Entropy and The Second Law of Thermodynamics
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Second Law of Thermodynamics: |
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To understand the second law of thermodynamics, let us consider a heat engine. A heat engine is
a device that converts internal energy to mechanical energy. With no change in internal energy, the
net work done by a heat engine is equal to the net energy flowing through it. If the engine absorbs
a quantity of energy equals to Qh from the hot reservoir, does work W, and then gives up a quantity
of energy Qc to the cold reservoir then the thermal efficiency
(e) of the heat engine is defined as the
ratio of the net work done by the engine during one cycle to the energy absorbed at the higher
temperature during the cycle:
This equation implies that a heat engine has 100% efficiency only if
Qc = 0. In other words, a heat
engine with perfect efficiency would have to expel all the absorbed energy as mechanical work. On
the basis of the fact that efficiencies of real engines are well below 100%,
the second law of
thermodynamics states that:
“It is impossible to construct a heat engine that operating in a cycle produces no effect other
than the absorption of energy from a reservoir and the performance of an equal amount of
work”. This statement is called Kelvin-Planck statement of the second law of thermodynamics.
The Clausius statement of second law of thermodynamics is as follows:
“It is impossible to construct a cyclical machine whose sole effect is the continuous transfer of
energy from one object to another object at a higher temperature without the input of energy by
work”. In simpler terms, energy does not flow spontaneously from a cold object to a hot object.
The first law of thermodynamics specifies that we cannot get more energy out of a cyclic
process by work than the amount of energy we put in and the second law of thermodynamics
states that we cannot break even because we must put more energy in, at the higher temperature,
than the net amount of energy we get out by work.
Entropy and Performance of Engines:The theoretical maximum efficiency of heat engines depend only on the temperatures it operates
between. This can be derived by using the Carnot’s heat engine. This heat engine is an ideal
imaginary heat engine. However, the other engines can also attain maximum efficiency.
The
maximum efficiency of a heat engine is given by,
where Tc is the temperature of the cold sink and
Th
is the temperature of the hot source. This
derivation of maximum efficiency is possible only when we assume the entropy of the cold
reservoir is the negative of that of the hot reservoir. This assumption is possible since in a
reversible process the net entropy change is zero. It can be noted that the change in entropy of the
cold reservoir is positive while the change in entropy of the hot reservoir is negative. In a reversible
process, entropy is over all not increased, but rather is moved from a hot system to a cold,
decreasing the entropy of the heat source and increasing the entropy of the heat sink. By second
law of thermodynamics, the Carnot efficiency is the theoretical upper bound of the efficiency of an
engine.
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