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Energy
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Energy
From the perspective of
physics, every physical system contains (alternatively, stores) a certain
amount of a continuous,
scalar quantity called energy; exactly how much is
determined by taking the sum of a number of special-purpose equations, each
designed to quantify energy stored in a particular way. There is no uniform way
to visualize energy; it is best regarded as an abstract quantity useful in
making predictions.
The first sort of prediction energy allows one to make is how
much
work a physical system could be made to do. Performing work requires energy,
and thus the amount of energy in a system limits the maximum amount of work that
a system could conceivably perform. In the one-dimensional case of applying a
force through a
distance, the energy required is ∫ f(x) dx, where f(x) gives the amount of
force being applied as a function of the distance moved.
Note, however, that not all energy in a system is stored in a
recoverable form; thus, in practice, the amount of energy in a system available
for performing work may be much less than the total amount of energy in the
system.
Energy also allows one to make predictions across problem
domains. For example, if we assume we are in a closed system (i.e. the
conservation of energy applies), we can predict how fast a particular resting
body would be made to move if a particular amount of heat were completely
transformed into motion in that body. Similarly, it allows us to predict how
much heat might result from breaking particular chemical bonds.
The
SI
unit for both energy and work is the
joule (J), named in honor of
James Prescott Joule and his experiments on the
mechanical equivalent of heat. In slightly more fundamental terms, 1 joule
is equal to 1
newton
metre, and in terms of
SI base units, 1 J equals 1 kg m2/s2. (Conversions.
In cgs
units, one
erg
is 1
g
cm2/s2.
The imperial/US unit for both energy and work is the foot pound.)
Noether's theorem relates the conservation of energy to the time invariance
of physical laws.
Energy is said to exist in a variety of forms, each of which
corresponds to a separate energy equation. Some of the more common forms of
energy are listed below.
Kinetic energy is that portion of energy associated with the motion of a
body.
-
KE = ∫ v·dp
For non-relativistic velocities, we can use the Newtonian approximation
-
KE = 1/2 mv2
(where KE is kinetic energy, m is mass of the body, v is velocity of the
body)
At near-light velocities, we use the relativistic formula:
-
KE = moc2(γ - 1) = γmoc2
- oc2 :γ = (1 - (v/c)2)-1/2
(where v is the velocity of the body, mo is its
rest mass, and c is the speed of light in a vacuum.)
The second term, mc2, is the rest mass energy and
the first term, γmc2 is the total energy of the body.
Heat
is related to the internal kinetic energy of a mass, but it is not a form of
energy. Heat is more akin to work in that it is a change in energy. The energy
that heat represents a change specifically refers to the energy associated with
the random translational motion of atoms and molecules in some identifiable
mass. The conservation of
heat
and work form the First law of
thermodynamics.
Potential energy is energy associated with being able to move to a
lower-energy state, releasing energy in some form. For example a mass released
above the
Earth has energy resulting from the
gravitational attraction of the Earth which is transferred in to kinetic
energy.
Equation:
-
Ep=mhg
where m is the mass, h is the height and
g
is the value of
acceleration due to gravity at the Earth's surface.
Chemical energy a form of potential energy related to the
breaking and forming of chemical bonds.
See
electromagnetic radiation.
In the
theory of relativity, the energy E of a particle is related to its
momentum p and
mass
m by:
-
E2 = m2c4
+ p2c2
where c is the
speed of light. This equation shows that the mass provides a contribution to
the energy. Even if p is zero, the particle has a rest energy
that is nonzero if the mass is nonzero. The rest energy is
-
E0 = m'c2
(i.e. 90
petajoule/kg)
See also:
Entropy,
Thermodynamics
-
Feynman, Richard. Six Easy Pieces: Essentials of Physics Explained by
Its Most Brilliant Teacher. Helix Book. See the chapter "conservation of
energy" for Feynman's explanation of what energy is, and how to think about
it.
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