Law of conservation of energy definition science

Derivation of the equation of motion by energy methods

The principle of energy conservation stipulates that the energy is conserved (i.e., it is stationary), which gives:

(122)E=E0=const

Hence, the derivative of energy with respect to time should be zero. Taking the time derivative of Eq. (119) and equating it to zero gives

(123)ddt[T(t)+V(t)]=ddt[12mu˙2(t)+12ku2(t)]=0

Upon performing the differentiation, we get

(124)mu¨(t)u˙(t)+ku˙(t)u(t)=0

Simplification by u(t) yields the equation of motion

(125)mu¨(t)+ku(t)=0

Equation (125) is identical with Eq. (12) derived from Newton law of motion.

(a) The maximum speed of the plate

According to the principle of energy conservation:

(4.66)12mvm2=∫0yo(Fe+Fk)dy

where m is the mass of the plate and vm is the maximum speed. From Eq. (4.66), we find:

12mvm2=AεεoV22(do−yo)yodo−12kyo2

and vm can be found from:

vm=AεεoV2m(do−yo)yodo−kyo2m

Once yo is calculated using Eq. (4.21) in §4.2.1, vm can be easily found.

2 The Physical Principle of Energy Conservation

The impetus for the principle of energy conservation originally is the observation that in simple systems on Earth, one may define an energy of position (the gravitational potential energy) and connect it to another form of energy, kinetic energy. For a simple mechanical system with no friction, using Newton's second law (F=ma), we recast the work as

∫r1r2F•dr=∫r1r2ma•dr=m∫r1r2a•dr=m∫t1t2a•drdtdt=m∫t1t2a•vdt=m∫v1v2v•dv=12mv22−12mv21.

The quantity T=12mv2is called the kinetic energy (it represents energy associated with the motion of a massive object). With this nomenclature, we find from the definition of potential energy that

Ur2−Ur1=−T2−T1,

and rewriting slightly, we obtain

T2+Ur2=T1+Ur1.

Note that the quantity on the left refers only to position 2, while that on the right refers only to position 1. Since 1 and 2 were completely unspecified, this equation states a general result: in such a simple system, the quantity T+U must be a constant (or conserved). This is referred to as conservation of mechanical energy (and of course, “conservative force” is a retrodiction that follows from the observation of conservation of mechanical energy).

More generally, the total potential energy is the sum of all the potential energies possible in a given situation. There is no new physics in the principle of conservation of mechanical energy. Everything follows from Newton's laws (refer back to the introduction of kinetic energy and potential energy).

It was natural to physicists to expand this idea by including every possible form of energy and to believe that the total amount of energy in a closed system is conserved. As a consequence of work by the German mathematical physicist Emmy Noether, it became clear that each conservation law (such as that of energy or momentum) is connected to a symmetry of the universe. The law of conservation of momentum is connected to translation invariance, the law of conservation of energy to temporal invariance. This means, respectively, that moving an experiment in a reference frame and repeating it when prepared identically has no effect of the observed relations among physical quantities, and that doing an experiment prepared identically at different times should produce identical results.

From these observations it is clear that relations among reference frames are essential to consider if discussing conservation laws. In the early 20th century, Albert Einstein worked to understand such relations in the context of electromagnetism and extended it beyond electromagnetism to more general physical situations. Einstein created two theories, the special theory of relativity (1905) regarding transformation among inertial reference frames, and the general theory of relativity (1915), which allowed extension of special relativity to accelerated (noninertial) reference frames.

In special relativity, in an inertial frame of reference an energy-momentum four-vector pμ consisting of a time component (E/c) and spatial momentum components px, py, and pz, may be defined that satisfies pμpμ=m2c2, which is an expression of energy conservation in special relativity (written in more conventional notation as E2−p2c2=m2c4). That is, the fact that the vector product of two four-vectors is invariant leads to conservation of energy. In special relativity, there is a special frame of reference for massive objects known as the rest frame; in that frame p=0, so the relativistic energy equation is E=mc2, a rather widely known result. All massive objects have energy by virtue of possessing mass, known as mass-energy.

The relativistic energy relation E2=p2c2+m2c4 may be recast as E=γmc2 for massive objects (and, of course, as E=pc for massless objects), where the relativistic momentum is p=γmv and γ=1−vc2−1/2. In this case, the kinetic energy is T=(γ−1)mc2 because T plus mass-energy (mc2) must be equal to total energy E.

In general relativity, the connection to the Noether theorem is clearer, as one defines a so-called stress-energy tensor, Tμν. The stress-energy tensor describes momentum flow across space-time boundaries. The flow (technically, flux) of the stress-energy tensor across space-time boundaries may be calculated in a covariant reference frame and the covariant derivative of the stress-energy tensor turns out to be zero. This means that energy is conserved in general relativity.

There is no proof of the principle of conservation of energy, but there has never so far been disproof, and so it is accepted. It is a bedrock of modern physics. In physics, as in other sciences, there is no possibility of proof, only of disproof. The cycle of model (hypothesis), prediction, experimental investigation, and evaluation leads to no new information if the experimental result is in accord with the prediction. However, if there is disagreement between prediction and experiment, the model must be replaced. Over the historical course of science, faulty models are thrown away and the surviving models must be regarded as having a special status (until shown to be false as described earlier). Special relativity, general relativity, and conservation of energy are theories that have withstood the test of time. (In fact, by superseding Newton's law of universal gravitation, Einstein's theory of General Relativity shows where Newton's successful theory's boundaries of applicability are.)

6.2 Thermodynamic analysis

Traditionally, thermodynamic analysis was based on the principle of energy conservation to assess the efficiency of processes and systems; it uses the first law of thermodynamics that states that energy can be transformed, but it cannot be created or destroyed, and it also states the internal energy as a state function. However, it does not provide information about the reversibility of the processes.

Thus, in a closed system, any change in its internal energy (dU) is the result of the crossing heat (Q) that flows through the boundaries and the work done (W); the total energy of an isolated system is constant:

(6.22)dU=dQ−dW

The first law of thermodynamic defines internal energy; it is associated with all thermodynamic systems, and since heat is an energy form, it states the energy conservation law. The two components that lead in a change of internal energy are heat and work; the surroundings can make work over the system or take work from the system, and heat can go into or out to the system; heat and work can be quantified and measured.

However, a natural process is not reversible; it runs only in one sense unless external work is done over the system. Heat always flows from the hotter to the colder body in a natural way; if it is needed to go in the opposite direction, an external work must be applied. Also, work can be fully converted into heat, but the heat cannot be entirely turned into work.

The unavailability to convert thermal energy into mechanical work in a system is called entropy (S); if a process is entirely reversible, its entropy will be zero; thus the entropy is a measurement of the irreversibility of the process, and it represents the thermal energy that is not available to perform work.

A reversible process is the one that keeps thermodynamic equilibrium while producing a maximum work; thus in real processes, part of the heat is lost, and it is not converted in useful work; the entropy of the system will increase showing the natural process irreversibility; there are no ideal machines.

Besides the internal energy is a measurement of the change between two equilibrium states, and it is a point function that is a function of the state of the system and not to the path that was followed to get from an initial to a final state. Thus the state function is determined by parameters such as temperature, surface area, and mass. Heat and work are not defined as state functions because they are not independent of the way that they transform into the other.

The second law of thermodynamics states that the total entropy of an isolated (closed) system will always state the same or increase over time; a system cannot destroy entropy. To stay the same (constant), there is thermodynamic equilibrium, or the system is under a (fictitious) reversible process.

The entropy of a system at a specific state can also be seen as the probability of its occurrence; higher entropies mean a higher likelihood of occurrence leading in a closed system from less to more probable states. Thus spontaneous processes only flow in one direction, and the first law of thermodynamics does not account for it.

When a closed system is in thermodynamic equilibrium, its entropy is at a maximum that cannot be changed unless additional external energy is applied. By analyzing ideal systems using the second law of thermodynamics, it provides knowledge to understand real systems. The second law of thermodynamics gives information about the quality of different forms of energy and the reason of processes happening spontaneously.

Useful energy such as work, kinetic, and potential energy has a low entropy, and energy forms such as heat that have high entropy are less valuable. Thus it is desirable to have sources with low entropy to perform a process. Based on the second law of thermodynamics, these processes will occur spontaneously. In addition, heat transfer will happen spontaneously way from higher to lower temperature.

For a reversible process (fictitious), the change in entropy of the system can be expressed as the ratio of the heat transferred to the system between the equilibrium temperatures of the system with its surroundings when the heat is supplied:

(6.23)dS=dQT=0

In the case of irreversible processes (real), the statement of the second law of thermodynamics states that entropy will always increase, such as it cannot be less than zero:

(6.24)dS=dQT>0

Now, for a compressible substance, heat and work can be expressed in terms of thermodynamic properties. Work in terms of pressure (P) and volume (V) is as follows:

(6.25)dW=PdV

And heat in terms of entropy (S) and temperature (T) is as follows:

(6.26)dQ=TdS

Thus the combined first and second law of thermodynamics in terms of state variables that is valid for reversible and irreversible processes can be written as follows:

(6.27)dU=Tds−PdV

A closed system can be in thermodynamic equilibrium or stable equilibrium, but it is not in balance with the surroundings outside of the closed system. This difference between the system and the environment is useful to produce shaft work, and exergy is defined as the maximum shaft work that can be performed by this difference. Exergy is a property of the system and its reference environment, the latter enclosed all other systems, and it is infinite and in equilibrium.

If a process is irreversible, then exergy is destroyed and maintained; if the process is reversible, exergy is proportional to the entropy that it is generated. Exergy analysis quantifies the imperfections in a thermodynamic system assuming the difference between different energy forms. It identifies the places of exergy that losses their causes and magnitudes to improve the efficiency of a system.

Balance exergy considers that the exergy that goes into a system produces an exergy output in the product (shaft work) plus exergy emitted with waste (external irreversibilities) and exergy that is destroyed (internal irreversibilities); thus an efficiency based on exergy can be written as follows:

(6.28)ψ=exergy output in productexergy input=1−exergy lossexergy input=1−exergy waste emission+exergy destructionexergy input

4 Modelling the steam power plant

Mathematical modeling of the steam cycle is based on conservation of mass and energy principles. Eq.(1) and Eq.(2) describes the mass and energy balance respectively.

(1)∑imin=∑imout

(2)∑iEin=∑iEout+ΔE

where ∑iminand ∑imoutrespectively are mass in and mass out of a unit (kg/h), ∑iEinand ∑iEoutrespectively are energy flow in and out of a unit (kJ/h), and ΔE is the change (e.g. power output of a turbine) in energy of a unit (kJ/h).

The energy flow rate, E (kJ/h), is the product of the specific enthalpy, e (kJ/kg), of each stream and the mass flow rate, m (kg/h). The specific enthalpy and other properties of water or vapor stream such as specific entropy, s (kJ/kg-K), saturation temperature, Tsat (K), are calculated by Water97. Water97 is an Add-In for MS Excel which provides a set of functions for calculating thermodynamic and transport properties of water and steam using the industrial standard IAPWS-IF97 (Spang, 2002). The boiler feed water pumps are assumed to operate at 100 % isentropic efficiency, ηpump, defined by Eq.(3).

(3)ηpump=(eout,s−ein)(eout−ein)×100%

where eout,s is enthalpy of the outlet stream of the pump at 100 % isentropic efficiency and eout is the actual enthalpy of the stream at ηpump. The turbines are assumed to operate at 80 % isentropic efficiency. The isentropic efficiency, ηturb, is define by Eq.(4)

(4)ηturb=(ein−eout)(ein−eout,s)×100%

ein and eout are the enthalpy values of the inlet and outlet streams of the turbine at the given isentropic efficiency respectively.

For the boiler, its heat duty depends on the lower heating value (LHV) of the fuel to be used and the boiler efficiency. The efficiency of the boiler, ηboiler, is assumed to be 90 % and the boiler duty, Qboiler (kJ/h), can be calculated as in Eq.(5).

(5)Qboiler=(E12−E11)ηboiler

The LHV (kJ/kg) of EFB depends on the moisture content, X (%), and is estimated by using the data provided by the ERCN, Netherland (2012) as in Eq.(6).

(6)LHVFEB=15820−X*181.99

When EFB is totally dried (i.e. 0 % moisture), the LHVEFB is 15,820 (kJ/kg). Hence, the feed rate of moist EFB, mEFB (kg/h), required to generate a specific amount of boiler heat duty, Qboiler (kJ/h), can be calculated by Eq.(7).

(7)mEFB=QboilerLHVEFB

The total power output, Pout (MW), for the closed cycle of the power plant in figure 1 for a given amount of EFB feed can be calculated by Eq.(8) using the Wi (the power output of the three turbines) and Pi (the pumping represents pumping power of the pumps.

(8)Pout=(W1+W2+W3)−(P1+P2+P3)

5.7 Second Law of Thermodynamics—Entropy Inequality

The previous section developed the basic energy balance or conservation of energy principle commonly known as the first law of thermodynamics. The differential form (5.6.12) can be viewed as a measure of the interconvertibility of heat and work while maintaining a proper energy balance. However, the expression provides no restrictions on the direction of any such interconvertibility processes, and this is an important issue in thermomechanical behavior of materials. When considering thermal effects with dissipation phenomena, the direction of energy transfer must satisfy certain criteria, and this introduces irreversible processes. For example, a process in which friction changes mechanical energy into heat energy cannot be reversed. Another common observable restriction is that heat only flows from warmer regions to cooler regions and not the other way. Collectively, such restrictions are connected to the second law of thermodynamics. Of course various restrictions relate to the second law in different ways, and we wish to establish a mathematical relationship applicable to the thermomechanical behavior of continuum materials. One particular mathematical statement associated with the second law is the Clausius–Duhem entropy inequality, and this relation has broad applications for many materials we wish to study. As we shall see in later chapters, this inequality will place restrictions on the material response functions. More detailed background on this topic can be found in Haupt (2002), Holzapfel (2006), Asaro and Lubarda (2006), and Tadmor et al. (2012).

Basic to our development in this section is the definition of entropy. This rather abstract variable can be interpreted as a measure of the microscopic randomness or disorder of the continuum system. In classical thermodynamics, it is commonly defined as a state function related to heat transfer. For a reversible process, the entropy per unit mass, s(x, t) is commonly defined by the relation

(5.7.1)ds=δqθrev

where θ is the absolute temperature (Kelvin-scale, always positive) and δq is the heat input per unit mass over a reversible process. Since relation (5.7.1) is an exact differential, we may write it between two states 1 and 2, or for an entire cycle as

(5.7.2)Δs=s2−s1=∫12δqθrev or ∮ds=∮δqθrev=0

However, for irreversible processes (the real world), observations indicate that

(5.7.3)∮δqθirrev<0

Since we interpret δq/θas the entropy input from the heat input δq, we conclude that over an irreversible cycle, the net entropy input is negative. However, as entropy is assumed to be a state variable, it must return to its initial value at the end of any cycle. Because of this, the negative entropy input shown in (5.7.3) implies that entropy has been created inside the system. In other words, dissipative irreversible processes produce a positive internal entropy production. Therefore, for an irreversible change of state 1 → 2, the entropy increase will be greater than the entropy input by heat transfer

(5.7.4)Δs>∫12δqθirrev

The previous relations form the fundamental basis for the second law.

However, for use in continuum mechanics, the second law is normally rephrased in a different form. First, consider a fixed group (closed system) of continuum particles Rm that occupying spatial region R:

(5.7.5)Entropy input rate=∫Rρhθdv−∫∂Rq⋅nθds

with again q being the rate of heat flux per unit area and h the specific energy source per unit mass. Note that the ds term in the surface integral is the differential surface area and not the differential entropy. Now according to relation (5.7.4), the rate of entropy increase in R must be greater than or equal to (for the reversible case) the entropy input rate, and thus

(5.7.6)DDT∫Rsρdv≥∫Rρhθdv−∫∂Rq⋅nθds

Using our usual procedures on the integral formulations, we apply relation (5.2.9) and the Divergence Theorem to get

(5.7.7)∫Rs˙ρ−ρhθ+qiθ,idv≥0

and this implies

(5.7.8)s˙≥hθ−1ρqiθ,is˙≥hθ−1ρ∇⋅qθ

Relations (5.7.7) and (5.7.8) are known as the integral and differential forms of the Clausius–Duhem inequality. They represent forms of the second law of thermodynamics for continuum mechanics applications.

It is easily shown that (5.7.8) can also be expressed as

(5.7.9)s˙≥hθ−1ρθ(∇⋅q)+1ρθ2(q⋅∇θ)

By using the energy equation (5.6.12), the entropy inequality can be expressed as

(5.7.10)ρ(θs˙−ε˙)+TijDij−1θ(q⋅∇θ)≥0

which is sometimes referred to as the reduced Clausius–Duhem or Dissipation inequality. In some applications, the free energy Ψ=ε−sθ, is introduced, and relation (5.7.10) would become

(5.7.11)−ρ(Ψ˙+sθ˙)+TijDij−1θ(q⋅∇θ)≥0

It should also be pointed out that the observable and accepted concept that heat only flows from regions of higher temperature to lower temperature implies that

(5.7.12)q⋅∇θ≤0

with equality only if ∇θ=0. This relation is sometimes called the classical heat conduction inequality. Using this relation with (5.7.9), we can argue the stronger statement

(5.7.13)s˙≥hθ−1ρθ(∇⋅q)

which is known as the Clausius–Planck inequality. Another form of this relation can be found using (5.7.10):

(5.7.14)ρ(θs˙−ε˙)+TijDij≥0

1.6.2.2 First Law of Thermodynamics

One of the main and fundamentally guiding laws of life is the conservation of energy principle, which means that energy is neither created nor destroyed, but just changes forms, for example, heat to work in thermal power plants and work to heat in refrigerators and heat pumps. It also confirms that the total amount of energy is always conserved and remains constant with no generation or destruction. Fig. 3 illustrates a nice example of the rolling rock to show the variation of total energy content in every step. Therefore, this example on the conservation of energy principle presents the change of energy kinetically and potentially throughout the process while having the total energy remain constant. As shown in Fig. 3, when the rock was on top of the hill and not moving, the energy that rock possessed was entirely potential energy at 10 units, making the total energy content 10 units only. Then, when the rock started to roll down the hill, the potential energy started to transform to kinetic energy with the assumption that there are no frictional losses including air and ground frictions. Through the rolling process, the total energy, which is in this case the sum of the potential energy and the kinetic energy, remained constant throughout the process. Since the reference point to the potential energy was the bottom of the hill, then the entire energy the rock has at the bottom of the hill is kinetic energy.

Another example of the conservation of energy principle is when a person is eating more than the amount of energy s/he needs to do the activities that s/he does during the day. Then, the total energy in is higher than the energy out, which means that excess part of the energy entering the body is stored in the body. Storing energy in the human body can take many forms, but all of them will result in an increase in the human body mass (which leads to weight gain, maybe ending up with obesity). From this example, we can conclude that the energy conservation principle was applied, and no energy was created or destroyed. The change in the energy content of a system is equal to the difference between the energy getting into the system minus the energy getting out of the system. The first law of thermodynamics is the expression of the principle of energy conservation, and it considers energy as a thermodynamic property. From the statement of the first law of thermodynamics, we can analyze the energy interactions of an energy device or an entire power plant since the first law of thermodynamics keeps track of the energy interactions and makes sure that no energy is created or destroyed, and the energy is just being converted from one form to another. The first law of thermodynamics helps in measuring the performance of energy devices and energy systems through the definition of what is referred to either the first law efficiency or the energy efficiency. However, the first law of thermodynamics has the disadvantage of not considering the quality of the energy it deals with, but rather only with its quantity. For example, if we consider the upper part of the water in the ocean, which is usually at the ambient temperature. Based on the first law of thermodynamics, it has a massive amount of energy; however, this massive amount of energy is useless since it is at the ambient temperature. It is because of this disadvantage that the first law has, that the second law of thermodynamics is necessary to account for irreversibilities, losses, inefficiencies, and destructions, respectively.

2.1.2 Exergy Analysis

Exergy analysis is a technique that uses the conservation of mass and conservation of energy principles together with the second law of thermodynamics for the analysis, design, and improvement of energy and other systems. Exergy is defined as the maximum amount of work that can be produced by a system or a flow of matter or energy as it comes to equilibrium with a reference environment [19]. The main objectives of the exergy analysis are to locate and characterize the causes of exergy destruction or exergy losses owing to irreversibilities in any real process, as well as to quantify the corresponding rate.

Exergy destroyed during absorption results from the temperature difference between the absorber plate and the sun. It is calculated as [20,21]:

(15)Exdes,sun-abs=η0SG(TambTabs−TambTsun)

where η0 is given by:

(16)η0=τCαabs1−ϕC(1−αabs)

The exergy destroyed during the heat transfer process from the absorber plate to the working fluid is given by:

(17)Exdes,abs-f=ntubeTambSgen

where Sgen is the rate of entropy generation over the length of duct, calculated as:

(18)Sgen=∫0LδQabs-fdx(1Tf−1Tabs)dx

Exergy losses are the exergy leakages rates to the surroundings owing to optical error and heat transfer to ambient surroundings, respectively expressed as:

(19)Exloss,opt=SG(1−TambTsun)(1−η0)

(20)Exloss,amb=(Uloss,t+Uloss,b+Uloss,eSeS)S(Tabs−Tamb)(1−TambTabs)

The top loss coefficient is expressed as:

(21)Uloss,t=11hr,C-sky+hcv,wind+111hcv,C-a+1hcv,abs-a+hr,C-abs

The exergy efficiency of the solar collector is calculated by dividing useful exergy gain to the exergy of solar radiation, so [11]:

(22)ηex=m˙fCf((Tf,out−Tf,in)−TambLn(Tf,outTf,in))SG(1−TambTsun)

2.3 A Relation among Energies

The Griffith theory for fracture of perfectly brittle elastic solids is founded on the principle of energy conservation that is, energy added to and released from the body must be the same as that dissipated during crack extension. It states that, during crack extension of da, the work done dWe by external forces, the increment of surface energy dWS, and the increment of elastic strain energy dU must satisfy

(2.21)dWS+dU=dWe

For a conservative force field, this condition can be expressed in the form

(2.22)∂(WS+U+V)/∂a=0

where

WS = total crack surface energy associated with the entire crack

U = total elastic strain energy of the cracked body

V = total potential of the external forces

Note that a negative dV implies a positive work dWe done by external forces.

Consider a single-edge-cracked elastic specimen subjected to a tensile load P or displacement δ as shown in Figure 2.5. The relationship between the applied tensile force P and the elastic extension, or displacement, δ, is

(2.23)δ=SP

where S denotes the elastic compliance of the specimen containing the crack. The strain energy stored in this specimen is

(2.24)U=∫δ=0δ=SPPdδ=∫δ=0δ=SPδSdδ =12S[δ2]0SP=12SP2

The compliance S is a function of the crack length. The incremental strain energy under the condition of varying a and P is

(2.25)dU=12P2dS+SPdP

Case 2.1

Suppose that the boundary is fixed during the extension of the crack so that

δ=SP=  constant

dδ=SdP+PdS=0

SdP=−PdS

(2.26)dUδ=−12P2dS

(2.27)dWS=−dUδ=12P2dS

Case 2.2

Suppose that the applied force is kept constant during crack extension; then

dP=0

(2.28)dUP=12P2dS

(2.29)dWe=Pdδ=P2dS

dWS=12P2dS

For both boundary conditions discussed before, the energy released during crack extension is

dW=dWe−dU=12P2dS

(2.30)G=dWda=12P2dSda

The two loading cases can be illustrated graphically as in Figures 2.6a and 2.6b, respectively. In the figures, point B indicates the beginning of crack extension and point C the termination of crack extension. The area OBC¯is the strain energy released, dW. It can be shown rather easily from the graphic illustration that the energies released in the two cases are equal.

Under the fixed load condition, we have

dW=dU=12dWe

Thus, the energy release rate can be obtained with

(2.31)G=dUda

in which the differentiation is performed assuming that the applied load is independent of a.

Under the fixed displacement condition, we have dW = −dU, and hence

(2.32)G=−dUda

In the previous equation, the applied load P should be considered as a function of crack length a in the differentiation. The result should be the same as that given by Eq. (2.31). It is noted that the relation dW=dU=dWe/2is not true for nonlinear solids.

Example 2.1

The double cantilever beam (DCB) is often used for measuring fracture toughness of materials. Consider the geometry shown in Figure 2.7 where b is the width of the beam, and the crack length a is much larger than h and, thus, the simple beam theory is suitable for modeling the deflection of the two split beams.

Noting that the unsplit portion of the DCB is not subjected to any load and that in each leg the bending moment is M = Px, we calculate the total strain energy stored in the two legs of the DCB as

UT=2∫0aP2x22EIdx=P2a33EI

I=bh312

U=UT/b

G=dUda=P2a2bEI

If the fracture toughness Gc of the material is known, then the load that could further split the beam is

What does law of conservation of energy mean in science?

What is the law of conservation of energy in simple terms?

What is conservation of energy definition?