Classical mechanics distinguishes between potential energy, which is a function of the position of an object, and kinetic energy, which is a function of its movement. Both position and movement are relative to a frame of reference, which must be specified: this is often (and originally) an arbitrary fixed point on the surface of the Earth, the terrestrial frame of reference. It has been attempted to categorize all forms of energy as either kinetic or potential: this is not incorrect, but neither is it clear that it is a real simplification, as Feynman points out:
These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy (below) is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.
Examples of the interconversion of energy Mechanical energy is converted
into by
Mechanical energy Lever
Thermal energy Brakes
Electric energy Dynamo
Electromagnetic radiation Synchrotron
Chemical energy Matches
Nuclear energy Particle accelerator
Mechanical energy
Mechanical energy manifest in many forms,but can be broadly classified into elastic potential energy and kinetic energy. The term potential energy is a very general term, because it exists in all force fields, such as gravitation, electrostatic and magnetic fields. Potential energy refers to the energy any object gets due to its position in a force field.
Main article: Potential energy
Potential energy, symbols Ep, V or Φ, is defined as the work done against a given force (= work of given force with minus sign) in changing the position of an object with respect to a reference position (often taken to be infinite separation). If F is the force and s is the displacement,
with the dot representing the scalar product of the two vectors.
The name "potential" energy originally signified the idea that the energy could readily be transferred as work—at least in an idealized system (reversible process, see below). This is not completely true for any real system, but is often a reasonable first approximation in classical mechanics.
The general equation above can be simplified in a number of common cases, notably when dealing with gravity or with elastic forces.
Elastic potential energy
As a ball falls freely under the influence of gravity, it accelerates downward, its initial potential energy converting into kinetic energy. On impact with a hard surface the ball deforms, converting the kinetic energy into elastic potential energy. As the ball springs back, the energy converts back firstly to kinetic energy and then as the ball re-gains height into potential energy. Energy conversion to heat due to inelastic deformation and air resistance cause each successive bounce to be lower than the last.Main article: Elastic potential energy
Elastic potential energy is defined as a work needed to compress (or expand) a spring. The force, F, in a spring or any other system which obeys Hooke's law is proportional to the extension or compression, x,
F = − kx
where k is the force constant of the particular spring (or system). In this case, the calculated work becomes
only when k is constant. Hooke's law is a good approximation for behaviour of chemical bonds under normal conditions, i.e. when they are not being broken or formed.
Kinetic energy
Main article: Kinetic energy
Kinetic energy, symbols Ek, T or K, is the work required to accelerate an object to a given speed. Indeed, calculating this work one easily obtains the following:
At speeds approaching the speed of light, c, this work must be calculated using Lorentz transformations, which results in the following:
This equation reduces to the one above it, at small (compared to c) speed. A mathematical by-product of this work (which is immediately seen in the last equation) is that even at rest a mass has the amount of energy equal to:
Erest = mc2
This energy is thus called rest mass energy.
Surface energy
If there is any kind of tension in a surface, such as a stretched sheet of rubber or material interfaces, it is possible to define surface energy. In particular, any meeting of dissimilar materials that don't mix will result in some kind of surface tension, if there is freedom for the surfaces to move then, as seen in capillary surfaces for example, the minimum energy will as usual be sought.
A minimal surface, for example, represents the smallest possible energy that a surface can have if its energy is proportional to the area of the surface. For this reason, (open) soap films of small size are minimal surfaces (small size reduces gravity effects, and openness prevents pressure from building up. Note that a bubble is a minimum energy surface but not a minimal surface by definition).
Sound energy
Sound is a form of mechanical vibration, which propagates through any mechanical medium.
Gravitational energy
Main article: Gravitational potential energy
The gravitational force near the Earth's surface varies very little with the height, h, and is equal to the mass, m, multiplied by the gravitational acceleration, g = 9.81 m/s². In these cases, the gravitational potential energy is given by
Ep,g = mgh
A more general expression for the potential energy due to Newtonian gravitation between two bodies of masses m1 and m2, useful in astronomy, is
,
where r is the separation between the two bodies and G is the gravitational constant, 6.6742(10)×10−11 m3kg−1s−2.[19] In this case, the reference point is the infinite separation of the two bodies.
Thermal energy
Examples of the interconversion of energy Thermal energy is converted
into by
Mechanical energy Steam turbine
Thermal energy Heat exchanger
Electric energy Thermocouple
Electromagnetic radiation Hot objects
Chemical energy Blast furnace
Nuclear energy Supernova
Main article: Thermal energy
Thermal energy (of some media - gas, plasma, solid, etc) is the energy associated with the microscopical random motion of particles constituting the media. For example, in case of monoatomic gas it is just a kinetic energy of motion of atoms of gas as measured in the reference frame of the center of mass of gas. In case of many-atomic gas rotational and vibrational energy is involved. In the case of liquids and solids there is also potential energy (of interaction of atoms) involved, and so on.
A heat is defined as a transfer (flow) of thermal energy across certain boundary (for example, from a hot body to cold via the area of their contact. A practical definition for small transfers of heat is
where Cv is the heat capacity of the system. This definition will fail if the system undergoes a phase transition—e.g. if ice is melting to water—as in these cases the system can absorb heat without increasing its temperature. In more complex systems, it is preferable to use the concept of internal energy rather than that of thermal energy (see Chemical energy below).
Despite the theoretical problems, the above definition is useful in the experimental measurement of energy changes. In a wide variety of situations, it is possible to use the energy released by a system to raise the temperature of another object, e.g. a bath of water. It is also possible to measure the amount of electric energy required to raise the temperature of the object by the same amount. The calorie was originally defined as the amount of energy required to raise the temperature of one gram of water by 1 °C (approximately 4.1855 J, although the definition later changed), and the British thermal unit was defined as the energy required to heat one pound of water by 1 °F (later fixed as 1055.06 J).
Electric energy
Main articles: Electromagnetism and Electricity
Examples of the interconversion of energy Electric energy is converted
into by
Mechanical energy Electric motor
Thermal energy Resistor
Electric energy Transformer
Electromagnetic radiation Light-emitting diode
Chemical energy Electrolysis
Nuclear energy Synchrotron
Electrostatic energy
The electric potential energy of given configuration of charges is defined as the work which must be done against the Coulomb force to rearrange charges from infinite separation to this configuration (or the work done by the Coulomb force separating the charges from this configuration to infinity). For two point-like charges Q1 and Q2 at a distance r this work, and hence electric potential energy is equal to:
where ε0 is the electric constant of a vacuum, 107/4πc0² or 8.854188…×10−12 F/m.[19] If the charge is accumulated in a capacitor (of capacitance C), the reference configuration is usually selected not to be infinite separation of charges, but vice versa - charges at an extremely close proximity to each other (so there is zero net charge on each plate of a capacitor). The justification for this choice is purely practical - it is easier to measure both voltage difference and magnitude of charges on a capacitor plates not versus infinite separation of charges but rather versus discharged capacitor where charges return to close proximity to each other (electrons and ions recombine making the plates neutral). In this case the work and thus the electric potential energy becomes
Electricity energy
If an electric current passes through a resistor, electric energy is converted to heat; if the current passes through an electric appliance, some of the electric energy will be converted into other forms of energy (although some will always be lost as heat). The amount of electric energy due to an electric current can be expressed in a number of different ways:
where U is the electric potential difference (in volts), Q is the charge (in coulombs), I is the current (in amperes), t is the time for which the current flows (in seconds), P is the power (in watts) and R is the electric resistance (in ohms). The last of these expressions is important in the practical measurement of energy, as potential difference, resistance and time can all be measured with considerable accuracy.
Magnetic energy
There is no fundamental difference between magnetic energy and electric energy: the two phenomena are related by Maxwell's equations. The potential energy of a magnet of magnetic moment m in a magnetic field B is defined as the work of magnetic force (actually of magnetic torque) on re-alignment of the vector of the magnetic dipole moment, and is equal:
while the energy stored in a inductor (of inductance L) when current I is passing via it is
.
This second expression forms the basis for superconducting magnetic energy storage.
Electromagnetic Energy
Examples of the interconversion of energy Electromagnetic radiation is converted
into by
Mechanical energy Solar sail
Thermal energy Solar collector
Electric energy Solar cell
Electromagnetic radiation Non-linear optics
Chemical energy Photosynthesis
Nuclear energy Mössbauer spectroscopy
Calculating work needed to create an electric or magnetic field in unit volume (say, in a capacitor or an inductor) results in the electric and magnetic fields energy densities:
and
,
in SI units.
Electromagnetic radiation, such as microwaves, visible light or gamma rays, represents a flow of electromagnetic energy. Applying the above expressions to magnetic and electric components of electromagnetic field both the volumetric density and the flow of energy in e/m field can be calculated. The resulting Poynting vector, which is expressed as
in SI units, gives the density of the flow of energy and its direction.
The energy of electromagnetic radiation is quantized (has discrete energy levels). The spacing between these levels is equal to
E = hν
where h is the Planck constant, 6.6260693(11)×10−34 Js,[19] and ν is the frequency of the radiation. This quantity of electromagnetic energy is usually called a photon. The photons which make up visible light have energies of 270–520 yJ, equivalent to 160–310 kJ/mol, the strength of weaker chemical bonds.
These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy (below) is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.
Examples of the interconversion of energy Mechanical energy is converted
into by
Mechanical energy Lever
Thermal energy Brakes
Electric energy Dynamo
Electromagnetic radiation Synchrotron
Chemical energy Matches
Nuclear energy Particle accelerator
Mechanical energy
Mechanical energy manifest in many forms,but can be broadly classified into elastic potential energy and kinetic energy. The term potential energy is a very general term, because it exists in all force fields, such as gravitation, electrostatic and magnetic fields. Potential energy refers to the energy any object gets due to its position in a force field.
Main article: Potential energy
Potential energy, symbols Ep, V or Φ, is defined as the work done against a given force (= work of given force with minus sign) in changing the position of an object with respect to a reference position (often taken to be infinite separation). If F is the force and s is the displacement,
with the dot representing the scalar product of the two vectors.
The name "potential" energy originally signified the idea that the energy could readily be transferred as work—at least in an idealized system (reversible process, see below). This is not completely true for any real system, but is often a reasonable first approximation in classical mechanics.
The general equation above can be simplified in a number of common cases, notably when dealing with gravity or with elastic forces.
Elastic potential energy
As a ball falls freely under the influence of gravity, it accelerates downward, its initial potential energy converting into kinetic energy. On impact with a hard surface the ball deforms, converting the kinetic energy into elastic potential energy. As the ball springs back, the energy converts back firstly to kinetic energy and then as the ball re-gains height into potential energy. Energy conversion to heat due to inelastic deformation and air resistance cause each successive bounce to be lower than the last.Main article: Elastic potential energy
Elastic potential energy is defined as a work needed to compress (or expand) a spring. The force, F, in a spring or any other system which obeys Hooke's law is proportional to the extension or compression, x,
F = − kx
where k is the force constant of the particular spring (or system). In this case, the calculated work becomes
only when k is constant. Hooke's law is a good approximation for behaviour of chemical bonds under normal conditions, i.e. when they are not being broken or formed.
Kinetic energy
Main article: Kinetic energy
Kinetic energy, symbols Ek, T or K, is the work required to accelerate an object to a given speed. Indeed, calculating this work one easily obtains the following:
At speeds approaching the speed of light, c, this work must be calculated using Lorentz transformations, which results in the following:
This equation reduces to the one above it, at small (compared to c) speed. A mathematical by-product of this work (which is immediately seen in the last equation) is that even at rest a mass has the amount of energy equal to:
Erest = mc2
This energy is thus called rest mass energy.
Surface energy
If there is any kind of tension in a surface, such as a stretched sheet of rubber or material interfaces, it is possible to define surface energy. In particular, any meeting of dissimilar materials that don't mix will result in some kind of surface tension, if there is freedom for the surfaces to move then, as seen in capillary surfaces for example, the minimum energy will as usual be sought.
A minimal surface, for example, represents the smallest possible energy that a surface can have if its energy is proportional to the area of the surface. For this reason, (open) soap films of small size are minimal surfaces (small size reduces gravity effects, and openness prevents pressure from building up. Note that a bubble is a minimum energy surface but not a minimal surface by definition).
Sound energy
Sound is a form of mechanical vibration, which propagates through any mechanical medium.
Gravitational energy
Main article: Gravitational potential energy
The gravitational force near the Earth's surface varies very little with the height, h, and is equal to the mass, m, multiplied by the gravitational acceleration, g = 9.81 m/s². In these cases, the gravitational potential energy is given by
Ep,g = mgh
A more general expression for the potential energy due to Newtonian gravitation between two bodies of masses m1 and m2, useful in astronomy, is
,
where r is the separation between the two bodies and G is the gravitational constant, 6.6742(10)×10−11 m3kg−1s−2.[19] In this case, the reference point is the infinite separation of the two bodies.
Thermal energy
Examples of the interconversion of energy Thermal energy is converted
into by
Mechanical energy Steam turbine
Thermal energy Heat exchanger
Electric energy Thermocouple
Electromagnetic radiation Hot objects
Chemical energy Blast furnace
Nuclear energy Supernova
Main article: Thermal energy
Thermal energy (of some media - gas, plasma, solid, etc) is the energy associated with the microscopical random motion of particles constituting the media. For example, in case of monoatomic gas it is just a kinetic energy of motion of atoms of gas as measured in the reference frame of the center of mass of gas. In case of many-atomic gas rotational and vibrational energy is involved. In the case of liquids and solids there is also potential energy (of interaction of atoms) involved, and so on.
A heat is defined as a transfer (flow) of thermal energy across certain boundary (for example, from a hot body to cold via the area of their contact. A practical definition for small transfers of heat is
where Cv is the heat capacity of the system. This definition will fail if the system undergoes a phase transition—e.g. if ice is melting to water—as in these cases the system can absorb heat without increasing its temperature. In more complex systems, it is preferable to use the concept of internal energy rather than that of thermal energy (see Chemical energy below).
Despite the theoretical problems, the above definition is useful in the experimental measurement of energy changes. In a wide variety of situations, it is possible to use the energy released by a system to raise the temperature of another object, e.g. a bath of water. It is also possible to measure the amount of electric energy required to raise the temperature of the object by the same amount. The calorie was originally defined as the amount of energy required to raise the temperature of one gram of water by 1 °C (approximately 4.1855 J, although the definition later changed), and the British thermal unit was defined as the energy required to heat one pound of water by 1 °F (later fixed as 1055.06 J).
Electric energy
Main articles: Electromagnetism and Electricity
Examples of the interconversion of energy Electric energy is converted
into by
Mechanical energy Electric motor
Thermal energy Resistor
Electric energy Transformer
Electromagnetic radiation Light-emitting diode
Chemical energy Electrolysis
Nuclear energy Synchrotron
Electrostatic energy
The electric potential energy of given configuration of charges is defined as the work which must be done against the Coulomb force to rearrange charges from infinite separation to this configuration (or the work done by the Coulomb force separating the charges from this configuration to infinity). For two point-like charges Q1 and Q2 at a distance r this work, and hence electric potential energy is equal to:
where ε0 is the electric constant of a vacuum, 107/4πc0² or 8.854188…×10−12 F/m.[19] If the charge is accumulated in a capacitor (of capacitance C), the reference configuration is usually selected not to be infinite separation of charges, but vice versa - charges at an extremely close proximity to each other (so there is zero net charge on each plate of a capacitor). The justification for this choice is purely practical - it is easier to measure both voltage difference and magnitude of charges on a capacitor plates not versus infinite separation of charges but rather versus discharged capacitor where charges return to close proximity to each other (electrons and ions recombine making the plates neutral). In this case the work and thus the electric potential energy becomes
Electricity energy
If an electric current passes through a resistor, electric energy is converted to heat; if the current passes through an electric appliance, some of the electric energy will be converted into other forms of energy (although some will always be lost as heat). The amount of electric energy due to an electric current can be expressed in a number of different ways:
where U is the electric potential difference (in volts), Q is the charge (in coulombs), I is the current (in amperes), t is the time for which the current flows (in seconds), P is the power (in watts) and R is the electric resistance (in ohms). The last of these expressions is important in the practical measurement of energy, as potential difference, resistance and time can all be measured with considerable accuracy.
Magnetic energy
There is no fundamental difference between magnetic energy and electric energy: the two phenomena are related by Maxwell's equations. The potential energy of a magnet of magnetic moment m in a magnetic field B is defined as the work of magnetic force (actually of magnetic torque) on re-alignment of the vector of the magnetic dipole moment, and is equal:
while the energy stored in a inductor (of inductance L) when current I is passing via it is
.
This second expression forms the basis for superconducting magnetic energy storage.
Electromagnetic Energy
Examples of the interconversion of energy Electromagnetic radiation is converted
into by
Mechanical energy Solar sail
Thermal energy Solar collector
Electric energy Solar cell
Electromagnetic radiation Non-linear optics
Chemical energy Photosynthesis
Nuclear energy Mössbauer spectroscopy
Calculating work needed to create an electric or magnetic field in unit volume (say, in a capacitor or an inductor) results in the electric and magnetic fields energy densities:
and
,
in SI units.
Electromagnetic radiation, such as microwaves, visible light or gamma rays, represents a flow of electromagnetic energy. Applying the above expressions to magnetic and electric components of electromagnetic field both the volumetric density and the flow of energy in e/m field can be calculated. The resulting Poynting vector, which is expressed as
in SI units, gives the density of the flow of energy and its direction.
The energy of electromagnetic radiation is quantized (has discrete energy levels). The spacing between these levels is equal to
E = hν
where h is the Planck constant, 6.6260693(11)×10−34 Js,[19] and ν is the frequency of the radiation. This quantity of electromagnetic energy is usually called a photon. The photons which make up visible light have energies of 270–520 yJ, equivalent to 160–310 kJ/mol, the strength of weaker chemical bonds.