter contains a very large amount of energy. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light. The

**total energy**of an object was understood to comprise its

**rest mass**as well as its

**increase of mass**caused by

**increase in kinetic energy**.

**In special theory of relativity** certain types of **matter may be created or destroyed**, but in all of these processes, the mass and energy associated with such matter **remains unchanged in quantity**. It was found the **rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons**. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (**E = mc ^{2}**) this binding energy is proportional to this mass difference and it is known as the

**mass defect**.

**mass defect**of a

**nucleus if the actual mass of**

^{63}Cu^{63}Cu in its

**nuclear ground state is 62.91367 u.**

^{63}Cu nucleus has 29 protons and also has (63 – 29) 34 neutrons.

The mass of a proton is **1.00728 u** and a neutron is **1.00867 u**.

The combined mass is: 29 protons x (1.00728 u/proton) + 34 neutrons x (1.00867 u/neutron) = **63.50590 u**

**The mass defect** is Δm = 63.50590 u – 62.91367 u = **0.59223 u**

**Convert the mass defect into energy (nuclear binding energy).**

(0.59223 u/nucleus) x (1.6606 x 10^{-27} kg/u) = **9.8346 x 10 ^{-28} kg/nucleus**

ΔE = (9.8346 x 10^{-28} kg/nucleus) x (2.9979 x 10^{8} m/s)^{2} = **8.8387 x 10 ^{-11} J/nucleus**

The energy calculated in the previous example is the **nuclear binding energy**. However, the nuclear binding energy may be expressed as kJ/mol (for better understanding).

Calculate the nuclear binding energy of 1 mole of ^{63}Cu:

(8.8387 x 10^{-11} J/nucleus) x (1 kJ/1000 J) x (6.022 x 10^{23} nuclei/mol) = **5.3227 x 10 ^{10} kJ/mol of nuclei.**

One mole of ^{63}Cu (~63 grams) is bound by the nuclear binding energy (5.3227 x 10^{10} kJ/mol) which is equivalent to:

**14.8 million kilowatt-hours (≈ 15 GW·h)****336,100 US gallons of automotive gasoline**

**mass defect**of the

**3000MW**reactor core after one year of operation.

_{th}It is known 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.

The **reaction rate** per entire **3000MW _{th}** reactor core is about

**9.33×10**.

^{19}fissions / second**The overall energy release** in the units of joules is:

200×10^{6} (eV) x 1.602×10^{-19} (J/eV) x 9.33×10^{19} (s^{-1}) x 31.5×10^{6} (seconds in year) = **9.4×10 ^{16} J/year**

The mass defect is calculated as:

Δm = ΔE/c^{2}

**Δm** = 9.4×10^{16} / (2.9979 x 10^{8})^{2} = **1.046 kg**

That means in a typical **3000MWth** reactor core about 1 kilogram of matter is **converted** into pure energy.

Note that, a typical annual uranium load for a **3000MWth **reactor core is about **20 tonnes** of **enriched uranium **(i.e. about **22.7 tonnes of UO _{2}**). Entire reactor core may contain about 80 tonnes of enriched uranium.

### Mass defect directly from E=mc^{2}

The mass defect can be calculated directly from the Einstein relationship (**E = mc ^{2}**) as:

Δm = ΔE/c^{2}

Δm = 3000×10^{6} (W = J/s) x 31.5×10^{6} (seconds in year) / (2.9979 x 10^{8})^{2 }= **1.051 kg**

During the **nuclear splitting** or **nuclear fusion**, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. **The nuclear binding energies** are enormous, they are of the order of a million times greater than the electron binding energies of atoms.

Generally, in both **chemical** and **nuclear reactions**, some conversion between rest mass and energy occurs, so that the products generally have smaller or greater mass than the reactants. Therefore the new conservation principle is **the conservation of mass-energy**.

See also: Energy Release from Fission

**Nuclear and Reactor Physics:**

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**Advanced Reactor Physics:**

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