In the previous section we have discussed
mechanical energy. We have seen that it can be
classified into two distinct categories : one based
on motion, namely kinetic energy; the other on
configuration (position), namely potential energy.
Energy comes in many a forms which transform
into one another in ways which may not often
be clear to us.
We have seen that the frictional force is not a
conservative force. However, work is associated
with the force of friction, Example 6.5. A block of
mass m sliding on a rough horizontal surface
with speed v0 comes to a halt over a distance x$_0$.
The work done by the force of kinetic friction f
over x0 is –f$x_0$. By the work-energy theorem
$\frac{1}{2}mv_0^ = fx_0$ If we confine our scope to
mechanics, we would say that the kinetic energy
of the block is ‘lost’ due to the frictional force.
On examination of the block and the table we
would detect a slight increase in their
temperatures. The work done by friction is not
‘lost’, but is transferred as heat energy. This
raises the internal energy of the block and the
table. In winter, in order to feel warm, we
generate heat by vigorously rubbing our palms
together. We shall see later that the internal
energy is associated with the ceaseless, often
random, motion of molecules. A quantitative idea
of the transfer of heat energy is obtained by
noting that 1 kg of water releases about 42000 J
of energy when it cools by10°C.
One of the greatest technical achievements of
humankind occurred when we discovered how
to ignite and control fire. We learnt to rub two
flint stones together (mechanical energy), got
them to heat up and to ignite a heap of dry leaves
(chemical energy), which then provided
sustained warmth. A matchstick ignites into a
bright flame when struck against a specially
prepared chemical surface. The lighted
matchstick, when applied to a firecracker,
results in a spectacular display of sound and
light.
Chemical energy arises from the fact that the
molecules participating in the chemical reaction
have different binding energies. A stable chemical
compound has less energy than the separated parts.
A chemical reaction is basically a rearrangement
of atoms. If the total energy of the reactants is more
than the products of the reaction, heat is released
and the reaction is said to be an exothermic
reaction. If the reverse is true, heat is absorbed and
the reaction is endothermic. Coal consists of
carbon and a kilogram of it when burnt releases
about $3 ×10^7$ J of energy.
Chemical energy is associated with the forces
that give rise to the stability of substances. These
forces bind atoms into molecules, molecules into
polymeric chains, etc. The chemical energy
arising from the combustion of coal, cooking gas,
wood and petroleum is indispensable to our daily
existence.
The flow of electrical current causes bulbs to
glow, fans to rotate and bells to ring. There are
laws governing the attraction and repulsion of
charges and currents, which we shall learn
later. Energy is associated with an electric
current. An urban Indian household consumes
about 200 J of energy per second on an average.
- The Equivalence of Mass and Energy
Till the end of the nineteenth century, physicists
believed that in every physical and chemical
process, the mass of an isolated system is
conserved. Matter might change its phase, e.g.
glacial ice could melt into a gushing stream, but
matter is neither created nor destroyed; Albert
Einstein (1879-1955) however, showed that mass
and energy are equivalent and are related by
the relation
E = mc$^2$
where c, the speed of light in vacuum is
approximately 3 ×10$^8$ m/s. Thus, a staggering
amount of energy is associated with a mere
kilogram of matter
E = 1 × $(3 ×10^8)^2$ J = 9 ×10$^{16}$ J.
This is equivalent to the annual electrical output
of a large (3000 MW) power generating station.
The most destructive weapons made by man, the
fission and fusion bombs are manifestations of the above equivalence of mass and energy [Eq.
(6.20)]. On the other hand the explanation of the
life-nourishing energy output of the sun is also
based on the above equation. In this case
effectively four light hydrogen nuclei fuse to form
a helium nucleus whose mass is less than the
sum of the masses of the reactants. This mass
difference, called the mass defect ∆m is the
source of energy (∆m)c$^2$. In fission, a heavy
nucleus like uranium $^{235}_{92}U$, is split by a neutron
into lighter nuclei. Once again the final mass is
less than the initial mass and the mass difference
translates into energy, which can be tapped to
provide electrical energy as in nuclear power
plants (controlled nuclear fission) or can be
employed in making nuclear weapons
(uncontrolled nuclear fission). Strictly, the energy
∆E released in a chemical reaction can also be
related to the mass defect ∆m = ∆E/c$^2$. However,
for a chemical reaction, this mass defect is much
smaller than for a nuclear reaction. Table 1
lists the total energies for a variety of events and
phenomena.
 |
| Table 1: Approximate energy associated with various phenomena |
Example 1
Examine Tables 6.1-6.3
and express (a) The energy required to
break one bond in DNA in eV; (b) The
kinetic energy of an air molecule ($10^{-21}$ J)
in eV; (c) The daily intake of a human adult
in kilocalories.
Answer
(a) Energy required to break one bond
of DNA is
$\frac{10^{-20}}{1.6 \times 10^{-19} \ J/s}=0.06$ eV
Note 0.1 eV = 100 meV (100 millielectron volt).
(b) The kinetic energy of an air molecule is
$\frac{10^{-21}}{1.6 \times 10^{-19} \ J/s}=0.0062$ eV
This is the same as 6.2 meV.
(c) The average human consumption in a day is
$\frac{10^7}{4.2 \times 10^3 \ J/kcal}$ = 2400 kcal
We point out a common misconception created
by newspapers and magazines. They mention
food values in calories and urge us to restrict
diet intake to below 2400 calories. What they
should be saying is kilocalories (kcal) and not
calories. A person consuming 2400 calories a
day will soon starve to death! 1 food calorie is
1 kcal.
- The Principle of Conservation of
Energy
We have seen that the total mechanical energy
of the system is conserved if the forces doing work
on it are conservative. If some of the forces
involved are non-conservative, part of the
mechanical energy may get transformed into
other forms such as heat, light and sound.
However, the total energy of an isolated system
does not change, as long as one accounts for all
forms of energy. Energy may be transformed from
one form to another but the total energy of an
isolated system remains constant. Energy can
neither be created, nor destroyed.
Since the universe as a whole may be viewed
as an isolated system, the total energy of the
universe is constant. If one part of the universe
loses energy, another part must gain an equal
amount of energy.
The principle of conservation of energy cannot
be proved. However, no violation of this principle
has been observed. The concept of conservation
and transformation of energy into various forms
links together various branches of physics,
chemistry and life sciences. It provides a
unifying, enduring element in our scientific
pursuits. From engineering point of view all
electronic, communication and mechanical
devices rely on some forms of energy
transformation.
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